Meteoritics amp Planetary Science 40 Nr 5 695ndash710 (2005)Abstract available online at httpmeteoriticsorg

695 copy The Meteoritical Society 2005 Printed in USA

Constraints on the depth and variability of the lunar regolith

B B WILCOX1 M S ROBINSON2 P C THOMAS3 and B R HAWKE1

1Hawairsquoi Institute of Geophysics and Planetology University of Hawairsquoi 2525 Correa Road Honolulu Hawairsquoi 96822 USA2Center for Planetary Sciences Northwestern University 1850 Campus Drive Evanston Illinois 60208 USA

3Center for Radiophysics and Space Research Cornell University Ithaca New York 14850 USACorresponding author E-mail bbwilcoxhigphawaiiedu

(Received 30 January 2004 revision accepted 24 March 2005)

AbstractndashKnowledge of regolith depth structure is important for a variety of studies of the Moon andother bodies such as Mercury and asteroids Lunar regolith depths have been estimated usingmorphological techniques (ie Quaide and Oberbeck 1968 Shoemaker and Morris 1969) cratercounting techniques (Shoemaker et al 1969) and seismic studies (ie Watkins and Kovach 1973Cooper et al 1974) These diverse methods provide good first order estimates of regolith depthsacross large distances (tens to hundreds of kilometers) but may not clearly elucidate the variability ofregolith depth locally (100 m to km scale) In order to better constrain the regional average depth andlocal variability of the regolith we investigate several techniques First we find that the apparentequilibrium diameter of a crater population increases with an increasing solar incidence angle andthis affects the inferred regolith depth by increasing the range of predicted depths (from sim7ndash15 mdepth at 100 m equilibrium diameter to sim8ndash40 m at 300 m equilibrium diameter) Second we examinethe frequency and distribution of blocky craters in selected lunar mare areas and find a range ofregolith depths (8ndash31 m) that compares favorably with results from the equilibrium diameter method(8ndash33 m) for areas of similar age (sim25 billion years) Finally we examine the utility of usingClementine optical maturity parameter images (Lucey et al 2000) to determine regolith depth Theresolution of Clementine images (100 mpixel) prohibits determination of absolute depths but thismethod has the potential to give relative depths and if higher resolution spectral data were availablecould yield absolute depths

INTRODUCTION

Regolith covers virtually the entire lunar surface and thusprovides a substantial amount of our information about theMoon The regolith has been imaged sieved raked coredwalked on driven across modeled studied and pondered yetits complexities continue to cloak details of its depth andstructure Studies dating back to the earliest days of lunarexploration have attempted to determine the depth of theregolith remotely by using small crater morphology (egQuaide and Oberbeck 1968) the blockiness of craters over arange of sizes (Shoemaker and Morris 1969) and the numberof craters per unit area (Shoemaker et al 1969) Howeverthere are important discrepancies among these morphologicalindicators which should draw attention to the variability ofthe regolith thickness and help elucidate the three-dimensional nature of the regolith Therefore we haveconducted a detailed study of crater size-frequencypopulations and the frequency and distribution of blocky

craters in selected lunar regions in order to investigatethickness variations in the mare regolith Finally weinvestigate the utility of using optical maturity maps to inferregolith depths and show this method to be promising butcurrently of limited utility due to a lack of 10 m scalemultispectral imaging

BACKGROUND

There has been significant debate as to what actuallyconstitutes the lunar regolith Merrill (1897) first defined theterm ldquoregolithrdquo for terrestrial applications He stated ldquoInplaces this covering is made up of material originatingthrough rock-weathering or plant growth in situ In otherinstances it is of fragmental and more or less decomposedmatter drifted by wind water or ice from other sources Thisentire mantle of unconsolidated material whatever its natureor origin it is proposed to call the regolithrdquo When adapted tothe Moon on the basis of observations at the Surveyor III site

696 B B Wilcox et al

the regolith was defined in a similar matter as a layer offragmental debris of relatively low cohesion overlying a morecoherent substratum (Shoemaker et al 1967) Subsequentlyin regards to the Surveyor VII site situated on the ejecta of theTycho crater Shoemaker et al (1968) refined their definitionof the regolith to exclude ldquowidespread blankets of fragmentalejecta associated with large individual cratersrdquo Instead thedefinition of regolith was restricted to include only the ldquothinlayer of material that forms and progressively evolves over alonger period of time as a result of an extremely large numberof individual eventsrdquo This definition sought to provide adistinction between the upper heavily reworked zone and thelower zone of debris of large-basin-forming or crater-formingevents Oberbeck et al (1973) took exception to thisdefinition because the ldquoregolith is not completely reworkedbut is frequently stratified with interlayers of reworked fine-grained material and little modified coarser-grained debrisAn upper reworked zone cannot be rigorously defined in theclassic localities nor is an unambiguous division possible inthose cases where ejecta breccias have been cratered andmodified subsequent to their depositionrdquo They proposed thata definition more similar to the original terrestrial definitionbe adopted They argued that the ldquoclassic mare regolith is notjust the reworked surface layer but is the entire blanket of rockdebris overlying cohesive substrate rocksrdquo In the highlandsthe picture is even more complicated as noted by Cintala andMcBride (1995) where the surfaces are ldquoso pulverized from

accumulated impacts that they have no bedrock layer forreferencerdquo and ldquothe local definition of regolith becomes morephilosophical in naturerdquo Here we adopt the looser definitionof Merrill (1897) as applied to the Moon by Oberbeck et al(1973) and include all fragmental debris overlying largelycoherent rock as regolith However we note that for mostlocalities there probably does not exist a clearly identifiablecontact between fractured material above and coherentmaterial below As Merrill (1897) explained the regolith canbe either ldquofound lying on a rocky floor of little changedmaterial or becomes less and less decomposed from thesurface downward until it passes by imperceptible gradationsinto solid rockrdquo

Traditionally the main method of estimating lunarregolith depth has been through the study of small crater(lt250 m) morphology which was shown by Quaide andOberbeck (1968) to be dependent on the nature and depth ofthe substrate From Lunar Orbiter (LO) images theyrecognized four classes of small craters normal bowl-shapedcentral mound flat-bottomed and concentric or bench(Fig 1) To understand the underlying causes of thesemorphologies they impacted various target materials with aprojectile from a high-velocity gun and thus showed thatstrength boundaries control crater interior morphologyQuaide and Oberbeck used a simple ldquofines-on-solidrdquo modelof 24-mesh quartz sand over a flat more coherent substrate torepresent regolith on top of basalt For the substrate materialthey used 24-mesh quartz sand bonded by epoxy resin tounconfined compressive strengths of sim14 and sim685 bar Withboth of these substrate strengths they were able to create eachof the observed small crater morphologies by varying thethickness of the unconsolidated surficial layer They showedthat normal craters form when the unconsolidated surficialmaterial has a relative thickness greater than some valuebetween DA38 and DA42 where DA is the apparent craterdiameter Similarly concentric craters form only when theregolith has a thickness less than some value between DA8and DA10 Quaide and Oberbeck (1968) and Oberbeck andQuaide (1968) used these relationships to estimate the depthof the surficial layer (regolith) on mare deposits from orbitalphotography finding depths ranging from 1ndash6 m to 1ndash16 m intheir various mare study areas

In their calculations it was assumed that the interfaceresponsible for producing the various crater morphologieswas the mare basalt bedrock surface However this interfaceis not necessarily bedrock and strictly speaking should onlybe described as an interface between materials withcontrasting physical properties While the 685 bar materialused in their experiments can represent coherent bedrock the14 bar material is so weak that it could easily be crushed byhand and thus does not represent physical properties ofcoherent bedrock That this weaker material when serving asldquocoherent substraterdquo still produced the same morphologiessuggests that any simple strength discontinuity could be the

Fig 1 Four classes of small craters as defined by Quaide andOberbeck (1968) a) Normal bowl-shaped morphology b) centralmound c) flat-bottomed d) concentric Crater morphology isdependent on depth to a strength interface craters trend AndashD withdecreasing depth of surficial layer Each scene is 119 m across fromLO3-188-H2

Constraints on the depth and variability of the lunar regolith 697

underlying cause of different crater morphologies in some ofthe observed craters In their experiments even a thin layer ofpaint between two layers of sand was sufficient to produce acrater with irregular walls (Oberbeck personalcommunication)

Evidence that weak strength discontinuities (ascompared to bedrock) can cause bench morphology camewhen Apollo astronauts visited several bench craters (Benchcrater at the Apollo 12 site the Station 9 crater at the Apollo15 site Plum crater at the Apollo 16 site and Van Serg craterat the Apollo 17 site) It was found that none of these cratersformed in bedrock and that the benches were due to impactsin targets with units of differing physical properties such as aresistant layer within the regolith (Shoemaker et al 1970Muehlberger et al 1972 1973 Swann et al 1972 Schmitt1973)

Another possible indicator that a portion of the benchcraters may be due to factors other than bedrock is theexistence of relatively fresh bench craters without large blockpopulations (Fig 2) Bench craters that penetrated through theregolith and partially formed in bedrock would excavate partof that bedrock thus forming blocks As discussed below thelack of blocks is another indicator that the bench morphologymay not always be due to bedrock Thus it is misleading toassume that bench morphology represents a regolithrockinterface in all cases

Another common method for estimating regoliththickness is based on the occurrence (or lack thereof) ofblocks produced during an impact event Rennilson et al(1966) suggested that the depth of the fragmental layer(regolith) could be estimated from the depth of the smallestcrater with a blocky rim This logic assumes that craters withblocks penetrated through the regolith to a more coherent orcoarser-grained substrate that fractures into blocks craterswithout blocks form solely in unconsolidated regolith Usingblocks as indicators of regolith thickness assumes that ingeneral small differences in age (and thus degradation state)of craters alone cannot account for the presence or absence ofblocks because blocks on the lunar surface erode slowlyErosion caused by impacts that are small compared to the sizeof the rock (ldquosingle particle abrasionrdquo) is at a rate on the orderof 1 mm106 years (Crozaz et al 1971 Gault et al 1972 Hˆrzet al 1974) ldquoCatastrophic rupturerdquo caused by impactsresulting in a crater the diameter of which is at least a quarterof the diameter of the rock is a more effective process inremoving blocks However these impact events occur lessfrequently and the median survival time for a boulderapproximately 3 m across (a size typical in this study) is stillon the order of 109 years (Hˆrz 1977) Though blocks canescape destruction for substantial periods of time they arelikely to spend part of their lifetime buried within the regolith(Hˆrz 1977) Thus the most degraded craters cannot be usedfor estimating regolith depth because of the likelihood of theirblock populations being buried

Relatively shallow regolith depths of between 2ndash15 cmand 8ndash10 m were estimated in the vicinity of Surveyor landersby mapping blocky craters (Shoemaker and Morris 1969)However the irregular spatial distribution of blocky cratershas not been fully considered Craters similar in diameter anddegradation state can be found in close proximity one with noblocks the other with many (Fig 3) These apparentlyinconsistent blocky crater pairings cannot be readilyexplained by a simple shallow regolith model and the

Fig 2 Bench craters with differing block populations The top crater(LO3-188-H2) has very few blocks while the bottom crater (LO3-196-H2) has abundant blocks indicating that it has excavated morecoherent material than the top crater Scale bar is 100 m

698 B B Wilcox et al

implications for the variability of regolith depth have not beenthoroughly examined

Another possible complication with the blocky cratermethod of determining regolith depth is the existence ofregolith breccia boulders In several cases astronautsobserved craters (eg Van Serg at the Apollo 17 site) thatappeared to have excavated large amounts of coherentsubstrate producing a significant population of blocks butupon inspection the blocks turned out to be extremely friableregolith breccias (Muehlberger et al 1973 Schmitt 1973) Inthese cases the blocks produced by a crater-forming event arenot excavated from the coherent substrate but rather areformed from induration of regolith probably during theimpact event that deposited them on the surface (Muehlbergeret al 1973 Schmitt 1973) From existing orbital photographyit is not possible to discriminate between these two types ofblocks regolith depth estimated from these impact-producedrocks would be shallower than the actual depth There is alsothe possibility that blocks around a crater were excavatedfrom a blocky layer in the regolith or from large isolatedburied blocks In this case too the regolith depth inferred

from this type of crater would be shallower than the actualdepth The depths estimated from this method are thus likelyto err on the shallow side

Because regolith on the Moon is produced by impactsthe thickness of the regolith should correlate directly withcrater abundance and thus regolith depth has also beenestimated by examining the size-frequency distribution ofcrater populations (Shoemaker et al 1969) As a craterpopulation matures the number of craters that are visible onthe surface is less than the number of craters that wereactually produced because new craters obliterate older onesThe diameter at which the cumulative number of craters seenon the surface is less than the number produced is theequilibrium diameter this diameter can be identified as abreak in slope in a cumulative histogram of crater size-frequency (Gault 1970 Schultz et al 1977) Below the breakin slope (larger diameters) the trend is representative of theproduction population of craters above the break in slope(smaller diameters) the trend represents the steady-statecraters of which more were produced than are still visible onthe surface For the steady-state craters the differencebetween the production population of craters and thepopulation of craters still visible on the surface represents thenumber of craters that were destroyed This population ofobliterated craters initially starts as voids in the surface but asthey age their uplifted rims erode and their interiors fill withregolith until they become shallow to the point that they areno longer distinguishable (Shoemaker et al 1969 Soderblom1970) The depth of the regolith in a local area is thus equal tothe initial depth of the destroyed craters minus the rim height(Shoemaker et al 1969) Over large areas the averageregolith depth must be proportional to the depth of theequilibrium crater population Thus accurate determinationof the diameter at which a crater population has reachedequilibrium is a powerful tool for estimating regolith depth ina given area

The incidence angle (deviation of sun vector fromsurface normal) affects the number of craters that can bereadily identified in an image fewer craters are visible inimages with lower incidence angles (angles closer to solarzenith) This effect is more important for degraded craters thewalls of which have shallower slopes The incidence angle ofan image may affect the identification of degraded cratersresulting in uncertainties in estimates of the equilibriumdiameter of a population

Regolith depth has also been examined seismically Atthe Apollo 12 14 and 15 sites some information about thethree-dimensional nature of the regolith was gleanedincidentally from passive seismic experiments designed tostudy deeper features (Latham et al 1970 1971 1972) At theApollo 14 16 and 17 sites active seismic experiments weredesigned to provide data to specifically characterize theregolith and regolith depth estimates were obtained fromseismic refraction profiling Apollos 14 and 16 landed in non-

Fig 3 An example of craters of similar size and morphology withdifferent block populations The top crater (595 m in diameter) hasabundant blocks the bottom crater (575 m in diameter) has nodetectable blocks possibly indicating heterogeneities in regolithdepth From LO2-161-H2

Constraints on the depth and variability of the lunar regolith 699

mare areas and the sites were estimated to have regolithdepths of 85 m and 122 m respectively (Watkins andKovach 1973) At the Apollo 17 mare site several distinctlayers were identified In a regional seismic profile model thefirst 4 m of the surface were interpreted to be regolith belowthat a layer interpreted to be rubble of older regolithextremely fractured rock or both extended from 4 m down to32 m Below 32 m was a layer interpreted to be fractured orvesicular basalt (Cooper et al 1974) An alternate regionalmodel includes only a 7ndash12 m layer of regolith atop afractured or vesicular basalt (Cooper et al 1974) Thesenumbers should be viewed with caution the results depend ona number of assumptions and can differ markedly (as in thetwo examples above) when parameters or assumptions arevaried For example it was reported that relief of up to 6 m insubsurface layers could be observed in the seismic data but inthe regional seismic model it is assumed that all layers areplanar and their physical properties are uniform resulting inan oversimplified representation of the regolith depth (Cooperet al 1974) Also the seismic data are not internallyconsistent the regional profile that incorporates all seismicsource data does not agree with an end-to-end profile whichuses only select seismic sources where there is an additionallayer at a depth of 65 m (Cooper et al 1974)

While these techniques (crater morphology blockpopulation equilibrium diameter and seismic) provide usefultools for estimating regolith depth many issues remain openWhy arenrsquot all fresh bench craters blocky If there are manylarge (gt100 m) buried craters why are such smallthicknesses (1ndash10 m) generally cited Why arenrsquot all large

fresh craters blocky How important is the variation inregolith thickness Shortcomings in previous estimates maybe due to a regolith that is more complex (not a simple two-layer model with regolith atop a planar bedrock layer) andora regolith with significantly variable depth in a local areaThe work presented in this paper is designed to furtherexamine regolith depth and local spatial heterogeneities inregolith depth

METHODS AND RESULTS

Equilibrium Diameters

We have employed the equilibrium diameter method todetermine regolith depth and investigated the effects of solarincidence angle on the equilibrium diameter of crater size-frequency distributions of mare areas of similar ages Becausehigher incidence angles enhance more subtle topographicfeatures the sun angle should have a direct effect on thenumber of craters visible in an image with more cratersdetectable at higher incidence angles (Soderblom 1972Young 1975) This in turn should have a direct effect on theregolith depth estimated using the crater size-frequencymethod of Shoemaker et al (1969) In order to investigate sunangle effects we compared the apparent crater populationsand equilibrium diameters of images with incidence angles of71deg 79deg and 89deg Each image was converted to digital formatby scanning the image at the highest resolution necessary topreserve all of the information inherent in the originalphotograph

Fig 4 The same area under different lighting conditions after Soderblom (1972) Scene is sim164 km across a) Our 89deg incidence angle studyarea (AS15-98-13347) b) A 70deg incidence angle LO image (LO4-163-H1) Many more craters are visible in the high incidence angle imageThe low resolution of the LO image (gt40 mpixel) did not allow direct quantitative comparison of crater populations

700 B B Wilcox et al

Our first study site is a 950 km2 area located in OceanusProcellarum (approximately 26degN 58degW) sim275 km from the40-km crater Aristarchus For this location there existsextremely high incidence angle data in fact the terminatorcrosses the image AS15-98-13347 The effective resolutionof this photograph is sim9 mpixel similar to the typical LOmedium resolution images (sim7 mpixel) and is sufficient forthe size range of craters we are investigating (gt25 m) (Fig 4)Soderblom (1972) observed that in the near-terminator imagecraters 100ndash300 m in diameter are so ubiquitous that they arepositioned ldquoshoulder-to-shoulderrdquo (Fig 5) While thisobservation has been widely cited no crater count data fromthis high incidence angle image was reported This site has anestimated age of 276 billion years (+030 minus018) (Hiesingeret al 2003) as determined by comparing the regional cratersize-frequency distribution to the lunar crater productionfunction established from radiometric ages of returnedsamples

The second and third sites are also in OceanusProcellarum Site number two is a 173 km2 area covered bythe 79deg incidence angle image LO3-165-M (sim17degN 421degW66 mpixel) This is one of the highest incidence angle LOimages and serves as a good intermediate between the nearterminator image (Fig 4a) and typical LO images (sim70degincidence angle) The third site is a 64 km2 area found in the71deg incidence angle image LO3-200-M (sim31degS 426degW64 mpixel) and is representative of typical LO mediumresolution images These sites have estimated ages of208 billion years (+065 minus039) and 254 billion years(+029 minus017) respectively (Hiesinger et al 2003) These areall young mare and because they are similar in age (the agesof all three sites are within the error bars of each other) theyshould have similar crater populations

We digitized craters in each image (over 20000 craterstotal) with an interactive monitor-cursor program that fit acircle to three points selected on a crater rim Craters were

identified as nearly continuous circular features with thecaveat that the extreme shadowing often complicates cratermorphology A simple criterion was used to limit the numberof false identifications and maintain consistency from onecounting session to the next if a mental debate occurred as towhether the feature was a crater or not it was not digitizedThe crater count data in Fig 6 are presented in standardcumulative histogram form (Arvidson et al 1979) Theequilibrium diameter where the slope of the cumulativehistogram begins to deviate from a log-log slope ofapproximately minus34 (Soderblom 1970) was found bycalculating the slope using points at smaller and smaller craterdiameter bins until the slope was less than minus34 The slopeswere found with an iterative least squares fitting routine fornon-linear functions originally described by Bevington(1969) In this way the equilibrium diameter for the 89degincidence image was found to be approximately 260 m 190m for the 79deg image and 165 m for the 71deg image Weinterpret that the incidence angle had a significant effect onthe number of craters identified and thus the equilibriumdiameter differed by nearly 100 m for these three areas eventhough they are of similar age

To estimate regolith depth in the 89deg image wecompared the percentage of the surface covered by theequilibrium population to the percent of the surface thatwould be covered by the production population (with a slopeof minus34) (Table 1) We assumed that the equilibriumpopulation actually followed a minus2 slope typical of equilibriumpopulations (Gault 1970 Schultz et al 1977) in thecumulative histogram rather than the flat line in Fig 6a Thevery low slope at small diameters is most likely due to smallcraters being hidden by shadows of larger craters as well asthe resolution limiting the number of craters detected at thesmallest sizes This assumption does not affect our regolithdepth estimates significantly because small (compared to theequilibrium diameter) craters do not contribute appreciably toregolith depth but rather simply rework it (Oberbeck et al1973) The difference between the area covered by cratersproduced on the surface and the area covered by theequilibrium population of craters still present on the surface isthe portion of the surface covered by craters that have beenobliterated mainly by infilling of regolith (Shoemaker et al1969) Regolith depth in that portion of the surface is equal tothe initial average depth of the craters that are now filled inThe maximum crater depth is 20 of crater diameterincluding excavation and compression (Pike 1974) Thecorresponding average crater depth of an idealized bowl-shaped crater with a depth to diameter ratio of 02 is 14 ofcrater diameter This approximation takes into account theshallowing of the crater near the edges and subtracts the rimheight which does not contribute to the depth of the craterbelow the preexisting surface

A key assumption in estimating regolith depth from thismethod is the initial depth of the craters While the maximum

Fig 5 A portion of our 89deg incidence angle study area (Fig 4aAS15-98-13347) showing the nearly ldquoshoulder-to-shoulderrdquodistribution of 100ndash300 m craters (Soderblom 1972) Scale bar is1 km

Constraints on the depth and variability of the lunar regolith 701

depth of primary craters is 20 of crater diameter (Pike1974) it has been suggested that secondary craters are sim50shallower than primaries (Pike 1980) However this is forsecondary craters that are close to their parent crater and areclustered so that they often share rims with adjoiningsecondaries Secondary craters become better developed withincreasing distance from their parent crater and isolatedsecondaries far from the parent crater are not significantlyaffected by debris surges as is the case with clusteredsecondaries (Morrison and Oberbeck 1978) Our study areasare relatively far from large secondary-producing impactsWe attempted to avoid areas with obvious secondary craters

using methods described by Neukum et al (1975) and thecriteria of Oberbeck and Morrison (1973) (herringbonepattern elongated shape and clustering) To investigate whateffects any isolated secondaries remaining in our data setmight have we carried out a cursory examination of thedepths of fresh secondary craters of a range of diameters inthe image LO3-165-M (outside of our crater count study area)(Fig 7) Because the incidence angle of this image is 79deg theshadow of any crater with a depth to diameter ratio of 02 willfall halfway across the crater floor Comparing the shadowsize to crater size of 50 secondary craters we find that 90 ofthe secondary craters have a depth to diameter ratio of ge02

Fig 6 Cumulative histograms of craters found in our three study areas The ldquocountrdquo population is the craters counted on the surface theproduction population was calculated from the best-fit of craters above the equilibrium diameter and equilibrium population is assumed tohave a minus2 log-log slope a) The 89deg incidence angle study area with an equilibrium diameter of sim260 m b) The 79deg incidence angle study areawith an equilibrium diameter of sim190 m Also shown is crater count data from a high-resolution LO image of a portion of the same area Thebreak in slope is consistent with the medium-resolution data and shows the equilibrium population of craters c) The 71deg incidence angle studyarea with an equilibrium diameter of sim165 m Error bars are 1 σ as defined by Arvidson et al (1979)

702 B B Wilcox et al

Thus it does not appear that isolated secondaries that mightremain in our crater count data were initially significantlyshallower or that they would influence our estimates ofregolith depth

Regolith depth estimates were calculated by taking thenumber of craters lost mainly due to infilling of regolith ofeach diameter bin and converting that to the percent of thesurface that those craters would cover The regolith depth forthat portion of the surface was taken to be 14 of craterdiameter as explained above This method suggests that forour 89deg incidence angle study area the regolith in nearly theentire area is at least 8 m deep (ie the surface is nearlycovered with craters 53 m in diameter that have been filled inwith regolith) In 53 of the area the regolith is 11 m deep in26 of the area the regolith is 15 m deep in 10 of the areathe regolith is 22 m deep and in 1 of the study area theregolith is 31 m deep We also examined the sensitivity of thedepth estimate to changes in equilibrium diameter whetherdue to different lighting conditions as in our three study areasor because of actual differences in the crater populations For

a production population with a slope of minus34 we varied theequilibrium diameter (break point in slope) and calculated theresulting estimated regolith depths (Fig 8) As theequilibrium diameter increases the average regolith depthincreases and covers a broader range of depths

Areas of similar age as our study areas have beenpreviously estimated to have a regolith depth of 1ndash6 m(Oberbeck and Quaide 1968) The median depth (11 m)inferred here is greater than previous estimates and the depthvaries significantly (8ndash31 m) in the region Our estimate of adeeper regolith is likely due in part to the fact that we found ahigher equilibrium diameter than the current paradigm ofsim100 m or less for Eratosthenian mare (Wilhelms 1987)

Block Populations

While extremely high incidence angle photography atsufficient resolution is limited to a very few local sites highresolution images (05ndash20 mpixel) at incidence angles ofsim70deg exist for a much broader sampling of the lunar surface

Table 1 Comparison of production and count populations of crater data from Fig 5aDiameter bin (m)

Equilibrium coverage ()

Production coverage()

Regolith coverage ()

Maximum depth(m)

Average depth (m)

38 14 182 168 8 553 14 110 96 11 875 14 67 53 15 11

107 14 40 26 21 15151 14 24 10 30 22213 14 15 1 43 31

Fig 7 A portion of LO3-165-M The incidence angle of the image is 79deg and thus the shadows of craters with depth to diameter ratios of 02(Pike 1974) should fall halfway across the crater floor most fresh craters show this relationship Likely secondary craters are indicated witharrows The inset box encloses our 79deg incidence angle study area specifically chosen to be away from most of the obvious secondariesResolution is 66 mpixel

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

Constraints on the depth and variability of the lunar regolith 697

underlying cause of different crater morphologies in some ofthe observed craters In their experiments even a thin layer ofpaint between two layers of sand was sufficient to produce acrater with irregular walls (Oberbeck personalcommunication)

Evidence that weak strength discontinuities (ascompared to bedrock) can cause bench morphology camewhen Apollo astronauts visited several bench craters (Benchcrater at the Apollo 12 site the Station 9 crater at the Apollo15 site Plum crater at the Apollo 16 site and Van Serg craterat the Apollo 17 site) It was found that none of these cratersformed in bedrock and that the benches were due to impactsin targets with units of differing physical properties such as aresistant layer within the regolith (Shoemaker et al 1970Muehlberger et al 1972 1973 Swann et al 1972 Schmitt1973)

Another possible indicator that a portion of the benchcraters may be due to factors other than bedrock is theexistence of relatively fresh bench craters without large blockpopulations (Fig 2) Bench craters that penetrated through theregolith and partially formed in bedrock would excavate partof that bedrock thus forming blocks As discussed below thelack of blocks is another indicator that the bench morphologymay not always be due to bedrock Thus it is misleading toassume that bench morphology represents a regolithrockinterface in all cases

Another common method for estimating regoliththickness is based on the occurrence (or lack thereof) ofblocks produced during an impact event Rennilson et al(1966) suggested that the depth of the fragmental layer(regolith) could be estimated from the depth of the smallestcrater with a blocky rim This logic assumes that craters withblocks penetrated through the regolith to a more coherent orcoarser-grained substrate that fractures into blocks craterswithout blocks form solely in unconsolidated regolith Usingblocks as indicators of regolith thickness assumes that ingeneral small differences in age (and thus degradation state)of craters alone cannot account for the presence or absence ofblocks because blocks on the lunar surface erode slowlyErosion caused by impacts that are small compared to the sizeof the rock (ldquosingle particle abrasionrdquo) is at a rate on the orderof 1 mm106 years (Crozaz et al 1971 Gault et al 1972 Hˆrzet al 1974) ldquoCatastrophic rupturerdquo caused by impactsresulting in a crater the diameter of which is at least a quarterof the diameter of the rock is a more effective process inremoving blocks However these impact events occur lessfrequently and the median survival time for a boulderapproximately 3 m across (a size typical in this study) is stillon the order of 109 years (Hˆrz 1977) Though blocks canescape destruction for substantial periods of time they arelikely to spend part of their lifetime buried within the regolith(Hˆrz 1977) Thus the most degraded craters cannot be usedfor estimating regolith depth because of the likelihood of theirblock populations being buried

Relatively shallow regolith depths of between 2ndash15 cmand 8ndash10 m were estimated in the vicinity of Surveyor landersby mapping blocky craters (Shoemaker and Morris 1969)However the irregular spatial distribution of blocky cratershas not been fully considered Craters similar in diameter anddegradation state can be found in close proximity one with noblocks the other with many (Fig 3) These apparentlyinconsistent blocky crater pairings cannot be readilyexplained by a simple shallow regolith model and the

Fig 2 Bench craters with differing block populations The top crater(LO3-188-H2) has very few blocks while the bottom crater (LO3-196-H2) has abundant blocks indicating that it has excavated morecoherent material than the top crater Scale bar is 100 m

698 B B Wilcox et al

implications for the variability of regolith depth have not beenthoroughly examined

Another possible complication with the blocky cratermethod of determining regolith depth is the existence ofregolith breccia boulders In several cases astronautsobserved craters (eg Van Serg at the Apollo 17 site) thatappeared to have excavated large amounts of coherentsubstrate producing a significant population of blocks butupon inspection the blocks turned out to be extremely friableregolith breccias (Muehlberger et al 1973 Schmitt 1973) Inthese cases the blocks produced by a crater-forming event arenot excavated from the coherent substrate but rather areformed from induration of regolith probably during theimpact event that deposited them on the surface (Muehlbergeret al 1973 Schmitt 1973) From existing orbital photographyit is not possible to discriminate between these two types ofblocks regolith depth estimated from these impact-producedrocks would be shallower than the actual depth There is alsothe possibility that blocks around a crater were excavatedfrom a blocky layer in the regolith or from large isolatedburied blocks In this case too the regolith depth inferred

from this type of crater would be shallower than the actualdepth The depths estimated from this method are thus likelyto err on the shallow side

Because regolith on the Moon is produced by impactsthe thickness of the regolith should correlate directly withcrater abundance and thus regolith depth has also beenestimated by examining the size-frequency distribution ofcrater populations (Shoemaker et al 1969) As a craterpopulation matures the number of craters that are visible onthe surface is less than the number of craters that wereactually produced because new craters obliterate older onesThe diameter at which the cumulative number of craters seenon the surface is less than the number produced is theequilibrium diameter this diameter can be identified as abreak in slope in a cumulative histogram of crater size-frequency (Gault 1970 Schultz et al 1977) Below the breakin slope (larger diameters) the trend is representative of theproduction population of craters above the break in slope(smaller diameters) the trend represents the steady-statecraters of which more were produced than are still visible onthe surface For the steady-state craters the differencebetween the production population of craters and thepopulation of craters still visible on the surface represents thenumber of craters that were destroyed This population ofobliterated craters initially starts as voids in the surface but asthey age their uplifted rims erode and their interiors fill withregolith until they become shallow to the point that they areno longer distinguishable (Shoemaker et al 1969 Soderblom1970) The depth of the regolith in a local area is thus equal tothe initial depth of the destroyed craters minus the rim height(Shoemaker et al 1969) Over large areas the averageregolith depth must be proportional to the depth of theequilibrium crater population Thus accurate determinationof the diameter at which a crater population has reachedequilibrium is a powerful tool for estimating regolith depth ina given area

The incidence angle (deviation of sun vector fromsurface normal) affects the number of craters that can bereadily identified in an image fewer craters are visible inimages with lower incidence angles (angles closer to solarzenith) This effect is more important for degraded craters thewalls of which have shallower slopes The incidence angle ofan image may affect the identification of degraded cratersresulting in uncertainties in estimates of the equilibriumdiameter of a population

Regolith depth has also been examined seismically Atthe Apollo 12 14 and 15 sites some information about thethree-dimensional nature of the regolith was gleanedincidentally from passive seismic experiments designed tostudy deeper features (Latham et al 1970 1971 1972) At theApollo 14 16 and 17 sites active seismic experiments weredesigned to provide data to specifically characterize theregolith and regolith depth estimates were obtained fromseismic refraction profiling Apollos 14 and 16 landed in non-

Fig 3 An example of craters of similar size and morphology withdifferent block populations The top crater (595 m in diameter) hasabundant blocks the bottom crater (575 m in diameter) has nodetectable blocks possibly indicating heterogeneities in regolithdepth From LO2-161-H2

Constraints on the depth and variability of the lunar regolith 699

mare areas and the sites were estimated to have regolithdepths of 85 m and 122 m respectively (Watkins andKovach 1973) At the Apollo 17 mare site several distinctlayers were identified In a regional seismic profile model thefirst 4 m of the surface were interpreted to be regolith belowthat a layer interpreted to be rubble of older regolithextremely fractured rock or both extended from 4 m down to32 m Below 32 m was a layer interpreted to be fractured orvesicular basalt (Cooper et al 1974) An alternate regionalmodel includes only a 7ndash12 m layer of regolith atop afractured or vesicular basalt (Cooper et al 1974) Thesenumbers should be viewed with caution the results depend ona number of assumptions and can differ markedly (as in thetwo examples above) when parameters or assumptions arevaried For example it was reported that relief of up to 6 m insubsurface layers could be observed in the seismic data but inthe regional seismic model it is assumed that all layers areplanar and their physical properties are uniform resulting inan oversimplified representation of the regolith depth (Cooperet al 1974) Also the seismic data are not internallyconsistent the regional profile that incorporates all seismicsource data does not agree with an end-to-end profile whichuses only select seismic sources where there is an additionallayer at a depth of 65 m (Cooper et al 1974)

While these techniques (crater morphology blockpopulation equilibrium diameter and seismic) provide usefultools for estimating regolith depth many issues remain openWhy arenrsquot all fresh bench craters blocky If there are manylarge (gt100 m) buried craters why are such smallthicknesses (1ndash10 m) generally cited Why arenrsquot all large

fresh craters blocky How important is the variation inregolith thickness Shortcomings in previous estimates maybe due to a regolith that is more complex (not a simple two-layer model with regolith atop a planar bedrock layer) andora regolith with significantly variable depth in a local areaThe work presented in this paper is designed to furtherexamine regolith depth and local spatial heterogeneities inregolith depth

METHODS AND RESULTS

Equilibrium Diameters

We have employed the equilibrium diameter method todetermine regolith depth and investigated the effects of solarincidence angle on the equilibrium diameter of crater size-frequency distributions of mare areas of similar ages Becausehigher incidence angles enhance more subtle topographicfeatures the sun angle should have a direct effect on thenumber of craters visible in an image with more cratersdetectable at higher incidence angles (Soderblom 1972Young 1975) This in turn should have a direct effect on theregolith depth estimated using the crater size-frequencymethod of Shoemaker et al (1969) In order to investigate sunangle effects we compared the apparent crater populationsand equilibrium diameters of images with incidence angles of71deg 79deg and 89deg Each image was converted to digital formatby scanning the image at the highest resolution necessary topreserve all of the information inherent in the originalphotograph

Fig 4 The same area under different lighting conditions after Soderblom (1972) Scene is sim164 km across a) Our 89deg incidence angle studyarea (AS15-98-13347) b) A 70deg incidence angle LO image (LO4-163-H1) Many more craters are visible in the high incidence angle imageThe low resolution of the LO image (gt40 mpixel) did not allow direct quantitative comparison of crater populations

700 B B Wilcox et al

Our first study site is a 950 km2 area located in OceanusProcellarum (approximately 26degN 58degW) sim275 km from the40-km crater Aristarchus For this location there existsextremely high incidence angle data in fact the terminatorcrosses the image AS15-98-13347 The effective resolutionof this photograph is sim9 mpixel similar to the typical LOmedium resolution images (sim7 mpixel) and is sufficient forthe size range of craters we are investigating (gt25 m) (Fig 4)Soderblom (1972) observed that in the near-terminator imagecraters 100ndash300 m in diameter are so ubiquitous that they arepositioned ldquoshoulder-to-shoulderrdquo (Fig 5) While thisobservation has been widely cited no crater count data fromthis high incidence angle image was reported This site has anestimated age of 276 billion years (+030 minus018) (Hiesingeret al 2003) as determined by comparing the regional cratersize-frequency distribution to the lunar crater productionfunction established from radiometric ages of returnedsamples

The second and third sites are also in OceanusProcellarum Site number two is a 173 km2 area covered bythe 79deg incidence angle image LO3-165-M (sim17degN 421degW66 mpixel) This is one of the highest incidence angle LOimages and serves as a good intermediate between the nearterminator image (Fig 4a) and typical LO images (sim70degincidence angle) The third site is a 64 km2 area found in the71deg incidence angle image LO3-200-M (sim31degS 426degW64 mpixel) and is representative of typical LO mediumresolution images These sites have estimated ages of208 billion years (+065 minus039) and 254 billion years(+029 minus017) respectively (Hiesinger et al 2003) These areall young mare and because they are similar in age (the agesof all three sites are within the error bars of each other) theyshould have similar crater populations

We digitized craters in each image (over 20000 craterstotal) with an interactive monitor-cursor program that fit acircle to three points selected on a crater rim Craters were

identified as nearly continuous circular features with thecaveat that the extreme shadowing often complicates cratermorphology A simple criterion was used to limit the numberof false identifications and maintain consistency from onecounting session to the next if a mental debate occurred as towhether the feature was a crater or not it was not digitizedThe crater count data in Fig 6 are presented in standardcumulative histogram form (Arvidson et al 1979) Theequilibrium diameter where the slope of the cumulativehistogram begins to deviate from a log-log slope ofapproximately minus34 (Soderblom 1970) was found bycalculating the slope using points at smaller and smaller craterdiameter bins until the slope was less than minus34 The slopeswere found with an iterative least squares fitting routine fornon-linear functions originally described by Bevington(1969) In this way the equilibrium diameter for the 89degincidence image was found to be approximately 260 m 190m for the 79deg image and 165 m for the 71deg image Weinterpret that the incidence angle had a significant effect onthe number of craters identified and thus the equilibriumdiameter differed by nearly 100 m for these three areas eventhough they are of similar age

To estimate regolith depth in the 89deg image wecompared the percentage of the surface covered by theequilibrium population to the percent of the surface thatwould be covered by the production population (with a slopeof minus34) (Table 1) We assumed that the equilibriumpopulation actually followed a minus2 slope typical of equilibriumpopulations (Gault 1970 Schultz et al 1977) in thecumulative histogram rather than the flat line in Fig 6a Thevery low slope at small diameters is most likely due to smallcraters being hidden by shadows of larger craters as well asthe resolution limiting the number of craters detected at thesmallest sizes This assumption does not affect our regolithdepth estimates significantly because small (compared to theequilibrium diameter) craters do not contribute appreciably toregolith depth but rather simply rework it (Oberbeck et al1973) The difference between the area covered by cratersproduced on the surface and the area covered by theequilibrium population of craters still present on the surface isthe portion of the surface covered by craters that have beenobliterated mainly by infilling of regolith (Shoemaker et al1969) Regolith depth in that portion of the surface is equal tothe initial average depth of the craters that are now filled inThe maximum crater depth is 20 of crater diameterincluding excavation and compression (Pike 1974) Thecorresponding average crater depth of an idealized bowl-shaped crater with a depth to diameter ratio of 02 is 14 ofcrater diameter This approximation takes into account theshallowing of the crater near the edges and subtracts the rimheight which does not contribute to the depth of the craterbelow the preexisting surface

A key assumption in estimating regolith depth from thismethod is the initial depth of the craters While the maximum

Fig 5 A portion of our 89deg incidence angle study area (Fig 4aAS15-98-13347) showing the nearly ldquoshoulder-to-shoulderrdquodistribution of 100ndash300 m craters (Soderblom 1972) Scale bar is1 km

Constraints on the depth and variability of the lunar regolith 701

depth of primary craters is 20 of crater diameter (Pike1974) it has been suggested that secondary craters are sim50shallower than primaries (Pike 1980) However this is forsecondary craters that are close to their parent crater and areclustered so that they often share rims with adjoiningsecondaries Secondary craters become better developed withincreasing distance from their parent crater and isolatedsecondaries far from the parent crater are not significantlyaffected by debris surges as is the case with clusteredsecondaries (Morrison and Oberbeck 1978) Our study areasare relatively far from large secondary-producing impactsWe attempted to avoid areas with obvious secondary craters

using methods described by Neukum et al (1975) and thecriteria of Oberbeck and Morrison (1973) (herringbonepattern elongated shape and clustering) To investigate whateffects any isolated secondaries remaining in our data setmight have we carried out a cursory examination of thedepths of fresh secondary craters of a range of diameters inthe image LO3-165-M (outside of our crater count study area)(Fig 7) Because the incidence angle of this image is 79deg theshadow of any crater with a depth to diameter ratio of 02 willfall halfway across the crater floor Comparing the shadowsize to crater size of 50 secondary craters we find that 90 ofthe secondary craters have a depth to diameter ratio of ge02

Fig 6 Cumulative histograms of craters found in our three study areas The ldquocountrdquo population is the craters counted on the surface theproduction population was calculated from the best-fit of craters above the equilibrium diameter and equilibrium population is assumed tohave a minus2 log-log slope a) The 89deg incidence angle study area with an equilibrium diameter of sim260 m b) The 79deg incidence angle study areawith an equilibrium diameter of sim190 m Also shown is crater count data from a high-resolution LO image of a portion of the same area Thebreak in slope is consistent with the medium-resolution data and shows the equilibrium population of craters c) The 71deg incidence angle studyarea with an equilibrium diameter of sim165 m Error bars are 1 σ as defined by Arvidson et al (1979)

702 B B Wilcox et al

Thus it does not appear that isolated secondaries that mightremain in our crater count data were initially significantlyshallower or that they would influence our estimates ofregolith depth

Regolith depth estimates were calculated by taking thenumber of craters lost mainly due to infilling of regolith ofeach diameter bin and converting that to the percent of thesurface that those craters would cover The regolith depth forthat portion of the surface was taken to be 14 of craterdiameter as explained above This method suggests that forour 89deg incidence angle study area the regolith in nearly theentire area is at least 8 m deep (ie the surface is nearlycovered with craters 53 m in diameter that have been filled inwith regolith) In 53 of the area the regolith is 11 m deep in26 of the area the regolith is 15 m deep in 10 of the areathe regolith is 22 m deep and in 1 of the study area theregolith is 31 m deep We also examined the sensitivity of thedepth estimate to changes in equilibrium diameter whetherdue to different lighting conditions as in our three study areasor because of actual differences in the crater populations For

a production population with a slope of minus34 we varied theequilibrium diameter (break point in slope) and calculated theresulting estimated regolith depths (Fig 8) As theequilibrium diameter increases the average regolith depthincreases and covers a broader range of depths

Areas of similar age as our study areas have beenpreviously estimated to have a regolith depth of 1ndash6 m(Oberbeck and Quaide 1968) The median depth (11 m)inferred here is greater than previous estimates and the depthvaries significantly (8ndash31 m) in the region Our estimate of adeeper regolith is likely due in part to the fact that we found ahigher equilibrium diameter than the current paradigm ofsim100 m or less for Eratosthenian mare (Wilhelms 1987)

Block Populations

While extremely high incidence angle photography atsufficient resolution is limited to a very few local sites highresolution images (05ndash20 mpixel) at incidence angles ofsim70deg exist for a much broader sampling of the lunar surface

Table 1 Comparison of production and count populations of crater data from Fig 5aDiameter bin (m)

Equilibrium coverage ()

Production coverage()

Regolith coverage ()

Maximum depth(m)

Average depth (m)

38 14 182 168 8 553 14 110 96 11 875 14 67 53 15 11

107 14 40 26 21 15151 14 24 10 30 22213 14 15 1 43 31

Fig 7 A portion of LO3-165-M The incidence angle of the image is 79deg and thus the shadows of craters with depth to diameter ratios of 02(Pike 1974) should fall halfway across the crater floor most fresh craters show this relationship Likely secondary craters are indicated witharrows The inset box encloses our 79deg incidence angle study area specifically chosen to be away from most of the obvious secondariesResolution is 66 mpixel

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

698 B B Wilcox et al

implications for the variability of regolith depth have not beenthoroughly examined

Another possible complication with the blocky cratermethod of determining regolith depth is the existence ofregolith breccia boulders In several cases astronautsobserved craters (eg Van Serg at the Apollo 17 site) thatappeared to have excavated large amounts of coherentsubstrate producing a significant population of blocks butupon inspection the blocks turned out to be extremely friableregolith breccias (Muehlberger et al 1973 Schmitt 1973) Inthese cases the blocks produced by a crater-forming event arenot excavated from the coherent substrate but rather areformed from induration of regolith probably during theimpact event that deposited them on the surface (Muehlbergeret al 1973 Schmitt 1973) From existing orbital photographyit is not possible to discriminate between these two types ofblocks regolith depth estimated from these impact-producedrocks would be shallower than the actual depth There is alsothe possibility that blocks around a crater were excavatedfrom a blocky layer in the regolith or from large isolatedburied blocks In this case too the regolith depth inferred

from this type of crater would be shallower than the actualdepth The depths estimated from this method are thus likelyto err on the shallow side

Because regolith on the Moon is produced by impactsthe thickness of the regolith should correlate directly withcrater abundance and thus regolith depth has also beenestimated by examining the size-frequency distribution ofcrater populations (Shoemaker et al 1969) As a craterpopulation matures the number of craters that are visible onthe surface is less than the number of craters that wereactually produced because new craters obliterate older onesThe diameter at which the cumulative number of craters seenon the surface is less than the number produced is theequilibrium diameter this diameter can be identified as abreak in slope in a cumulative histogram of crater size-frequency (Gault 1970 Schultz et al 1977) Below the breakin slope (larger diameters) the trend is representative of theproduction population of craters above the break in slope(smaller diameters) the trend represents the steady-statecraters of which more were produced than are still visible onthe surface For the steady-state craters the differencebetween the production population of craters and thepopulation of craters still visible on the surface represents thenumber of craters that were destroyed This population ofobliterated craters initially starts as voids in the surface but asthey age their uplifted rims erode and their interiors fill withregolith until they become shallow to the point that they areno longer distinguishable (Shoemaker et al 1969 Soderblom1970) The depth of the regolith in a local area is thus equal tothe initial depth of the destroyed craters minus the rim height(Shoemaker et al 1969) Over large areas the averageregolith depth must be proportional to the depth of theequilibrium crater population Thus accurate determinationof the diameter at which a crater population has reachedequilibrium is a powerful tool for estimating regolith depth ina given area

The incidence angle (deviation of sun vector fromsurface normal) affects the number of craters that can bereadily identified in an image fewer craters are visible inimages with lower incidence angles (angles closer to solarzenith) This effect is more important for degraded craters thewalls of which have shallower slopes The incidence angle ofan image may affect the identification of degraded cratersresulting in uncertainties in estimates of the equilibriumdiameter of a population

Regolith depth has also been examined seismically Atthe Apollo 12 14 and 15 sites some information about thethree-dimensional nature of the regolith was gleanedincidentally from passive seismic experiments designed tostudy deeper features (Latham et al 1970 1971 1972) At theApollo 14 16 and 17 sites active seismic experiments weredesigned to provide data to specifically characterize theregolith and regolith depth estimates were obtained fromseismic refraction profiling Apollos 14 and 16 landed in non-

Fig 3 An example of craters of similar size and morphology withdifferent block populations The top crater (595 m in diameter) hasabundant blocks the bottom crater (575 m in diameter) has nodetectable blocks possibly indicating heterogeneities in regolithdepth From LO2-161-H2

Constraints on the depth and variability of the lunar regolith 699

mare areas and the sites were estimated to have regolithdepths of 85 m and 122 m respectively (Watkins andKovach 1973) At the Apollo 17 mare site several distinctlayers were identified In a regional seismic profile model thefirst 4 m of the surface were interpreted to be regolith belowthat a layer interpreted to be rubble of older regolithextremely fractured rock or both extended from 4 m down to32 m Below 32 m was a layer interpreted to be fractured orvesicular basalt (Cooper et al 1974) An alternate regionalmodel includes only a 7ndash12 m layer of regolith atop afractured or vesicular basalt (Cooper et al 1974) Thesenumbers should be viewed with caution the results depend ona number of assumptions and can differ markedly (as in thetwo examples above) when parameters or assumptions arevaried For example it was reported that relief of up to 6 m insubsurface layers could be observed in the seismic data but inthe regional seismic model it is assumed that all layers areplanar and their physical properties are uniform resulting inan oversimplified representation of the regolith depth (Cooperet al 1974) Also the seismic data are not internallyconsistent the regional profile that incorporates all seismicsource data does not agree with an end-to-end profile whichuses only select seismic sources where there is an additionallayer at a depth of 65 m (Cooper et al 1974)

While these techniques (crater morphology blockpopulation equilibrium diameter and seismic) provide usefultools for estimating regolith depth many issues remain openWhy arenrsquot all fresh bench craters blocky If there are manylarge (gt100 m) buried craters why are such smallthicknesses (1ndash10 m) generally cited Why arenrsquot all large

fresh craters blocky How important is the variation inregolith thickness Shortcomings in previous estimates maybe due to a regolith that is more complex (not a simple two-layer model with regolith atop a planar bedrock layer) andora regolith with significantly variable depth in a local areaThe work presented in this paper is designed to furtherexamine regolith depth and local spatial heterogeneities inregolith depth

METHODS AND RESULTS

Equilibrium Diameters

We have employed the equilibrium diameter method todetermine regolith depth and investigated the effects of solarincidence angle on the equilibrium diameter of crater size-frequency distributions of mare areas of similar ages Becausehigher incidence angles enhance more subtle topographicfeatures the sun angle should have a direct effect on thenumber of craters visible in an image with more cratersdetectable at higher incidence angles (Soderblom 1972Young 1975) This in turn should have a direct effect on theregolith depth estimated using the crater size-frequencymethod of Shoemaker et al (1969) In order to investigate sunangle effects we compared the apparent crater populationsand equilibrium diameters of images with incidence angles of71deg 79deg and 89deg Each image was converted to digital formatby scanning the image at the highest resolution necessary topreserve all of the information inherent in the originalphotograph

Fig 4 The same area under different lighting conditions after Soderblom (1972) Scene is sim164 km across a) Our 89deg incidence angle studyarea (AS15-98-13347) b) A 70deg incidence angle LO image (LO4-163-H1) Many more craters are visible in the high incidence angle imageThe low resolution of the LO image (gt40 mpixel) did not allow direct quantitative comparison of crater populations

700 B B Wilcox et al

Our first study site is a 950 km2 area located in OceanusProcellarum (approximately 26degN 58degW) sim275 km from the40-km crater Aristarchus For this location there existsextremely high incidence angle data in fact the terminatorcrosses the image AS15-98-13347 The effective resolutionof this photograph is sim9 mpixel similar to the typical LOmedium resolution images (sim7 mpixel) and is sufficient forthe size range of craters we are investigating (gt25 m) (Fig 4)Soderblom (1972) observed that in the near-terminator imagecraters 100ndash300 m in diameter are so ubiquitous that they arepositioned ldquoshoulder-to-shoulderrdquo (Fig 5) While thisobservation has been widely cited no crater count data fromthis high incidence angle image was reported This site has anestimated age of 276 billion years (+030 minus018) (Hiesingeret al 2003) as determined by comparing the regional cratersize-frequency distribution to the lunar crater productionfunction established from radiometric ages of returnedsamples

The second and third sites are also in OceanusProcellarum Site number two is a 173 km2 area covered bythe 79deg incidence angle image LO3-165-M (sim17degN 421degW66 mpixel) This is one of the highest incidence angle LOimages and serves as a good intermediate between the nearterminator image (Fig 4a) and typical LO images (sim70degincidence angle) The third site is a 64 km2 area found in the71deg incidence angle image LO3-200-M (sim31degS 426degW64 mpixel) and is representative of typical LO mediumresolution images These sites have estimated ages of208 billion years (+065 minus039) and 254 billion years(+029 minus017) respectively (Hiesinger et al 2003) These areall young mare and because they are similar in age (the agesof all three sites are within the error bars of each other) theyshould have similar crater populations

We digitized craters in each image (over 20000 craterstotal) with an interactive monitor-cursor program that fit acircle to three points selected on a crater rim Craters were

identified as nearly continuous circular features with thecaveat that the extreme shadowing often complicates cratermorphology A simple criterion was used to limit the numberof false identifications and maintain consistency from onecounting session to the next if a mental debate occurred as towhether the feature was a crater or not it was not digitizedThe crater count data in Fig 6 are presented in standardcumulative histogram form (Arvidson et al 1979) Theequilibrium diameter where the slope of the cumulativehistogram begins to deviate from a log-log slope ofapproximately minus34 (Soderblom 1970) was found bycalculating the slope using points at smaller and smaller craterdiameter bins until the slope was less than minus34 The slopeswere found with an iterative least squares fitting routine fornon-linear functions originally described by Bevington(1969) In this way the equilibrium diameter for the 89degincidence image was found to be approximately 260 m 190m for the 79deg image and 165 m for the 71deg image Weinterpret that the incidence angle had a significant effect onthe number of craters identified and thus the equilibriumdiameter differed by nearly 100 m for these three areas eventhough they are of similar age

To estimate regolith depth in the 89deg image wecompared the percentage of the surface covered by theequilibrium population to the percent of the surface thatwould be covered by the production population (with a slopeof minus34) (Table 1) We assumed that the equilibriumpopulation actually followed a minus2 slope typical of equilibriumpopulations (Gault 1970 Schultz et al 1977) in thecumulative histogram rather than the flat line in Fig 6a Thevery low slope at small diameters is most likely due to smallcraters being hidden by shadows of larger craters as well asthe resolution limiting the number of craters detected at thesmallest sizes This assumption does not affect our regolithdepth estimates significantly because small (compared to theequilibrium diameter) craters do not contribute appreciably toregolith depth but rather simply rework it (Oberbeck et al1973) The difference between the area covered by cratersproduced on the surface and the area covered by theequilibrium population of craters still present on the surface isthe portion of the surface covered by craters that have beenobliterated mainly by infilling of regolith (Shoemaker et al1969) Regolith depth in that portion of the surface is equal tothe initial average depth of the craters that are now filled inThe maximum crater depth is 20 of crater diameterincluding excavation and compression (Pike 1974) Thecorresponding average crater depth of an idealized bowl-shaped crater with a depth to diameter ratio of 02 is 14 ofcrater diameter This approximation takes into account theshallowing of the crater near the edges and subtracts the rimheight which does not contribute to the depth of the craterbelow the preexisting surface

A key assumption in estimating regolith depth from thismethod is the initial depth of the craters While the maximum

Fig 5 A portion of our 89deg incidence angle study area (Fig 4aAS15-98-13347) showing the nearly ldquoshoulder-to-shoulderrdquodistribution of 100ndash300 m craters (Soderblom 1972) Scale bar is1 km

Constraints on the depth and variability of the lunar regolith 701

depth of primary craters is 20 of crater diameter (Pike1974) it has been suggested that secondary craters are sim50shallower than primaries (Pike 1980) However this is forsecondary craters that are close to their parent crater and areclustered so that they often share rims with adjoiningsecondaries Secondary craters become better developed withincreasing distance from their parent crater and isolatedsecondaries far from the parent crater are not significantlyaffected by debris surges as is the case with clusteredsecondaries (Morrison and Oberbeck 1978) Our study areasare relatively far from large secondary-producing impactsWe attempted to avoid areas with obvious secondary craters

using methods described by Neukum et al (1975) and thecriteria of Oberbeck and Morrison (1973) (herringbonepattern elongated shape and clustering) To investigate whateffects any isolated secondaries remaining in our data setmight have we carried out a cursory examination of thedepths of fresh secondary craters of a range of diameters inthe image LO3-165-M (outside of our crater count study area)(Fig 7) Because the incidence angle of this image is 79deg theshadow of any crater with a depth to diameter ratio of 02 willfall halfway across the crater floor Comparing the shadowsize to crater size of 50 secondary craters we find that 90 ofthe secondary craters have a depth to diameter ratio of ge02

Fig 6 Cumulative histograms of craters found in our three study areas The ldquocountrdquo population is the craters counted on the surface theproduction population was calculated from the best-fit of craters above the equilibrium diameter and equilibrium population is assumed tohave a minus2 log-log slope a) The 89deg incidence angle study area with an equilibrium diameter of sim260 m b) The 79deg incidence angle study areawith an equilibrium diameter of sim190 m Also shown is crater count data from a high-resolution LO image of a portion of the same area Thebreak in slope is consistent with the medium-resolution data and shows the equilibrium population of craters c) The 71deg incidence angle studyarea with an equilibrium diameter of sim165 m Error bars are 1 σ as defined by Arvidson et al (1979)

702 B B Wilcox et al

Thus it does not appear that isolated secondaries that mightremain in our crater count data were initially significantlyshallower or that they would influence our estimates ofregolith depth

Regolith depth estimates were calculated by taking thenumber of craters lost mainly due to infilling of regolith ofeach diameter bin and converting that to the percent of thesurface that those craters would cover The regolith depth forthat portion of the surface was taken to be 14 of craterdiameter as explained above This method suggests that forour 89deg incidence angle study area the regolith in nearly theentire area is at least 8 m deep (ie the surface is nearlycovered with craters 53 m in diameter that have been filled inwith regolith) In 53 of the area the regolith is 11 m deep in26 of the area the regolith is 15 m deep in 10 of the areathe regolith is 22 m deep and in 1 of the study area theregolith is 31 m deep We also examined the sensitivity of thedepth estimate to changes in equilibrium diameter whetherdue to different lighting conditions as in our three study areasor because of actual differences in the crater populations For

a production population with a slope of minus34 we varied theequilibrium diameter (break point in slope) and calculated theresulting estimated regolith depths (Fig 8) As theequilibrium diameter increases the average regolith depthincreases and covers a broader range of depths

Areas of similar age as our study areas have beenpreviously estimated to have a regolith depth of 1ndash6 m(Oberbeck and Quaide 1968) The median depth (11 m)inferred here is greater than previous estimates and the depthvaries significantly (8ndash31 m) in the region Our estimate of adeeper regolith is likely due in part to the fact that we found ahigher equilibrium diameter than the current paradigm ofsim100 m or less for Eratosthenian mare (Wilhelms 1987)

Block Populations

While extremely high incidence angle photography atsufficient resolution is limited to a very few local sites highresolution images (05ndash20 mpixel) at incidence angles ofsim70deg exist for a much broader sampling of the lunar surface

Table 1 Comparison of production and count populations of crater data from Fig 5aDiameter bin (m)

Equilibrium coverage ()

Production coverage()

Regolith coverage ()

Maximum depth(m)

Average depth (m)

38 14 182 168 8 553 14 110 96 11 875 14 67 53 15 11

107 14 40 26 21 15151 14 24 10 30 22213 14 15 1 43 31

Fig 7 A portion of LO3-165-M The incidence angle of the image is 79deg and thus the shadows of craters with depth to diameter ratios of 02(Pike 1974) should fall halfway across the crater floor most fresh craters show this relationship Likely secondary craters are indicated witharrows The inset box encloses our 79deg incidence angle study area specifically chosen to be away from most of the obvious secondariesResolution is 66 mpixel

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

Constraints on the depth and variability of the lunar regolith 699

mare areas and the sites were estimated to have regolithdepths of 85 m and 122 m respectively (Watkins andKovach 1973) At the Apollo 17 mare site several distinctlayers were identified In a regional seismic profile model thefirst 4 m of the surface were interpreted to be regolith belowthat a layer interpreted to be rubble of older regolithextremely fractured rock or both extended from 4 m down to32 m Below 32 m was a layer interpreted to be fractured orvesicular basalt (Cooper et al 1974) An alternate regionalmodel includes only a 7ndash12 m layer of regolith atop afractured or vesicular basalt (Cooper et al 1974) Thesenumbers should be viewed with caution the results depend ona number of assumptions and can differ markedly (as in thetwo examples above) when parameters or assumptions arevaried For example it was reported that relief of up to 6 m insubsurface layers could be observed in the seismic data but inthe regional seismic model it is assumed that all layers areplanar and their physical properties are uniform resulting inan oversimplified representation of the regolith depth (Cooperet al 1974) Also the seismic data are not internallyconsistent the regional profile that incorporates all seismicsource data does not agree with an end-to-end profile whichuses only select seismic sources where there is an additionallayer at a depth of 65 m (Cooper et al 1974)

While these techniques (crater morphology blockpopulation equilibrium diameter and seismic) provide usefultools for estimating regolith depth many issues remain openWhy arenrsquot all fresh bench craters blocky If there are manylarge (gt100 m) buried craters why are such smallthicknesses (1ndash10 m) generally cited Why arenrsquot all large

fresh craters blocky How important is the variation inregolith thickness Shortcomings in previous estimates maybe due to a regolith that is more complex (not a simple two-layer model with regolith atop a planar bedrock layer) andora regolith with significantly variable depth in a local areaThe work presented in this paper is designed to furtherexamine regolith depth and local spatial heterogeneities inregolith depth

METHODS AND RESULTS

Equilibrium Diameters

We have employed the equilibrium diameter method todetermine regolith depth and investigated the effects of solarincidence angle on the equilibrium diameter of crater size-frequency distributions of mare areas of similar ages Becausehigher incidence angles enhance more subtle topographicfeatures the sun angle should have a direct effect on thenumber of craters visible in an image with more cratersdetectable at higher incidence angles (Soderblom 1972Young 1975) This in turn should have a direct effect on theregolith depth estimated using the crater size-frequencymethod of Shoemaker et al (1969) In order to investigate sunangle effects we compared the apparent crater populationsand equilibrium diameters of images with incidence angles of71deg 79deg and 89deg Each image was converted to digital formatby scanning the image at the highest resolution necessary topreserve all of the information inherent in the originalphotograph

Fig 4 The same area under different lighting conditions after Soderblom (1972) Scene is sim164 km across a) Our 89deg incidence angle studyarea (AS15-98-13347) b) A 70deg incidence angle LO image (LO4-163-H1) Many more craters are visible in the high incidence angle imageThe low resolution of the LO image (gt40 mpixel) did not allow direct quantitative comparison of crater populations

700 B B Wilcox et al

Our first study site is a 950 km2 area located in OceanusProcellarum (approximately 26degN 58degW) sim275 km from the40-km crater Aristarchus For this location there existsextremely high incidence angle data in fact the terminatorcrosses the image AS15-98-13347 The effective resolutionof this photograph is sim9 mpixel similar to the typical LOmedium resolution images (sim7 mpixel) and is sufficient forthe size range of craters we are investigating (gt25 m) (Fig 4)Soderblom (1972) observed that in the near-terminator imagecraters 100ndash300 m in diameter are so ubiquitous that they arepositioned ldquoshoulder-to-shoulderrdquo (Fig 5) While thisobservation has been widely cited no crater count data fromthis high incidence angle image was reported This site has anestimated age of 276 billion years (+030 minus018) (Hiesingeret al 2003) as determined by comparing the regional cratersize-frequency distribution to the lunar crater productionfunction established from radiometric ages of returnedsamples

The second and third sites are also in OceanusProcellarum Site number two is a 173 km2 area covered bythe 79deg incidence angle image LO3-165-M (sim17degN 421degW66 mpixel) This is one of the highest incidence angle LOimages and serves as a good intermediate between the nearterminator image (Fig 4a) and typical LO images (sim70degincidence angle) The third site is a 64 km2 area found in the71deg incidence angle image LO3-200-M (sim31degS 426degW64 mpixel) and is representative of typical LO mediumresolution images These sites have estimated ages of208 billion years (+065 minus039) and 254 billion years(+029 minus017) respectively (Hiesinger et al 2003) These areall young mare and because they are similar in age (the agesof all three sites are within the error bars of each other) theyshould have similar crater populations

We digitized craters in each image (over 20000 craterstotal) with an interactive monitor-cursor program that fit acircle to three points selected on a crater rim Craters were

identified as nearly continuous circular features with thecaveat that the extreme shadowing often complicates cratermorphology A simple criterion was used to limit the numberof false identifications and maintain consistency from onecounting session to the next if a mental debate occurred as towhether the feature was a crater or not it was not digitizedThe crater count data in Fig 6 are presented in standardcumulative histogram form (Arvidson et al 1979) Theequilibrium diameter where the slope of the cumulativehistogram begins to deviate from a log-log slope ofapproximately minus34 (Soderblom 1970) was found bycalculating the slope using points at smaller and smaller craterdiameter bins until the slope was less than minus34 The slopeswere found with an iterative least squares fitting routine fornon-linear functions originally described by Bevington(1969) In this way the equilibrium diameter for the 89degincidence image was found to be approximately 260 m 190m for the 79deg image and 165 m for the 71deg image Weinterpret that the incidence angle had a significant effect onthe number of craters identified and thus the equilibriumdiameter differed by nearly 100 m for these three areas eventhough they are of similar age

To estimate regolith depth in the 89deg image wecompared the percentage of the surface covered by theequilibrium population to the percent of the surface thatwould be covered by the production population (with a slopeof minus34) (Table 1) We assumed that the equilibriumpopulation actually followed a minus2 slope typical of equilibriumpopulations (Gault 1970 Schultz et al 1977) in thecumulative histogram rather than the flat line in Fig 6a Thevery low slope at small diameters is most likely due to smallcraters being hidden by shadows of larger craters as well asthe resolution limiting the number of craters detected at thesmallest sizes This assumption does not affect our regolithdepth estimates significantly because small (compared to theequilibrium diameter) craters do not contribute appreciably toregolith depth but rather simply rework it (Oberbeck et al1973) The difference between the area covered by cratersproduced on the surface and the area covered by theequilibrium population of craters still present on the surface isthe portion of the surface covered by craters that have beenobliterated mainly by infilling of regolith (Shoemaker et al1969) Regolith depth in that portion of the surface is equal tothe initial average depth of the craters that are now filled inThe maximum crater depth is 20 of crater diameterincluding excavation and compression (Pike 1974) Thecorresponding average crater depth of an idealized bowl-shaped crater with a depth to diameter ratio of 02 is 14 ofcrater diameter This approximation takes into account theshallowing of the crater near the edges and subtracts the rimheight which does not contribute to the depth of the craterbelow the preexisting surface

A key assumption in estimating regolith depth from thismethod is the initial depth of the craters While the maximum

Fig 5 A portion of our 89deg incidence angle study area (Fig 4aAS15-98-13347) showing the nearly ldquoshoulder-to-shoulderrdquodistribution of 100ndash300 m craters (Soderblom 1972) Scale bar is1 km

Constraints on the depth and variability of the lunar regolith 701

depth of primary craters is 20 of crater diameter (Pike1974) it has been suggested that secondary craters are sim50shallower than primaries (Pike 1980) However this is forsecondary craters that are close to their parent crater and areclustered so that they often share rims with adjoiningsecondaries Secondary craters become better developed withincreasing distance from their parent crater and isolatedsecondaries far from the parent crater are not significantlyaffected by debris surges as is the case with clusteredsecondaries (Morrison and Oberbeck 1978) Our study areasare relatively far from large secondary-producing impactsWe attempted to avoid areas with obvious secondary craters

using methods described by Neukum et al (1975) and thecriteria of Oberbeck and Morrison (1973) (herringbonepattern elongated shape and clustering) To investigate whateffects any isolated secondaries remaining in our data setmight have we carried out a cursory examination of thedepths of fresh secondary craters of a range of diameters inthe image LO3-165-M (outside of our crater count study area)(Fig 7) Because the incidence angle of this image is 79deg theshadow of any crater with a depth to diameter ratio of 02 willfall halfway across the crater floor Comparing the shadowsize to crater size of 50 secondary craters we find that 90 ofthe secondary craters have a depth to diameter ratio of ge02

Fig 6 Cumulative histograms of craters found in our three study areas The ldquocountrdquo population is the craters counted on the surface theproduction population was calculated from the best-fit of craters above the equilibrium diameter and equilibrium population is assumed tohave a minus2 log-log slope a) The 89deg incidence angle study area with an equilibrium diameter of sim260 m b) The 79deg incidence angle study areawith an equilibrium diameter of sim190 m Also shown is crater count data from a high-resolution LO image of a portion of the same area Thebreak in slope is consistent with the medium-resolution data and shows the equilibrium population of craters c) The 71deg incidence angle studyarea with an equilibrium diameter of sim165 m Error bars are 1 σ as defined by Arvidson et al (1979)

702 B B Wilcox et al

Thus it does not appear that isolated secondaries that mightremain in our crater count data were initially significantlyshallower or that they would influence our estimates ofregolith depth

Regolith depth estimates were calculated by taking thenumber of craters lost mainly due to infilling of regolith ofeach diameter bin and converting that to the percent of thesurface that those craters would cover The regolith depth forthat portion of the surface was taken to be 14 of craterdiameter as explained above This method suggests that forour 89deg incidence angle study area the regolith in nearly theentire area is at least 8 m deep (ie the surface is nearlycovered with craters 53 m in diameter that have been filled inwith regolith) In 53 of the area the regolith is 11 m deep in26 of the area the regolith is 15 m deep in 10 of the areathe regolith is 22 m deep and in 1 of the study area theregolith is 31 m deep We also examined the sensitivity of thedepth estimate to changes in equilibrium diameter whetherdue to different lighting conditions as in our three study areasor because of actual differences in the crater populations For

a production population with a slope of minus34 we varied theequilibrium diameter (break point in slope) and calculated theresulting estimated regolith depths (Fig 8) As theequilibrium diameter increases the average regolith depthincreases and covers a broader range of depths

Areas of similar age as our study areas have beenpreviously estimated to have a regolith depth of 1ndash6 m(Oberbeck and Quaide 1968) The median depth (11 m)inferred here is greater than previous estimates and the depthvaries significantly (8ndash31 m) in the region Our estimate of adeeper regolith is likely due in part to the fact that we found ahigher equilibrium diameter than the current paradigm ofsim100 m or less for Eratosthenian mare (Wilhelms 1987)

Block Populations

While extremely high incidence angle photography atsufficient resolution is limited to a very few local sites highresolution images (05ndash20 mpixel) at incidence angles ofsim70deg exist for a much broader sampling of the lunar surface

Table 1 Comparison of production and count populations of crater data from Fig 5aDiameter bin (m)

Equilibrium coverage ()

Production coverage()

Regolith coverage ()

Maximum depth(m)

Average depth (m)

38 14 182 168 8 553 14 110 96 11 875 14 67 53 15 11

107 14 40 26 21 15151 14 24 10 30 22213 14 15 1 43 31

Fig 7 A portion of LO3-165-M The incidence angle of the image is 79deg and thus the shadows of craters with depth to diameter ratios of 02(Pike 1974) should fall halfway across the crater floor most fresh craters show this relationship Likely secondary craters are indicated witharrows The inset box encloses our 79deg incidence angle study area specifically chosen to be away from most of the obvious secondariesResolution is 66 mpixel

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

700 B B Wilcox et al

Our first study site is a 950 km2 area located in OceanusProcellarum (approximately 26degN 58degW) sim275 km from the40-km crater Aristarchus For this location there existsextremely high incidence angle data in fact the terminatorcrosses the image AS15-98-13347 The effective resolutionof this photograph is sim9 mpixel similar to the typical LOmedium resolution images (sim7 mpixel) and is sufficient forthe size range of craters we are investigating (gt25 m) (Fig 4)Soderblom (1972) observed that in the near-terminator imagecraters 100ndash300 m in diameter are so ubiquitous that they arepositioned ldquoshoulder-to-shoulderrdquo (Fig 5) While thisobservation has been widely cited no crater count data fromthis high incidence angle image was reported This site has anestimated age of 276 billion years (+030 minus018) (Hiesingeret al 2003) as determined by comparing the regional cratersize-frequency distribution to the lunar crater productionfunction established from radiometric ages of returnedsamples

The second and third sites are also in OceanusProcellarum Site number two is a 173 km2 area covered bythe 79deg incidence angle image LO3-165-M (sim17degN 421degW66 mpixel) This is one of the highest incidence angle LOimages and serves as a good intermediate between the nearterminator image (Fig 4a) and typical LO images (sim70degincidence angle) The third site is a 64 km2 area found in the71deg incidence angle image LO3-200-M (sim31degS 426degW64 mpixel) and is representative of typical LO mediumresolution images These sites have estimated ages of208 billion years (+065 minus039) and 254 billion years(+029 minus017) respectively (Hiesinger et al 2003) These areall young mare and because they are similar in age (the agesof all three sites are within the error bars of each other) theyshould have similar crater populations

We digitized craters in each image (over 20000 craterstotal) with an interactive monitor-cursor program that fit acircle to three points selected on a crater rim Craters were

identified as nearly continuous circular features with thecaveat that the extreme shadowing often complicates cratermorphology A simple criterion was used to limit the numberof false identifications and maintain consistency from onecounting session to the next if a mental debate occurred as towhether the feature was a crater or not it was not digitizedThe crater count data in Fig 6 are presented in standardcumulative histogram form (Arvidson et al 1979) Theequilibrium diameter where the slope of the cumulativehistogram begins to deviate from a log-log slope ofapproximately minus34 (Soderblom 1970) was found bycalculating the slope using points at smaller and smaller craterdiameter bins until the slope was less than minus34 The slopeswere found with an iterative least squares fitting routine fornon-linear functions originally described by Bevington(1969) In this way the equilibrium diameter for the 89degincidence image was found to be approximately 260 m 190m for the 79deg image and 165 m for the 71deg image Weinterpret that the incidence angle had a significant effect onthe number of craters identified and thus the equilibriumdiameter differed by nearly 100 m for these three areas eventhough they are of similar age

To estimate regolith depth in the 89deg image wecompared the percentage of the surface covered by theequilibrium population to the percent of the surface thatwould be covered by the production population (with a slopeof minus34) (Table 1) We assumed that the equilibriumpopulation actually followed a minus2 slope typical of equilibriumpopulations (Gault 1970 Schultz et al 1977) in thecumulative histogram rather than the flat line in Fig 6a Thevery low slope at small diameters is most likely due to smallcraters being hidden by shadows of larger craters as well asthe resolution limiting the number of craters detected at thesmallest sizes This assumption does not affect our regolithdepth estimates significantly because small (compared to theequilibrium diameter) craters do not contribute appreciably toregolith depth but rather simply rework it (Oberbeck et al1973) The difference between the area covered by cratersproduced on the surface and the area covered by theequilibrium population of craters still present on the surface isthe portion of the surface covered by craters that have beenobliterated mainly by infilling of regolith (Shoemaker et al1969) Regolith depth in that portion of the surface is equal tothe initial average depth of the craters that are now filled inThe maximum crater depth is 20 of crater diameterincluding excavation and compression (Pike 1974) Thecorresponding average crater depth of an idealized bowl-shaped crater with a depth to diameter ratio of 02 is 14 ofcrater diameter This approximation takes into account theshallowing of the crater near the edges and subtracts the rimheight which does not contribute to the depth of the craterbelow the preexisting surface

A key assumption in estimating regolith depth from thismethod is the initial depth of the craters While the maximum

Fig 5 A portion of our 89deg incidence angle study area (Fig 4aAS15-98-13347) showing the nearly ldquoshoulder-to-shoulderrdquodistribution of 100ndash300 m craters (Soderblom 1972) Scale bar is1 km

Constraints on the depth and variability of the lunar regolith 701

depth of primary craters is 20 of crater diameter (Pike1974) it has been suggested that secondary craters are sim50shallower than primaries (Pike 1980) However this is forsecondary craters that are close to their parent crater and areclustered so that they often share rims with adjoiningsecondaries Secondary craters become better developed withincreasing distance from their parent crater and isolatedsecondaries far from the parent crater are not significantlyaffected by debris surges as is the case with clusteredsecondaries (Morrison and Oberbeck 1978) Our study areasare relatively far from large secondary-producing impactsWe attempted to avoid areas with obvious secondary craters

using methods described by Neukum et al (1975) and thecriteria of Oberbeck and Morrison (1973) (herringbonepattern elongated shape and clustering) To investigate whateffects any isolated secondaries remaining in our data setmight have we carried out a cursory examination of thedepths of fresh secondary craters of a range of diameters inthe image LO3-165-M (outside of our crater count study area)(Fig 7) Because the incidence angle of this image is 79deg theshadow of any crater with a depth to diameter ratio of 02 willfall halfway across the crater floor Comparing the shadowsize to crater size of 50 secondary craters we find that 90 ofthe secondary craters have a depth to diameter ratio of ge02

Fig 6 Cumulative histograms of craters found in our three study areas The ldquocountrdquo population is the craters counted on the surface theproduction population was calculated from the best-fit of craters above the equilibrium diameter and equilibrium population is assumed tohave a minus2 log-log slope a) The 89deg incidence angle study area with an equilibrium diameter of sim260 m b) The 79deg incidence angle study areawith an equilibrium diameter of sim190 m Also shown is crater count data from a high-resolution LO image of a portion of the same area Thebreak in slope is consistent with the medium-resolution data and shows the equilibrium population of craters c) The 71deg incidence angle studyarea with an equilibrium diameter of sim165 m Error bars are 1 σ as defined by Arvidson et al (1979)

702 B B Wilcox et al

Thus it does not appear that isolated secondaries that mightremain in our crater count data were initially significantlyshallower or that they would influence our estimates ofregolith depth

Regolith depth estimates were calculated by taking thenumber of craters lost mainly due to infilling of regolith ofeach diameter bin and converting that to the percent of thesurface that those craters would cover The regolith depth forthat portion of the surface was taken to be 14 of craterdiameter as explained above This method suggests that forour 89deg incidence angle study area the regolith in nearly theentire area is at least 8 m deep (ie the surface is nearlycovered with craters 53 m in diameter that have been filled inwith regolith) In 53 of the area the regolith is 11 m deep in26 of the area the regolith is 15 m deep in 10 of the areathe regolith is 22 m deep and in 1 of the study area theregolith is 31 m deep We also examined the sensitivity of thedepth estimate to changes in equilibrium diameter whetherdue to different lighting conditions as in our three study areasor because of actual differences in the crater populations For

a production population with a slope of minus34 we varied theequilibrium diameter (break point in slope) and calculated theresulting estimated regolith depths (Fig 8) As theequilibrium diameter increases the average regolith depthincreases and covers a broader range of depths

Areas of similar age as our study areas have beenpreviously estimated to have a regolith depth of 1ndash6 m(Oberbeck and Quaide 1968) The median depth (11 m)inferred here is greater than previous estimates and the depthvaries significantly (8ndash31 m) in the region Our estimate of adeeper regolith is likely due in part to the fact that we found ahigher equilibrium diameter than the current paradigm ofsim100 m or less for Eratosthenian mare (Wilhelms 1987)

Block Populations

While extremely high incidence angle photography atsufficient resolution is limited to a very few local sites highresolution images (05ndash20 mpixel) at incidence angles ofsim70deg exist for a much broader sampling of the lunar surface

Table 1 Comparison of production and count populations of crater data from Fig 5aDiameter bin (m)

Equilibrium coverage ()

Production coverage()

Regolith coverage ()

Maximum depth(m)

Average depth (m)

38 14 182 168 8 553 14 110 96 11 875 14 67 53 15 11

107 14 40 26 21 15151 14 24 10 30 22213 14 15 1 43 31

Fig 7 A portion of LO3-165-M The incidence angle of the image is 79deg and thus the shadows of craters with depth to diameter ratios of 02(Pike 1974) should fall halfway across the crater floor most fresh craters show this relationship Likely secondary craters are indicated witharrows The inset box encloses our 79deg incidence angle study area specifically chosen to be away from most of the obvious secondariesResolution is 66 mpixel

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

Constraints on the depth and variability of the lunar regolith 701

depth of primary craters is 20 of crater diameter (Pike1974) it has been suggested that secondary craters are sim50shallower than primaries (Pike 1980) However this is forsecondary craters that are close to their parent crater and areclustered so that they often share rims with adjoiningsecondaries Secondary craters become better developed withincreasing distance from their parent crater and isolatedsecondaries far from the parent crater are not significantlyaffected by debris surges as is the case with clusteredsecondaries (Morrison and Oberbeck 1978) Our study areasare relatively far from large secondary-producing impactsWe attempted to avoid areas with obvious secondary craters

using methods described by Neukum et al (1975) and thecriteria of Oberbeck and Morrison (1973) (herringbonepattern elongated shape and clustering) To investigate whateffects any isolated secondaries remaining in our data setmight have we carried out a cursory examination of thedepths of fresh secondary craters of a range of diameters inthe image LO3-165-M (outside of our crater count study area)(Fig 7) Because the incidence angle of this image is 79deg theshadow of any crater with a depth to diameter ratio of 02 willfall halfway across the crater floor Comparing the shadowsize to crater size of 50 secondary craters we find that 90 ofthe secondary craters have a depth to diameter ratio of ge02

Fig 6 Cumulative histograms of craters found in our three study areas The ldquocountrdquo population is the craters counted on the surface theproduction population was calculated from the best-fit of craters above the equilibrium diameter and equilibrium population is assumed tohave a minus2 log-log slope a) The 89deg incidence angle study area with an equilibrium diameter of sim260 m b) The 79deg incidence angle study areawith an equilibrium diameter of sim190 m Also shown is crater count data from a high-resolution LO image of a portion of the same area Thebreak in slope is consistent with the medium-resolution data and shows the equilibrium population of craters c) The 71deg incidence angle studyarea with an equilibrium diameter of sim165 m Error bars are 1 σ as defined by Arvidson et al (1979)

702 B B Wilcox et al

Thus it does not appear that isolated secondaries that mightremain in our crater count data were initially significantlyshallower or that they would influence our estimates ofregolith depth

Regolith depth estimates were calculated by taking thenumber of craters lost mainly due to infilling of regolith ofeach diameter bin and converting that to the percent of thesurface that those craters would cover The regolith depth forthat portion of the surface was taken to be 14 of craterdiameter as explained above This method suggests that forour 89deg incidence angle study area the regolith in nearly theentire area is at least 8 m deep (ie the surface is nearlycovered with craters 53 m in diameter that have been filled inwith regolith) In 53 of the area the regolith is 11 m deep in26 of the area the regolith is 15 m deep in 10 of the areathe regolith is 22 m deep and in 1 of the study area theregolith is 31 m deep We also examined the sensitivity of thedepth estimate to changes in equilibrium diameter whetherdue to different lighting conditions as in our three study areasor because of actual differences in the crater populations For

a production population with a slope of minus34 we varied theequilibrium diameter (break point in slope) and calculated theresulting estimated regolith depths (Fig 8) As theequilibrium diameter increases the average regolith depthincreases and covers a broader range of depths

Areas of similar age as our study areas have beenpreviously estimated to have a regolith depth of 1ndash6 m(Oberbeck and Quaide 1968) The median depth (11 m)inferred here is greater than previous estimates and the depthvaries significantly (8ndash31 m) in the region Our estimate of adeeper regolith is likely due in part to the fact that we found ahigher equilibrium diameter than the current paradigm ofsim100 m or less for Eratosthenian mare (Wilhelms 1987)

Block Populations

While extremely high incidence angle photography atsufficient resolution is limited to a very few local sites highresolution images (05ndash20 mpixel) at incidence angles ofsim70deg exist for a much broader sampling of the lunar surface

Table 1 Comparison of production and count populations of crater data from Fig 5aDiameter bin (m)

Equilibrium coverage ()

Production coverage()

Regolith coverage ()

Maximum depth(m)

Average depth (m)

38 14 182 168 8 553 14 110 96 11 875 14 67 53 15 11

107 14 40 26 21 15151 14 24 10 30 22213 14 15 1 43 31

Fig 7 A portion of LO3-165-M The incidence angle of the image is 79deg and thus the shadows of craters with depth to diameter ratios of 02(Pike 1974) should fall halfway across the crater floor most fresh craters show this relationship Likely secondary craters are indicated witharrows The inset box encloses our 79deg incidence angle study area specifically chosen to be away from most of the obvious secondariesResolution is 66 mpixel

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

702 B B Wilcox et al

Thus it does not appear that isolated secondaries that mightremain in our crater count data were initially significantlyshallower or that they would influence our estimates ofregolith depth

Regolith depth estimates were calculated by taking thenumber of craters lost mainly due to infilling of regolith ofeach diameter bin and converting that to the percent of thesurface that those craters would cover The regolith depth forthat portion of the surface was taken to be 14 of craterdiameter as explained above This method suggests that forour 89deg incidence angle study area the regolith in nearly theentire area is at least 8 m deep (ie the surface is nearlycovered with craters 53 m in diameter that have been filled inwith regolith) In 53 of the area the regolith is 11 m deep in26 of the area the regolith is 15 m deep in 10 of the areathe regolith is 22 m deep and in 1 of the study area theregolith is 31 m deep We also examined the sensitivity of thedepth estimate to changes in equilibrium diameter whetherdue to different lighting conditions as in our three study areasor because of actual differences in the crater populations For

a production population with a slope of minus34 we varied theequilibrium diameter (break point in slope) and calculated theresulting estimated regolith depths (Fig 8) As theequilibrium diameter increases the average regolith depthincreases and covers a broader range of depths

Areas of similar age as our study areas have beenpreviously estimated to have a regolith depth of 1ndash6 m(Oberbeck and Quaide 1968) The median depth (11 m)inferred here is greater than previous estimates and the depthvaries significantly (8ndash31 m) in the region Our estimate of adeeper regolith is likely due in part to the fact that we found ahigher equilibrium diameter than the current paradigm ofsim100 m or less for Eratosthenian mare (Wilhelms 1987)

Block Populations

While extremely high incidence angle photography atsufficient resolution is limited to a very few local sites highresolution images (05ndash20 mpixel) at incidence angles ofsim70deg exist for a much broader sampling of the lunar surface

Table 1 Comparison of production and count populations of crater data from Fig 5aDiameter bin (m)

Equilibrium coverage ()

Production coverage()

Regolith coverage ()

Maximum depth(m)

Average depth (m)

38 14 182 168 8 553 14 110 96 11 875 14 67 53 15 11

107 14 40 26 21 15151 14 24 10 30 22213 14 15 1 43 31

Fig 7 A portion of LO3-165-M The incidence angle of the image is 79deg and thus the shadows of craters with depth to diameter ratios of 02(Pike 1974) should fall halfway across the crater floor most fresh craters show this relationship Likely secondary craters are indicated witharrows The inset box encloses our 79deg incidence angle study area specifically chosen to be away from most of the obvious secondariesResolution is 66 mpixel

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

Constraints on the depth and variability of the lunar regolith 703

These are the Lunar Orbiter (LO) high-resolution images andat meter resolution they are well-suited for studying the blockpopulations of craters (Hansen 1970 Anderson and Miller1971) We investigated craters and their block populations in23 images (Table 2) Eight of our images are located inwestern Oceanus Procellarum two in eastern OceanusProcellarum two in Sinus Medii eight in MareTranquillitatis and three in Mare Fecunditatis The angularresolution of these images ranges from 65 cmpixel to 94 cmpixel with an average angular resolution of 78 cmpixel

A caution for the LO data is that these are digital scans ofsecond or third generation photographic prints so theeffective resolution is estimated to be around a factor of twoless than the angular resolution (sim2 mp) This is important forthe study of block populations the identification of which isdependent on the effective resolution For example manyblocks and crater morphologies that are clearly visible in theLO high resolution set are not detectable or are barelydetectable in the LO medium resolution set at 8 times lowerresolution (Fig 9) To avoid this kind of resolution effect wehave only included craters larger than 50 m in our dataset Thelargest blocks associated with craters 50 m in diameter thathave not undergone significant degradation typically range insize from 29 to 44 m (Moore 1971) and are thus largeenough to be detected in the LO high resolution images

We classified all craters (over 800 total) in our images bythe density of their block populations (A B or C) Craters ofclass A were distinctly blocky craters of class B had one to afew blocks and craters of class C had no blocks While wemade a distinction between craters with abundant blocks andthose with just a few blocks it is not clear that this separationis necessarily significant A few blocks in a crater couldsimply represent random ldquoerraticsrdquo from nearby crater(s) orcould have been buried in the regolith and simply re-excavated by the impact event However if even one or twoblocks were excavated from the coherent substrate by thatcratering event these blocks are potentially an indicator ofregolith depth In addition especially for the smaller craters acrater might have abundant blocks but only the largest few(gt2 m) would be detectable at this resolution We also notedcrater morphology and excluded from our dataset those thatwere heavily degraded In these craters any primary blockswould have a significant chance of being obliterated or buriedby the regolith filling the crater

The craters show a trend of increasing blockiness withincreasing diameter (Fig 10a) If the regolith were of uniformdepth one would expect a single diameter and thus a singledepth of excavation greater than which all craters in a givenarea would be blocky The regolith depth in this case would bethe depth of excavation of this cutoff diameter wheremaximum depth of excavation is roughly 10 of the craterdiameter (Pike 1974) All craters smaller than this thresholddiameter would be excavating only regolith and all craterslarger than the threshold would excavate the coherent

substrate to some extent This simple model is not the caseInstead the data show a more gradual trend where onlysim10 of craters in the 75 m bin are excavating blocks withthis number increasing with diameter until all craters gt525 mare excavating blocks As discussed below this observation isconsistent with a regolith that is not all one depth but hasconsiderable lateral variability and does not have a strictboundary between coherent and incoherent material

Maria of different ages show distinct block populationtrends (Figs 10b and 10c) The portion of our study arealocated in Oceanus Procellarum near the Surveyor I landingsite is the youngest with an estimated age of sim25 billionyears (Boyce 1976 Whitford-Stark and Head 1980 Hiesingeret al 2003) The oldest portion of our study area issim36 billion years in Mare Tranquillitatis (Boyce 1976Hiesinger et al 2000) For the oldest surface 10 of thecraters 75 m in diameter are blocky and all craters gt475 m areblocky Thus in this older area 90 of the regolith is gt8 mdeep and all of the regolith is lt48 m deep This estimate isdeeper than previous estimates of 3ndash5 m for MareTranquillitatis at the Surveyor V site (Shoemaker and Morris1969) and a range of 1ndash10 m for three selected sites in MareTranquillitatis (Oberbeck and Quaide 1968) As expected theyounger surface (Oceanus Procellarum) has a distinctlyblockier surface At 75 m in diameter 10 of all craters areblocky Above 325 m all craters are blocky Thus 90 of theregolith is gt8 m deep and the regolith everywhere is lt33 mdeep in the younger area However these depths arenecessarily approximate because of possible origins for theblocks other than from coherent bedrock As noted above

Fig 8 Regolith depth versus equilibrium diameter curves representincreasing equilibrium diameter From left to right 100 m 150 m200 m 250 m and 300 m respectively The depths were calculatedby varying the equilibrium diameter assuming a production slope ofminus34 and an equilibrium slope of minus2 Average regolith depth and therange of depths increase with equilibrium diameter

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

704 B B Wilcox et al

Table 2 Lunar Orbiter images used in the study of block populations

ImageArea (km2) Latitude Longitude

Resolution(mp) Locationa

LO3-205-H2 1405 minus216 minus4479 09 PR-WLO 3-188-H2 1782 minus246 minus4425 08 PR-WLO 3-191-H3 999 minus262 minus4383 08 PR-WLO 3-181-H2 992 minus222 minus4350 08 PR-WLO 3-195-H2 1004 minus283 minus4326 08 PR-WLO 3-184-H2 2738 minus238 minus4307 08 PR-WLO 3-200-H2 1010 minus310 minus4256 08 PR-WLO 3-167-H2 1047 155 minus4183 08 PR-WLO 3-153-H2 823 minus297 minus2351 07 PR-ELO 3-148-H1 810 minus285 minus2274 07 PR-ELO 3-94-H1 677 092 minus163 07 SMLO 3-99-H2 654 069 minus103 07 SMLO 2-69-H3 680 270 2462 07 TRLO 2-83-H3 826 100 2466 07 TRLO 2-70-H1 680 267 2475 07 TRLO 2-73-H1 684 260 2511 07 TRLO 3-12-H1 1090 271 3225 08 TRLO 3-10-H1 1126 282 3495 08 TRLO 3-16-H2 1082 249 3582 08 TRLO 3-20-H1 1043 227 3639 08 TRLO 3-26-H1 1004 minus085 4212 08 MFLO 3-35-H3 1203 minus105 4281 09 MFLO 3-32-H1 1013 minus116 4293 08 MF

Total area Average resolution24371 08

aPR-W = Oceanus Procellarum West PR-E = Oceanus Procellarum East SM = Sinus Medii TR = Mare Tranquillitatis MF = Mare Fecunditatis

Fig 9 a) A medium-resolution LO image that shows the locations of the high-resolution LO images (bndashd) b) Blocky ejecta blanket only thelargest blocks are also detectable in (a) c) A crater with irregular morphology indicative of more coherent substrate d) A crater with normalbowl-shaped morphology Note that the different morphologies of (c) and (d) are indistinguishable in the LO medium-resolution image Thescale bar for (a) is 500 m the scale bar for bndashd is 50 m LO3-185-M (64 mpixel) LO3-205-H (09 mpixel)

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

Constraints on the depth and variability of the lunar regolith 705

some could have been buried blocks that were simply re-excavated from the regolith or blocks that were producedfrom induration of the regolith Both of these cases wouldlead to underestimation of the actual regolith depth

The young Procellarum surface (254 billion years) isestimated to be similar in age to our 89deg incidence angle studyarea (276 billion years) (Hiesinger et al 2003) and theresults for regolith depth using these two different methods(block population and equilibrium diameter) comparefavorably From both methods the regolith in each of theyounger areas is estimated to be sim8ndash32 m deep compared toprevious estimates of 1ndash3 m at the Surveyor I site (Shoemakerand Morris 1969) and a range of 1ndash6 m for this same site(Oberbeck and Quaide 1968) Oberbeck and Quaide (1968)also find a median thickness of 33 m for this site comparedto our median thickness of 11 m

In the younger Procellarum area (thinner regolith) thereare 50 small (50ndash250 m in diameter) craters per km2

(1098 km2 sample area) while in the older Tranquillitatisarea (thicker regolith) there are 22 small craters per km2

(721 km2 sample area) Thus in the younger mare there are23 times as many small craters per unit area than in the oldermare a seemingly counterintuitive result The difference inthe populations of craters in the diameter range of 50 to 250 mis most likely due to the more efficient degradation of smallcraters in areas of deeper regolith (older mare) Because theypenetrate only to a shallow depth small craters form mostly inloose regolith instead of coherent bedrock and thus are moreeasily degraded per unit of time in the older mare (Trask andRowan 1967 Lucchitta and Sanchez 1975 Robinson et al2002 Wilcox et al 2002) A similar phenomenon occurs inthe highlands where there are fewer small craters per unitarea than in the mare despite the older age of the highlandsThis difference is attributed to the thicker regolith in thehighlands and thus more efficient degradation of craters thatform mainly in regolith (Robinson et al 2002)

Small Crater Optical Maturity

Clementine multi-spectral images provide a furtherconstraint on regolith depth Optical maturity (OMAT)parameter images (Lucey et al 2000) show the relativematurity or ldquofreshnessrdquo of a material exposed on the lunarsurface OMAT values are based on the relative positions on aplot of the ratio of 950750 nm reflectances versus 750 nmreflectance The further the radial distance from ahypothetical fully mature end member the higher the OMATvalue and the higher degree of immaturity (Lucey et al 2000)Thoroughly gardened regolith that has been exposed for along period of time will have low OMAT values morerecently exposed regolith or rock will have higher OMATvalues (Lucey et al 2000) The utility of OMAT in terms ofestimating regolith depth lies in the fact that the amount offresh material excavated by a crater will depend on the ratio of

the craterrsquos depth to the depth of the regolith In a thickregolith a large portion of the material excavated by smallcraters will be material that has reached varying degrees ofoptical maturity In areas of thinner regolith small craters willpenetrate through the mature regolith and excavate a larger

Fig 10 a) The distribution of blocky craters classes AndashC by diameterin our study areas b) The percent of blocky craters versus diameter inwestern Procellarum the youngest portion of our study area c) Thepercent of blocky craters versus diameter in Tranquillitatis the oldestportion of our study area Craters with the most degradedmorphology have been excluded Numbers overlying graph are thenumber of craters in each bin

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

706 B B Wilcox et al

portion of fresh material that will be detectable in the OMATimage This method is similar in principle to the blocky cratermethod with fresh material analogous to blocks as indicatorsof penetration through the regolith

For determination of absolute regolith depths in an areathe resolution of Clementine images is prohibitively low(100 mpixel) To determine absolute depths it would benecessary to be able to measure craters as small as 10 m thatexcavate to a depth of as little as 1 m However a comparisonof the relative number of small optically immature cratersbetween different mare and highland units could potentiallyindicate relative regolith depths Areas of shallow regolithwould have the most small immature craters areas of deepregolith would have the fewest small immature craters assmall craters would be less likely to excavate opticallyimmature material (Fig 11) To test this hypothesis weselected all of the fresh craters smaller than 500 m in eightmare and highlands regions (Table 3) A cutoff value of

OMAT gt03 was chosen because this represents the leastmature material 23 of the lunar surface (Lucey 2004) Anabsolute determination of crater diameter is hindered by thefact that the craters of interest are near the resolution limit ofthe images and because their bright ejecta blankets mask theboundary of the crater rim Thus we can only bracket theirdiameters as between 100ndash500 m

The abundance of the small immature craters per unitarea would suggest the increasing order of regolith depths aslisted in Table 3 This order is consistent with the order ofages of the regions with the exception of Mare Tranquillitatis(Wilhelms 1987) The high opaque mineral content of MareTranquillitatis could be affecting the OMAT parameter in thisregion as noted by Lucey et al (2000) thus affecting thenumber of craters that are identified as immature The OMATmethod is promising and could become a powerful regolithdepth indicator with the eventual acquisition of high-resolution (10 mpixel or better) multispectral data

Fig 11 OMAT images (brighter or higher values indicate immature material while darker or lower values indicate mature material) of MareHumorum on the left (centered at minus2339 minus3718) and a highlands area on the right (centered at minus952 534) In the image on the left thegreater number of small immature craters in Mare Humorum can be seen (047 of image has OMAT gt 03) and the marehighlands borderis visible as a sharp drop-off in the number of small immature craters In the image on the right the highlands show relatively few smallimmature craters (004 of image has OMAT gt 03) Scale bar applies to both images

Table 3 Abundance of small (lt500 m) immature craters in selected mare and highlands sites

Region Number of small immature cratersStudy area(km2) Small immature craterskm2

Oceanus Procellarum 1229 142100 86 times 10minus3

Mare Serenitatis 764 101300 75 times 10minus3

Mare Frigoris 156 35500 44 times 10minus3

Lacus Somniorum 53 33100 16 times 10minus3

Mare Nectaris 44 73300 60 times 10minus4

Apollo 16 highlands 22 38273 57 times 10minus4

Apollo 14 highlands 6 23726 25 times 10minus4

Mare Tranquillitatis 28 299000 94 times 10minus5

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

Constraints on the depth and variability of the lunar regolith 707

DISCUSSION

A key finding of this work is that the equilibriumdiameter predicted from crater counts is sensitive to the solarincidence angle of the image(s) used for crater counting asfirst proposed by Young (1975) In our three study areas wefound that as incidence angle increases from 71deg to 79deg to 89degthe estimate of equilibrium diameter grows from 165 m to190 m to 260 m due to an increase in the number of cratersthat are visible The equilibrium diameter in turn hassignificant implications for inferred regolith depth (Fig 8)For example a change from an equilibrium diameter of 100 mto 150 m translates to a 25 increase in the median regolithdepth the difference between a 100 m and 250 m equilibriumdiameter results in a 50 increase in the median depthestimate The range of regolith depths also increases withequilibrium diameter the minimum depth estimate changeslittle while the maximum increases significantly At 100 mequilibrium diameter the estimated regolith depth rangesfrom sim7 to 15 m At 300 m equilibrium diameter the inferreddepth ranges from sim8 to 40 m Accurate determination of theequilibrium diameter is thus critical for determining regolithdepth

Usually it is difficult to determine unambiguously thediameter at which the transition to equilibrium crateringoccurs Instead of a sharp break in slope from minus34 to minus20 ona cumulative plot there is often more of a gradual rollingover Cumulative histogram slopes and breakpoints might beenhanced and the equilibrium diameter might become morereadily apparent if larger areas were included in the cratercounts In some cases this is not possible as in the 89degincidence angle image where there is only limited

photographic coverage Though near terminator imagesclearly allow the detection of more craters on the surface thando images at 70deg incidence they are still not ideal Theshadows of even small topographic features become sopronounced that they often hide any nearby smaller featuresThis effect results in the smaller craters often being hidden inthe shadows of larger ones and in cumulative histograms thisis seen as a flattening of the slope to nearly zero at smalldiameters (Soderblom 1972)

A further test of the effects of incidence angle withexisting data would be to compare the Apollo pan images attheir full resolution (sim2 mpixel at the center of the imagedegrading radially outward) to LO images (Masursky et al1978) The pan images exist at a wider variety of incidenceangles because they were taken in an equatorial orbit fromterminator to terminator and have overlapping coverage at adifferent incidence angle from the LO images which arenearly all sim70deg incidence because they were taken in polarorbit Laser altimetry or stereo image-based digital elevationmodels from future missions at 5 mpixel or better wouldallow unambiguous crater counts down a diameter of sim25 mthus allowing confident identification of slope breakpoints inthe crater size-frequency distributions and equilibrium sizesSuch data at 5 mpixel might be more accurate than imaging at1 mpixel because of the ability to produce shaded reliefimages at any desired incidence angle

Identifying the distribution of blocky craters over a largearea provides an independent test to the equilibrium diametermethod for determining regolith depth Previously thismethod was applied in the immediate vicinity of Surveyorlanders where only a limited number of craters of the desiredsize range were observable (Shoemaker and Morris 1969)

Fig 12 A model of the lunar regolith showing the uneven irregular and fractured bedrock surface that grades upward into less cohesivematerial Craters with blocks were formed during impact into bedrock craters without blocks formed only in regolith Concentric craters areshown both as the result of impact into a strength discontinuity such as an ejecta blanket and impact into bedrock Regolith depth can vary byapproximately a factor of five within a small area (hundreds of meters) In the highlands the substrate is most likely composed of hundredsof meters to kilometers of basin ejecta (megaregolith) while in the mare the substrate consists of layered basaltic material possibly withintercalated ejecta and regolith layers

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

708 B B Wilcox et al

Since the craters observed in the Surveyor images are onlyrepresentative of the depth at one small spot (tens of meters indiameter) they probably do not represent regolith depths overa broader area (ie the whole geologic unit sampled by aparticular Surveyor spacecraft) In our study we haveobserved a wide range of crater sizes over a much larger areaand find a range in regolith depth predicted by blockpopulations that is in agreement with the range obtained fromthe equilibrium diameter method

Studying the number of small optically immature cratershas the potential to give relative regolith depths (Table 3)though areas with high opaque content like MareTranquillitatis are an exception and a correction forcomposition would have to be developed This method hasthe potential to give absolute depths through the study of thesize-frequency distribution of small fresh craters but muchhigher resolution images (1ndash10 mpixel) would be required tomeasure and count craters as small as 10ndash50 m in diameter

A close examination of the various definitions of regolithhas been given in order to determine whether there aredifferences in regolith depth estimates simply because ofdifferences in the definition of regolith itself The differencebetween our regolith depth estimates and previous estimatesis not just a question of definition Quaide and Oberbeck(1968) using the most inclusive definition of regolith stillfind a shallower regolith depth (1ndash6 m) for Eratosthenianmare surfaces similar to those that we investigated Wesuggest the difference is due to the fact that their cratermorphology method is not necessarily always indicating theregolith-bedrock transition but perhaps a transition of grainsizes buried ejecta layers or any kind of strengthdiscontinuity A key question that remains is what percentageof the bench or concentric craters are actually due to theregolith-bedrock interface and what percent are due tofactors such as those listed above

Using two independent methods we estimate that theregolith depth in three Eratosthenian (20 to 25 billion years)mare areas ranges from approximately 8 to 32 m locally(median depth of 11 m) The significance of the variability ofthe regolith depth within a local area (same unit) is not alwaysappreciated and this is reflected in the flat simple regolithstructure paradigm that often prevails-a tabular layer of looseregolith atop a planar bedrock surface (see eg Fig 15 ofCooper et al 1974 Figs 1023 1112 and 1215 of Wilhelms1987 Fig 1019 of Heiken et al 1991) Such a model is notsupported by our data or previous work A morerepresentative model of the regolith has an unevenundulating and fractured bedrock surface that grades upwardinto less and less cohesive material (Fig 12)

Knowledge of regolith depths is important for theinterpretation of remote sensing data and the planning ofsample retrieval on the Moon and on other bodies Regolithexcavated from different depths transfers materials to thesurface from different portions of a layered target mixingspectral signatures for remote sensing and also determining

what is easily obtained for samples Interpretation of theresults from the upcoming Dawn mission to explore theasteroids Ceres and Vesta (Russell et al 2003) will depend onunderstanding the regolith where questions of exposure ofvaried differentiation products and surface modification willbe affected by the amount and distribution of regolithInterpretive problems from varied and gradational regolithproperties on asteroid Eros have been noted by variousauthors (Thomas et al 2001 Robinson et al 2002 Chapmanet al 2002)

Understanding the regolith will also be important in theupcoming MESSENGER mission which will map thesurface of Mercury in the UV-VIS-NIR to a scale of sim200 mpixel and locally return much higher resolution (10 mpixel)BW images One of the key science goals is unraveling theevolution of the mercurian crust through superposition andcolormineralogic interpretations (Solomon et al 2001)These interpretations may critically depend on an awarenessof mixing processes caused by regolith development in alayered target (ie volcanic flows) with thicknesses at thescale of significant regolith overturn Previous studies of thelunar regolith as well as the results presented here emphasizethe need for a thorough understanding of the depth of aregolith to maximize the science return from remote sensingas well as landed science and returned samples

Editorial HandlingmdashDr Beth Ellen Clark

AcknowledgmentsndashWe thank Paul Spudis and Mary AnnHager for providing ready access to the Lunar Orbiter imagesat the Lunar and Planetary Institute We also wish to thankJeff Taylor (University of Hawaii) for his helpful ideas andinput during the progress of this work and we are grateful forthe useful comments of Verne Oberbeck and Richard YoungMark Cintala (Johnson Space Center) and Ben Bussey (JohnsHopkins University) provided thorough reviews This workwas support by NASA PGG grants NAG5-12018 and NAG5-12632 and NAG5-13208 This is HIGP publication 1387and SOEST publication 6606

REFERENCES

Anderson A T and Miller E R 1971 Lunar Orbiter photographicsupporting data NASA National Space Science Data CenterPublication 71ndash13 511 p

Arvidson R E Boyce J Chapman C Cintala M Fulchignoni MMoore H Neukum G Schultz P Soderblom L Strom RWoronow A and Young R 1979 Standard techniques forpresentation and analysis of crater size-frequency data Icarus37467ndash474

Arvidson R E Drozd R J Hohoenberg C M Morgan C J andPoupeau G 1975 Horizontal transport of the regolithmodification of features and erosion rates on the lunar surfaceThe Moon 1367ndash79

Bevington P 1969 Data reduction and error analysis for the physicalsciences New York McGraw-Hill pp 237ndash239

Boyce J M 1976 Ages of flow units in the lunar nearside maria

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

Robinson M S Thomas P C Veverka J Murchie S L and WilcoxB B 2002 The geology of 433 Eros Meteoritics amp PlanetaryScience 371651ndash1684

Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

Constraints on the depth and variability of the lunar regolith 709

based on Lunar Orbiter IV photographs Proceedings 7th LunarScience Conference pp 2717ndash2728

Chapman C R Merline W J Thomas P C Joseph J Cheng A Fand Izenberg N 2002 Impact history of Eros Craters andboulders Icarus 155104ndash118

Cintala M J and McBride K M 1995 Block distribution on thelunar surface A comparison between measurements obtainedfrom surface and orbital photography NASA TechnicalMemorandum 104804 Houston NASA Johnson Space Center41 p

Cooper M R Kovach R L and Watkins J S 1974 Lunar near-surface structure Reviews of Geophysics and Space Physics 12291ndash308

Crozaz G Walker R and Woolum D 1971 Nuclear track studies ofdynamic surface processes on the Moon and the constancy ofsolar activity Proceedings 2nd Lunar Science Conference pp2543ndash2558

Gault D E 1970 Saturation and equilibrium conditions for impactcratering on the lunar surface Criteria and implications RadioScience 5273ndash291

Gault D E Hˆrz F and Hartung J B 1972 Effects ofmicrocratering on the lunar surface Proceedings 3rd LunarScience Conference pp 2713ndash2734

Hansen T P 1970 Guide to Lunar Orbiter photographs NASASpecial Paper 242 Washington DC US GovernmentPrinting Office 125 p

Heiken G H Vaniman D T and French B M 1991 Lunarsourcebook A userrsquos guide to the Moon Cambridge CambridgeUniversity Press 736 p

Hiesinger H Jaumann R Neukum G and Head J W III 2000Ages of mare basalts on the lunar nearside Journal ofGeophysical Research 10529239ndash29275

Hiesinger H Head J W III Wolf U Jaumann R and Neukum G2003 Ages and stratigraphy of mare basalts in OceanusProcellarum Mare Nubium Mare Cognitum and MareInsularum Journal of Geophysical Research 108 doi1010292002JE001985

Hˆrz F 1977 Impact cratering and regolith dynamics Physics andChemistry of the Earth 103ndash15

Hˆrz F Schneider E and Hill R 1974 Micrometeoroid abrasion oflunar rocks A Monte Carlo simulation Proceedings 5th LunarScience Conference Geochimica et Cosmochimica ActaSupplement 52397ndash2412

Latham G V Ewing M Press F Sutton G Dorman J NakamuraY Toksˆz N Wiggins R and Kovach R 1970 Passive seismicexperiment In Apollo 12 preliminary science report NASASpecial Paper 235 Washington DC US GovernmentPrinting Office pp 39ndash54

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Duennebier F and Lammlein D 1971Passive seismic experiment In Apollo 14 preliminary sciencereport NASA Special Paper 272 Washington DC USGovernment Printing Office pp 133ndash162

Latham G V Ewing M Press F Sutton G Dorman JNakamura Y Toksˆz N Lammlein D and Duennebier F 1972Passive seismic experiment In Apollo 15 preliminary sciencereport NASA Special Paper 289 Washington DC USGovernment Printing Office pp 8-1ndash8-25

Lucchitta B K and Sanchez A G 1975 Crater studies in the Apollo17 region Proceedings 6th Lunar and Planetary ScienceConference pp 2427ndash2441

Lucey P G 2004 Mineral maps of the Moon Geophysical ResearchLetters 31 doi1010292003GL019406

Lucey P G Blewett D T Taylor G J and Hawke B R 2000Imaging of lunar surface maturity Journal of GeophysicalResearch 10520377ndash20386

Masursky H Colton G W and El-Baz F 1978 Apollo over theMoon NASA Special Paper 362 Washington DC USGovernment Printing Office 255 p

Melosh H J 1989 Impact cratering A geologic process New YorkOxford University Press 245 p

Merrill G P 1897 Rocks rock-weathering and soils New YorkMacMillan Company 411 p

Moore H J 1971 Large blocks around lunar craters In Analysis ofApollo 10 photography and visual observations NASA SpecialPaper 232 Washington DC US Government PrintingOffice pp 26ndash27

Morrison R H and Oberbeck V R 1978 A comparison andthickness model for lunar impact crater and basin depositsProceedings 9th Lunar and Planetary Science Conference pp3763ndash3785

Muehlberger W R Batson R M Boudette E L Duke C MEggleton R E Elston D P England A W Freeman V LHait M H Hall T A Head J W Hodges C A Holt H EJackson E D Jordan J A Larson K B Milton D J Reed VS Rennilson J J Schaber G G Schafer J P Silver L TStuart-Alexander D Sutton R L Swann G A Tyner R LUlrich G E Wilshire H G Wolfe E W and Young J W 1972Preliminary investigation of the Apollo 16 landing site In Apollo16 Preliminary science report NASA Special Paper 315Washington DC US Government Printing Office pp 6-1ndash6-81

Muehlberger W R Batson R M Cernan E A Freeman V LHait M H Holt H E Howard K A Jackson E D Larson KB Reed V S Rennilson J J Schmitt H H Scott D H SuttonR L Stuart-Alexander D Swann G A Trask N J UlrichG E Wilshire H G and Wolfe E W 1973 Preliminarygeologic investigation of the Apollo 17 landing site In Apollo 17preliminary science report NASA Special Paper 330Washington DC US Government Printing Office pp 6-1ndash6-71

Neukum G Koenig B and Arkani-Hamed J 1975 A study of lunarimpact crater-size distributions The Moon 12201ndash229

Oberbeck V R and Morrison R H 1973 On the formation of thelunar herringbone pattern Proceedings 4th Lunar ScienceConference Geochimica et Cosmochimica Acta Supplement 4107ndash123

Oberbeck V R and Quaide W L 1968 Genetic implications of lunarregolith thickness variations Icarus 9446ndash465

Oberbeck V R Quaide W L Mahan M and Paulson J 1973Monte Carlo calculations of lunar regolith thicknessdistributions Icarus 1987ndash107

Pike R J 1974 Depthdiameter relations of fresh lunar cratersRevision from spacecraft data Geophysical Research Letters 1291ndash294

Pike R J 1980 Geometric interpretation of lunar craters Apollo 15ndash17 orbital investigations US Geological Survey ProfessionalPaper 1046-C Washington DC US Government PrintingOffice

Quaide W L and Oberbeck V R 1968 Thickness determinations ofthe lunar surface layer from lunar impact craters Journal ofGeophysical Research 735247ndash5270

Rennilson J J Dragg J L Morris E C Shoemaker E M andTurkevich A 1966 Lunar surface topography In Surveyor Imission report part II Scientific data and results NASA JPLTechnical Report 32-1023 pp 7ndash44

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Russell C T Coradini A De Sanctis M C Feldman W CJaumann R Konopliv A S McCord T B McFadden L AMcSween H Y Mottola S Neukum G Pieters C M

710 B B Wilcox et al

Prettyman T H Raymond C A Smith D E Sykes M VWilliams B G Wise J and Zuber M T 2003 Dawn mission Ajourney in space and time (abstract 1473) 34th Lunar andPlanetary Science Conference CD-ROM

Schultz P H Greeley R and Gault D 1977 Interpreting statisticsof small lunar craters Proceedings 8th Lunar and PlanetaryScience Conference pp 3539ndash3564

Schmitt H H 1973 Apollo 17 report on the Valley of Taurus-LittrowScience 182681ndash690

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