Tectonics, Fracturing of Rock, And Erosion

8/6/2019 Tectonics, Fracturing of Rock, And Erosion

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Tectonics, fracturing of rock, and erosion

Peter Molnar,1,2 Robert S. Anderson,1,3 and Suzanne Prestrud Anderson3,4

Received 2 November 2005; revised 23 March 2007; accepted 30 April 2007; published 9 August 2007.

[1] We argue that by fracturing rock, not by raising it relative to base level, tectonics playsits most important role in causing rapid incision of valleys and rapid erosion of hillslopes.Tectonic deformation riddles the upper crust with fractures, which not only provideavenues for water flow and thus promote weathering and further disintegration of rock butalso fragment bedrock into debris that is readily extracted and transported by surfaceprocesses. Bends in active faults require straining of adjacent rock masses. Aftershocksthat occur subsequent to slip on primary faults reflect penetrative brittle deformation of theupper crust. At least some aftershocks must nucleate or lengthen cracks, whichcontribute to the comminution of these rock masses. Scaling rules suggest that dimensionsof ruptures for very small (M < 2) earthquakes can be meters or less. TheGutenberg-Richter recurrence relationship implies that such earthquakes are common, ashigh-magnification seismographs in low-noise environments confirm. Moreover, large

differences among fault plane solutions for aftershocks show that the small faults on whichthey occur are not parallel to one another; some faults must intersect. Thus the uppercrust in tectonically active regions should be fragmented into blocks down to the scale ofboulders or smaller. Dismembered rock arrives at the Earths surface already prepared tobe transported away. As a corollary, both deeply exhumed lower crust and posttectonicigneous rock, never deformed under brittle conditions and not deformed recently,should be less susceptible to detachment and subsequent transport than fractured rock.

Citation: Molnar, P., R. S. Anderson, and S. P. Anderson (2007), Tectonics, fracturing of rock, and erosion, J. Geophys. Res., 112,

F03014, doi:10.1029/2005JF000433.

All indurated rocks and most earths are bound together by a

force of cohesion which must be overcome before they can be

divided and removed. The natural processes by which the

division and removal are accomplished make up erosion. They

are called disintegration and transportation.

[Gilbert, 1877, pp. 9394]

Erosion is the result of two complex process. The first group

comprises those which accomplish the disintegration of the

rocks, reducing them to fragments, pebbles, sand, and clay. The

second comprises those process which remove the debris and

carry it away to another part of the world.[Dutton, 1882, p. 64]

1. Introduction

[2] In the past 15 years, following the synthesis byDahlen and Suppe [1988] and then accelerating with work

of Koons [1989, 1990], Beaumont et al. [1992], and others,geomorphologists and structural geologists have focused

attention on the interaction between tectonics and geomorphology, instead of treating each in isolation of the other.

Removal of material from the Earths surface by erosionshould reduce magnitudes of vertical compressive stress,and as a result horizontal deviatoric stresses should increasein regions undergoing horizontal shortening, even with nochange in magnitudes of horizontal compressive stressesacross the belts. (To remind readers, deviatoric stress, tij, isstress, sij, minus pressure, p, if we treat compressive stressas positive: tij = sij pdii. Stress does physical work;deviatoric stress causes deformation.) Thus erosion facili-tates further crustal shortening [e.g., Dahlen and Suppe,1988]. Moreover, because of isostasy, as erosion removesrock from the surface, exhumed rock rises to a meanelevation nearly the same as that of the rock eroded, a factrecognized by Wager [1937] and probably others, and

included in elementary textbooks [e.g., Holmes, 1944, pp.189190, 1965, pp. 575576]. Thus a belt of high terrain, amountain belt, can be sustained simply by erosion andisostasy for a much longer period than the division of

present-day elevations by current erosion rates might sug-gest [e.g., Sleep, 1971].

[3] Many studies of the interaction between geomorphol-ogy and tectonics continue to assign tectonics a causal role,with tectonics seen solely as the source of relief, and erosionits consequence. Our purpose here is to argue that tectonicsmay play a more important role in accelerating erosion rates

by fracturing rock than by creating large-scale relief. Frac-

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1Department of Geological Sciences, University of Colorado, Boulder,Colorado, USA.

2Cooperative Institute for Research in Environmental Science,University of Colorado, Boulder, Colorado, USA.

3Institute of Arctic and Alpine Research, University of Colorado,Boulder, Colorado, USA.

4Department of Geography, University of Colorado, Boulder, Colorado,USA.

Copyright 2007 by the American Geophysical Union.0148-0227/07/2005JF000433$09.00

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turing can both reduce rock strength, which will lead togreater erosion rates (all else equal), and broaden the rangeof geomorphic processes that can operate (e.g., mass lossthrough pervasive weathering of fractured rock, glacial orfluvial quarrying, or deep-seated landslides along fracture

planes). Perhaps more important than reducing the strengthof the rock, however, may be the disaggregation of bedrockinto blocks that are easily extracted and transported bygeomorphic processes. Although we claim nothing originalin suggesting either that tectonics fractures rock or thatfracturing of rock facilitates its removal, these concepts doseem poorly appreciated.

[4] The fracturing of rock can affect geomorphic processesin two obvious ways, but most discussions seem to focus ononly one. First, because jointed rock with cracks penetratingthrough it is weaker than intact rock [e.g., Pettifer and

Fookes, 1994; Segall, 1984; Selby, 1980], rivers, debrisflows, glaciers, or simply gravity acting directly on hill-slopes should be able to dislodge fragments of it more easilythan when these erosive agents are confronted with intact

bedrock. The preponderance of slopes near the angle ofrepose suggests that only in special circumstances is rockexposed at the Earths surface strong enough to produce tall,near vertical walls of rock like those of El Capitan inYosemite Valley, the North Face of the Eiger in the SwissAlps, or the south face Dhaulagiri in Nepal [e.g., Burbank etal., 1996; Schmidt and Montgomery, 1995; Selby, 1980].

[5] The vast majority of sediment carried by rivers, and asubstantial part of that carried by glaciers, is derived fromadjacent hillslopes. Yet, if rivers and glaciers are to incisevalleys, they must remove bedrock, and the degree to whichthe bedrock has been fragmented into transportable debris(sediment) before rushing water or sliding ice come incontact with it, the more rapidly will rivers and glaciersincise their valley floors. Accordingly, the second role of

rock fracture is to provide debris that can be plucked orquarried by rivers and glaciers from valley floors withoutrequiring that rivers, debris flows, or glaciers perform thework of fracturing the rock.

[6] Weak rock will certainly erode more quickly thanstrong rock, as shown qualitatively by river profiles [e.g.,

Hack, 1957, 1973] and quantitatively by laboratory experi-ments of abrasion using pebbles and cobbles in rapidly

flowing water [e.g., Attal and Lave, 2006; Sklar andDietrich, 2001, 2004], by applications of these experimentsto field settings [Stock et al., 2005], and by field experi-ments in which samples are glued to bedrock beneathglaciers [ Boulton and Vivian, 1973]. In addition, mostwould assume that fractured rock is more easily erodedthan intact rock and that fracture density plays a role insetting erodibility. In his strength classification, Selby[1980] found fracture spacing to be the feature mostimportant in limiting hillslopes, more important than intrin-sic strength of intact rock. Yet, insofar as tests made withdrilling [e.g., Thuro, 1997] or with dredging of rock fromthe seafloor [e.g., Vervoort and De Wit, 1997] are represen-tative, where the spacing of fractures exceeds the dimen-

sions of tools attacking the rock, the existence of fracturesappears to play no more than a minor role in weakening therock. For instance, Thuro [1997, p. 433] showed that wherethe spacing of joints or fractures is large compared with thedimensions of a drill bit, these discontinuities do not affectthe drilling rate (Figure 1). Similarly, the excavation of rockwith large fracture spacing remains difficult, either untilfracture spacing is small enough or where the intrinsicstrength of the material, measured by the point load index,is low [ Pettifer and Fookes, 1994]. Because plucking orquarrying of blocks from valley floors, by both rivers [e.g.,

Hancock et al., 1998] and glaciers [e.g.,Briner and Swanson,1998], is thought to be more effective than abrasion, thissecond role of fracturing as a geomorphic agent, by trans-forming intact bedrock into separate fragments of debris thatcan be efficiently transported by rivers, debris flows, orglaciers, deserves more attention than it has received.

[7] It seems to us that these two effects of fracturing areoften conflated. Some modern treatments of fluvial erosion[e.g., Sklar and Dietrich, 2004], erosion by debris flows[e.g., Stock and Dietrich, 2006; Stock et al., 2005], andglacial erosion [e.g., Lliboutry, 1994] treat the disintegrationand initial transportation as occurring simultaneously, as ofcourse they often, but not always, do. Others seem to treatfractures as unchanging and uniform conditions, tied eitherto the rocks or to the surface, and whose formation remainsunaddressed. We see tectonics as playing a key role incontrolling the condition of the rock upon arrival at thesurface by dictating the strain history to which a parcel ofrock has been subjected in the brittle zone. Here, we followthe view expressed by Dutton [1882] and Gilbert [1877],and quoted above: that the two processes of disintegrationand transportation can occur separately.

2. Tectonics, Mountain Building, and Fracturingof Rock

[8] Tectonically active belts like the Himalaya, Taiwan,or the Southern Alps of New Zealand and some recentlyactive belts like the Western Alps of Europe seem to be

Figure 1. Drilling rates as a function of the spacing offractures in limestone (Muschelkalk), modified from Figure17 of Thuro [1997]. The % scale on the right shows theenhancement in drilling rate with decreased spacing offractures. Thuro did not report the dimensions of the drill bitused to carry out the tests, but we suppose it to be a fewcentimeters in diameter. The light blue boxes presumablyshow the scatter in data, the horizontal black lines the mean

values, and dashed red line an empirical fit. Where thespacing of the fractures is large compared to the dimensionsof the drill bit, the presence of fractures does not weaken therock attacked by the drill bit.

F03014 MOLNAR ET AL.: TECTONICS, FRACTURING, AND EROSION

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eroding more quickly than tectonically quiescent regions. Atthe same time, some elevated regions with steep slopes anddeep canyons, like the Guyana Shield [Brown et al., 1992;Stallard, 1988], the Western Ghats along the west coast ofIndia [Gunnell et al., 2003], or Sri Lanka [Vanacker et al.,2007; von Blanckenburg et al., 2004], do not erode rapidly,despite high rainfall and high relief in these regions. Few

would doubt that tectonic deformation generates rock frac-tures, and some have explicitly noted that this processshould affect erosion rates [e.g., Koons and Craw, 2002].For instance, in contrasting rapid erosion of the Andes andslow erosion of comparably high terrain of the GuyanaShield, Stallard [1988, p. 225] wrote: In tectonically activeenvironments, most of the material exposed to weatheringhas undergone rapid tectonic uplift involving brittle defor-mation, where surely brittle deformation means fractur-ing of rock (and we ignore his comparable emphasis onrapid tectonic uplift). Weissel and Seidl [1997] showedhow not only the presence of joints, but also their orienta-tions affected river incision and hillslope evolution inescarpment retreat. Kellogg [2001] mapped both fresh and

early Cenozoic fractures in the Front Range of Colorado andrecognized that these fractures have facilitated the current,relatively rapid erosion. Finally, Loveless et al. [2005]demonstrated pervasive tectonic cracking at the surface innorthern Chile, where erosion rates are so low and soil isvirtually absent that the cracks can be seen on the surface.

Nevertheless, despite several studies that specifically men-tion tectonics and fracturing, we suspect that many do notappreciate the degree to which such fracturing must occur,or the variety of arguments that show it to be noteworthy.Although most readers recognize that the exposed Earthssurface in many regions is fractured, in many regions, such

as in the Sierra Nevada, Wind River Range, Wyoming, andWestern Ghats of India, fractures are sparse, tens of metersapart. Accordingly, we develop the argument that tectonicdeformation, commonly associated with slip on one or just afew major faults, facilitates erosion by fracturing rockadjacent to major faults.

[9] Below we argue first that the shapes of major faults,which are rarely planar, require additional deformation of

the adjacent rock masses for slip to occur on them. Second,seismicity, at least within continental regions, also suggeststhat tectonic movements require the fracturing of rock, not

just the transport of large blocks with respect to one another.(We do not argue that each earthquake reflects the creationor extension of a new fault; few earthquakes do this.)Finally, treatments not only of earthquakes, but also offaulting in general, suggest scale invariance, and hence

justify extrapolations to small dimensions of faulting andof the blocks that result from such faulting.

2.1. Strain Within Deforming Belts Caused by Slipon Nonplanar Faults

[10] Deformation in all major thrust belts should include

large strain, simply because dip-slip faults that approach thesurface cannot be planar [e.g., Suppe, 1983, 1985]. At leastone of the hanging wall and footwall must deform adjacentto faults that are not planar, and where such strain occurs inthe upper crust, brittle deformation should prevail.

[11] The straining of blocks of crust that slide past oneanother on faults that are not planar has been widely notedand studied in hanging walls of thrust faults. Suppes [1983,1985] method for balancing cross sections, for instance,approximates fault surfaces as connected planar segments.This approach predicts that strain will be localized nearregions where two planar segments intersect (Figure 2) andcan be manifest as minor faults that rupture the surface [e.g.,

Ishiyama et al., 2004]. In a similar situation but above a

concave upward major fault zone, pervasive reverse faultingcan slice rock, as for example in Ventura Basin [Shaw andSuppe, 1994] and on the eastern flank of the Southern Alpsin New Zealand [e.g., Little et al., 2002]. Moreover, detailedmapping in the Southern Alps reveals highly fractured rock[Cox et al., 1997], as required by the subsurface faulting onsegments that are not parallel to one another, proposed by

Little et al. [2002].[12] As a specific example, consider the Himalaya, where

a major thrust fault dips gently beneath the Lesser Himalaya(with dips of 3 6) and more steeply beneath at least partof the Greater Himalaya. Using receiver functions deter-mined with an array of broadband seismographs in theHimalaya and southern Tibet, Schulte-Pelkum et al.

[2005] reported a dip of 1215 beneath the GreaterHimalaya. The large flexural rigidity of the Indian plateimplies that it cannot be bent sharply and that it slides

beneath the Himalaya as a nearly rigid block. Thus the$6 9 difference in the dips of the segments of the thrustfault that underlie the Lesser and Greater Himalaya suggeststhat the hanging wall must deform (Figure 3), and as Indiaconverges with the Himalaya, the vertical components ofvelocity above these segments of fault must also differ. Therock in the Greater Himalaya must rise more rapidly thanrock in the Lesser Himalaya by an amount approximatelyequal to the rate of underthrusting (v) times the sine of the

Figure 2. Cartoon illustrating strain within a layer of crustthat bends where a fault is not planar. One of the roles oftectonics is the generation of faults (cracks) within rock thatis ultimately delivered to the surface of the Earth. In theexample shown here, rock in the hanging wall moveslaterally to the left, then through a region where the layer is

bent, and finally upward on the dipping segment of thefault. Cracks, shown as red lines, form to accommodatestrain associated with bending where the fault is curved; this

bending serves as a tectonic, crustal-scale rock crusher.Crack lengths and densities increase with time spent in the

bend. The resulting fracture field, with inactive cracksshown in blue, is then translated to the surface, where thefractures influence surface processes.


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difference in dips: v sin 6 = 0.1 v. For underthrusting at$20 mm/yr, this implies a difference in vertical displace-ment rate of 2 mm/yr. Judging by the width of the zonewhere earthquakes occur [e.g., Pandey et al., 1995], whichis comparable with the width of the transition from lowelevations of the Lesser Himalaya and high elevations of theGreater Himalaya, this difference in vertical movementoccurs over a zone no more than a few tens of kilometerswide, say 20 km. For underthrusting at 20 mm/yr, shearing

of the hanging wall on vertical planes would be accom-plished in 1 Myr, and the total accumulated strain would be0.1(=2 km/20 km). As most rock cannot sustain strains of0.001 without breaking, strains of 0.1 require that thehanging wall be fractured. Moreover, if this shear occurson planes that dip not vertically but less steeply, shear onthose planes must be more rapid [e.g., Molnar, 1987].

[13] Wobus et al. [2005] showed that in this part of theHimalaya in Nepal, faulting occurs with a vertical compo-nent of slip rate of 0.6 0.2 mm/yr, less than half and

perhaps only 20% of the total rate of $ 2 mm/yr suggestedabove. Thus slip on the fault recognized by Wobus et al.[2005] accounts for only part of the strain that mustaccumulate in this region. Moreover, Burbank[2005] point-

ed out that the fault discovered by Wobus et al. [2005] doesnot manifest itself clearly in the relief in the Annapurnaregion a few tens of kilometers to the west. Apparentlydeformation, which must accommodate $2 mm/yr of rela-tive movement, is yet more diffuse in the region to the west.The occurrence of brittle strain of$0.1 does not require thatfractures be closely spaced, and hence does not guaranteethat fractures will slice and dice the rock into fragmentseasily transported by rivers. The diffuse zone of accuratelylocated microearthquakes, however, does imply pervasivestraining of the hanging wall near the ramp [Pandey et al.,1995].

2.2. Seismicity and Fracturing

[14] Two aspects of seismicity are relevant to our argu-ment. First, many of the earthquakes that occur in theimmediate aftermath of major earthquakes (aftershocks)occur off the main fault or faults that rupture in the mainshock [e.g., King et al., 1985; Yielding et al., 1981]. Second,the size distribution of small earthquakes suggests a distri-

bution of dimensions of faults in the affected rock.

[15] 1. Locations of aftershocks indicate diffuse brittledeformation in areas adjacent to major faults. Althoughaftershocks of great earthquakes commonly are used todefine the rupture areas of such earthquakes [e.g., Dasand Henry, 2003; Fedotov, 1965; Kelleher et al., 1973;Sykes, 1971], many, and in some cases most, aftershocks ofintracontinental earthquakes do not occur on the fault thatruptured during the main shock. Accordingly, these after-shocks do not register continued slip on major faults.Instead they reflect deformation within the blocks of crustthat moved past one another during the main shocks. This isthe norm for earthquakes in Greece, where aftershockscommonly occur in both the hanging and footwalls of thecausative normal faults [e.g., Hatzfeld et al., 1986, 1997,2000; King et al., 1985; Soufleris et al., 1982]. For instance,aftershocks of the Kozani-Grevena earthquake in northernGreece on 13 May 1995 (Figure 4) require slip on conjugatefaults, as well as activity not on these faults [Hatzfeld et al.,1997]. Recent relocations, with reported uncertainties ofonly 150 m in all three coordinates and coupled with surfacedeformation based on radar interferometry, demonstrate thatslip occurred on at least three intersecting faults [Resor etal., 2005]. Moreover, the scatter in these locations requiresinternal deformation of both the footwall and hanging wall(Figure 4).

[16] Similarly for thrust regimes, like the 1981 El-Asnamearthquake in Algeria [e.g., Ouyed et al., 1983; Yielding etal., 1981] (Figure 5), the 1994 Northridge earthquake insouthern California [Shearer et al., 2003], the 2000 Bhujearthquake, Gujarat, India [ Bodin and Horton, 2004;

Negishi et al., 2002], or the 2003 San Simeon earthquakein central California [ Hardebeck et al., 2004], aftershocksoccurred throughout the hanging walls and in parts of thefootwalls of the thrust faults. By correlating waveforms,

Figure 3. (bottom) Idealized cross section across theHimalaya showing a sharply curved thrust fault and (top)sketch of the expected vertical component of movement ofthe rock above it. The Indian lithosphere flexes down

beneath the Ganga Basin, where sediment accumulates, andunderthrusts the Lesser Himalaya. Beneath the GreaterHimalaya, the fault dips more steeply than beneath thelesser Himalaya. Thus rock in the hanging wall over the

steeper segment is ramped upward more rapidly than abovethe gently dipping segment.

Figure 4. Northwest-southeast cross section of after-shocks of the Kozani-Grevena (Greece) earthquake of 13May 1995, whose locations were determined by Hatzfeld etal. [1997]. Note that the distribution of earthquakes does not

permit them to lie on a single listric, let alone planar, fault.


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Shearer et al. [2003] showed not only that numerous shortfaults with different orientations ruptured following the

Northridge earthquake, but also that the styles of faultingin the hanging wall and footwall differ.

[17] Most aftershocks of major earthquakes on majorstrike-slip faults like the San Andreas fault [e.g., Eaton et

al., 1970] occur on the fault segments that ruptured in themain shocks, but those following moderate earthquakes,which rupture short faults slipping at low slip rates, com-monly do not occur on the faults that ruptured in the mainshocks. For instance, Stein and Lisowski [1983] showed thatfor the relatively small Homestead Valley earthquakes in1979, which ruptured a vertical strike-slip fault $46 kmlong that extended to a depth of 5 km in southern California,

aftershocks occurred many kilometers east and west of thenorth-south trending rupture, over an area 15 km 25 kmin dimensions and hence also east and west of the surface

Figure 5. (a) Map of aftershocks relocated by Ouyed et al.[1983] and (b) example of a cross section through theseismicity whose location, A-B, is shown by the red line inFigure 5a. In both plots, solid symbols denote earthquakeswith the most accurate locations: those for which root-mean-square residuals were less than 0.15 s, locations wereassigned horizontal and vertical uncertainties of less than2 km, and at least one station lay within an epicentraldistance less than twice the computed focal depth. Opensymbols denote less precisely located events. Symbol sizesscale with magnitudes. Again, note that the distribution ofearthquakes requires than many faults be active during theaftershock sequence.

Figure 6. Map of aftershocks of the 1979 Homestead

Valley earthquake in southern California, located by Steinand Lisowski [1983], and contours of Coulomb stresschange from King et al. [1994]. The plot is from King et al.[1994], who used the aftershock locations to show that theyoccurred largely in regions where failure was facilitated bythe change in Coulomb stress (the combination of increasedshear stress on planes oriented favorably and decreasednormal stress across such planes). Although the main shockruptured a plane trending nearly north-south, aftershocksoccurred throughout a large region far from the mainrupture and hence require deformation within a finitevolume, not just slip on a single plane.


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rupture (Figure 6). Similar phenomena occurred followingthe 1992 Joshua Tree earthquake (M= 6.1) [Hauksson et al.,1993; King et al., 1994] and the 1994 Arthurs Passearthquake in New Zealand [e.g., Abercrombie et al.,2000, 2001; Robinson and McGinty, 2000].

[18] In addition, in tectonically active regions, large perturbations to the tectonic stress field by nuclear explo-sions have triggered widespread aftershock activity [e.g.,

Hamilton and Healy, 1969; Hamilton et al., 1972] and the

creation of new faults [ McKeown and Dickey, 1969].Regardless of whether dynamic or static changes in stresstriggered such aftershocks, because the majority of after-shocks occurred far from the region where the explosionsthemselves created large permanent strain, only tectonicstresses could have caused slip on both preexisting andnewly created faults.

[19] Fault plane solutions of aftershocks commonly re-veal a coherent average regional straining, but by no meansdo all such solutions resemble that of the main shock oreach other [e.g., Bodin and Horton, 2004; Hamilton and

Healy, 1969; Hamilton et al., 1972; Hardebeck et al., 2004; Hatzfeld et al., 1986, 1997, 2000; Ouyed et al., 1983;Shearer et al., 2003; Soufleris et al., 1982]. Such solutions

commonly share a consistent P or Taxis, axes of principalcompressive or extensile strains (Figure 7), but faultingcommonly occurs on planes with a variety of orientations.For instance, the consistent NW-SE orientation ofPaxes forthe El Asnam earthquake [Ouyed et al., 1983], with Taxesforming a girdle around the NW-SE orientation of maxi-mum compressive strain, implies that a mixture of purethrust, pure strike-slip, and oblique-slip faulting accommo-dated strain in the region of aftershocks (Figure 7a). Thesimilar pattern, but with a consistent NNW-SSE orientationof T axes for the Kozani-Grevena earthquake [Hatzfeld etal., 1997], shows a similar variety of solutions, but with

normal in place of thrust faulting (Figure 7b). Thus the widevariety of orientations of faults that slipped implies thatsome faults must intercept others, as Hatzfeld et al. [1997]and Resor et al. [2005] showed well for the Kozani-Grevenaearthquake. In regions pervaded by aftershocks, we shouldexpect the rock to be broken into blocks (whose dimensionswe discuss below).

[20] 2. Rupture areas of faulting in small earthquakes

imply pervasive fragmentation. Enough is known of typicaldimensions of ruptures in earthquakes with different mag-nitudes to extrapolate this relationship to estimate rupturedimensions for tiny earthquakes. Among the quantities thatcharacterize an earthquake source, the one most easily andaccurately measured is the seismic moment:

MO mADu 1

where m is the shear modulus, A is the area that ruptured,andDu is the average slip on the fault during the earthquake[Aki, 1966]. Independent measurements of the rupture area,and, particularly for small events, of the average displace-ment are much harder to make. For earthquakes that rupturethe Earths surface, surface faulting places a bound on oneof the dimensions of rupture. Where aftershocks defineclearly the fault that ruptured, their maximum depths, or thatof background seismicity, constrain the other dimension of arupture. For smaller earthquakes, the spectral content of the

body waves from the earthquakes allow estimates of bothseismic moment and source dimensions to be made.

Figure 7. Lower hemisphere stereographic projection ofPand Taxes for (a) the El Asnam aftershocks, determined byOuyed et al. [1983], and (b) the Kozani-Grevena earth-quake, determined by Hatzfeld et al. [1997]. Red and bluetriangles show mean orientations of P and T axes,respectively. The scatter both of T axes for the El Asnamaftershocks and of P axes for the Kozani-Grevena earth-

quake require that for both sequences, faults with differentorientations were activated. Therefore some of these faultsmust intercept others.

Figure 8. Seismic moments versus estimated radii ofequivalent circular ruptures for earthquakes spanning 9orders of magnitude in seismic moment. Lines showrelationships between radius and moment for constant stressdrops. We replotted the data used by Hanks [1977]. Thecommon relationship that stress drops lie within 1 order ofmagnitude of 0.1 MPa suggests that small and largeearthquakes differ from one another only in dimensionsand that scaling relationships can be extrapolated to smallevents.


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[21] Using estimates of rupture dimensions and seismicmoments for earthquakes with magnitudes greater than $3,

Hanks [1977] showed their logarithms plot on a straightline, implying a simple power law relationship (Figure 8).Subsequent analyses of similar data corroborate the patternin Figure 8 and extend it to magnitudes as small as 1[Abercrombie, 1995; McGarr et al., 1981; Spottiswoode and

McGarr, 1975]. This scaling implies that the stress drop, the

average decrease in shear stress across the fault that slips inan earthquake, typically ranges between 0.1 and 10 MPa,with an approximately lognormal distribution and a geo-metric average near 1 MPa. Exceptions do exist, for whichsource dimensions appear to be atypically small for themagnitudes and moments of the earthquakes, and stressdrops are larger than 10 MPa; for such events, fracturing ofintact rock seems inescapable [e.g., Nadeau and Johnson,1994; Nadeau et al., 1994], as clearly occurs locally withsome earthquakes due to excavations in mines [e.g.,

McGarr et al., 1975; Yamada et al., 2007]. Nevertheless,Ide and Beroza [2001] argued that if corrections were madeto account for limited bandwidths of recording, the energyradiated by most earthquakes as seismic waves is propor-

tional to the seismic moment over 17 orders of magnitude ofmoment; hence stress drops are indeed approximatelyconstant for earthquakes with magnitudes smaller than 3to larger than 8. As we show next, knowledge of both thestress drop and the seismic moment for smaller earthquakesallows an estimate of the dimensions of ruptures in suchearthquakes.

[22] As slip occurs during an earthquake, both the shearstress and the elastic strain across a fault drop. The straindrop is proportional to the ratio of average slip on the fault,Du, to the typical dimension of the rupture (or the smallerof the dimensions if the fault is long and narrow), so that thedimensionless constant depends on the geometry of fault-ing. The stress drop, in turn, is given by the product of thestrain drop and the shear modulus, m. For small events, thesimplest assumption is a circular rupture of radius r acrosswhich the slip varies smoothly from zero on the circumfer-ence to a maximum at the center. For this case the stressdrop can be expressed as [Eshelby, 1957]

Ds7p

16mDu

r2

[23] Using the seismic moment defined by (1) and A =pr2, (2) can be written as

r 3ffiffiffiffiffiffiffiffiffiffiffiffi

7M0

16Ds

r3

[24] Thus, if we know MO, and we assume that forvery small earthquakes Ds % 1 MPa [e.g., Hanks, 1977;

Ide and Beroza, 2001], we may deduce their typical rupturedimensions.

[25] Magnitudes scale with the seismic moments [e.g., Hanks and Kanamori, 1979]:

log10 M0 1:5MW 9:0 4

where M0 is measured in Newton-meters, and MW is themagnitude calculated from the seismic moment. (Hanks and

Kanamori [1979] originally tested (4) with magnitudesmeasured as Gutenberg and Richter had defined themearlier, but now, because seismic moments are commonlymeasured for moderate and large earthquakes, seismologistsuse MW defined by (4). In the following, we use MW forearthquake magnitude, regardless of how it was measured.)From (3) and (4) we can estimate typical spatial dimensionsof faults or portions of faults that slip in earthquake with

different magnitudes or seismic moments.[26] Suppose, for geomorphologic purposes, that faulting

creates fracture spacing of 1 m. Because two faults cannotintersect one another without one displacing the other andhence creating 3 faults, for a network of faults to create

blocks with dimensions of a meter, some faults must be only1 m (or shorter) in dimension. The application of (3) and (4)suggests that an earthquake with MW = 2.4 will rupture afault with radius r = 0.5 m (diameter of 1 m). Thus, whereseismicity is common, as in tectonically active regions, weexpect that blocks with dimensions of boulders, if not yetsmaller, participate in regional deformation, insofar as suchsmall earthquakes occur.

[27] Most of the studies of aftershocks cited above

consider earthquakes with magnitudes of 1 to 3 (or larger).Seismographs record even smaller earthquakes, however,where they can be installed with high sensitivity, such as onthe seafloor [Butler, 2003], underground [e.g., Gibowicz etal., 1991; McGarr and Green, 1978], or in boreholes [e.g.,

Abercrombie, 1995; Teng and Henyey, 1981]. Boreholeinstruments in southern California, and those in mines inCanada and South Africa, have recorded earthquakes withmagnitudes as small as 3, nanoearthquakes. Moreover,working in a deep mine, McGarr and Green [1978] couldrecord essentially all earthquakes with magnitudes as smallas 3. They showed that for MW > 3 the seismicity obeysthe Gutenberg-Richter frequency magnitude relationship:

log10 N MW a bMW 5

where N(MW) is the number of earthquakes with magnitudegreater than or equal to MW, and a and b are empiricalconstants. At a yet smaller dimension, Scholz [1968] foundthat the Gutenberg-Richter relationship in (5) applies also toacoustic emissions due to microcracking within sampleswith dimensions of a few centimeters that he stressed in thelaboratory. Thus we have no reason to doubt that earth-quakes with MW 3 occur frequently in activelydeforming regions.

[28] We note that McGarr and Green [1978] found thatb = 0.50.75 in (5), which is somewhat smaller than the

typical values of b = 0.91.0 and hence might suggest adifference between nanoearthquakes and larger earthquakes.Scholz[1968] showed, however, that the value of b dependson the level of stress difference, the maximum minusminimum compressive stress applied to a sample in thelaboratory; b is lower for samples deformed at large stressdifference. Stresses that caused earthquakes in the mine arelikely to have been larger than those causing earthquakeselsewhere [e.g., McGarr et al., 1975]. Thus the fact that thevalue of b found by McGarr and Green [1978] is smallerthan that characteristic of larger earthquakes does not implya fundamental difference between tiny earthquakes andthose we feel.


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[29] Small earthquakes contribute less total strain to aregion than large events, and might seem unimportant inthis context. Because the scaling between frequency ofoccurrence and average area that ruptures in earthquakes,the total surface area that slips in earthquakes of anymagnitude or moment is the same (one event of MW $ 7ruptures roughly the same area as the 10 events of MW $ 6expected from (5) with b = 1) [Hanks, 1992].

[30] Because only rare earthquakes seem to rupture newfaults, we do not claim that the occurrence of a few smallearthquakes with MW $ 3 implies that another block withdimensions of $1 m has been created. Most earthquakesoccur on preexisting faults, and the total displacement onmost faults accumulates with many earthquakes. Thus, tosome extent, seismicity can give a biased measure of therate of tectonic fracturing. Because faults can be reactivatedat different times, some might argue that most faults onwhich earthquakes occur existed before the most recent

phase of tectonic activity. Yet, because we commonly datetectonic activity by dating when faults rupture rock ofknown age, some, if not most, faults must become activewhen a region becomes active. Moreover, as relatively

warm, unfractured rock in the lower crust is exhumed, ifthe region is tectonically active, new faults must formwithin that rock as it cools, and as brittle deformation

becomes possible. In any case, although we associate tinyearthquakes with small rupture areas, only some smallrupture areas bound small blocks, and only rare earthquakesextend or create new faults, and hence new blocks.

2.3. Earthquakes and Faults as Fractals andSelf-Similarity

[31] The power law distribution that characterizes theGutenberg-Richter relationship for earthquake magnitudesin (5) implies scale invariance. Thus small earthquakesdiffer little from large ones, except in dimensions of

ruptures and averaged displacements on faults. Analysesof populations of faults with a wide range of dimensionsand offsets also show power law distributions and thereforealso scale invariance [e.g., Hirata, 1989; Marrett and

Allmendinger, 1990; Scholz and Cowie, 1990; Walsh andWatterson, 1987, 1992; Walsh et al., 1991]. A fractaldistribution of fault dimensions implies a fractal distributionof dimensions of blocks that the fractures separate, andindeed, areas of lithospheric plates also obey power law, orfractal, distributions [Bird, 2003; Sornette and Pisarenko,2003]. By analogy, we expect that the crust consists of a fewlarge blocks, many smaller ones, and yet many more tiny

blocks, such that the number of blocks larger than a certainsize will scale with that size raised to a negative power.

King [1983] showed that the commonly observed b % 1 in(5) can be explained by assuming, first, that for each blockwith a certain volume V or larger, there are another $10

blocks of volume 0.1 Vor larger, and so on, and, second thata similar scaling applies to rupture dimensions of faults thatslip in earthquakes with different magnitudes [see alsoSammis and King, 2007].

[32] Scale invariance encourages extrapolations to dimen-sions of faults smaller than can be studied thoroughly in thefield. Accordingly, much attention has been paid to thequestion of what fraction of regional deformation occurs

because of slip on the largest faults, with views ranging

from most (perhaps 90%) occurring on the main faults [e.g.,Scholz and Cowie, 1990; Scholz et al., 1993] to as much as3050% of the regional strain contributed by slip on smallfaults, those for which dimensions and amounts of slip areorders of magnitude smaller than the dimensions and offsetsof the larger faults [e.g., Kautz and Sclater, 1988; Marrettand Allmendinger, 1992; Turcotte, 1986; Walsh et al.,1991]. Differences in deductions derive in large part from

different estimates of the frequency-magnitude distributionsof fault lengths and of offsets [e.g., Cowie and Scholz, 1992;Gillespie et al., 1992; Marrett and Allmendinger, 1991;Scholz et al., 1993]. Insofar as the discussion given abovefor earthquakes can be extrapolated to dimensions compa-rable to boulders, relatively small earthquakes, those whosemagnitude is smaller than the largest possible earthquake ina region by one unit or more, contribute tens of percent ofthe strain, but almost surely less than 50% of the total strain[e.g., Chen and Molnar, 1977; Molnar, 1979].

[33] Analyses of faults in settings where strain is largesuggest that the power law distribution that works so wellfor earthquakes gives way to an exponential distribution[e.g., Cowie et al., 1993; Spyropoulos et al., 1999]. As

strain accumulates, stresses associated with slip on majorfaults interact so as to suppress continued slip on someminor faults [e.g., Gupta et al., 1998]. Analyses of claygouges in fault zones also show that the fractal distributionfails when the dimensions of clay particles are reached[Wilson et al., 2005]. Thus, in regions of high strain, a

power law relationship overestimates the contribution ofslip on small faults to the strain rate. Spyropoulos et al.[2002] showed that as strain accumulates, faults that rupturethe characteristic dimension of the deforming region, suchas the thickness of the seismogenic layer of the crust, set thescale for the exponential distribution. Similarly, joint spac-ing in layered rock scales with layer thickness [e.g., Pollardand Segall, 1987; Wu and Pollard, 1995], and the degree towhich such scaling develops quickly and accuratelydepends on the initial distribution of flaws and their fracturetoughness [e.g., Fischer and Polansky, 2006; Olson, 2004].If the patterns observed in the laboratory by Spyropoulos etal. [1999, 2002] and Wu and Pollard [1995], in computersimulations [e.g., Fischer and Polansky, 2006; Olson,2004], at mid-ocean ridges by Cowie et al. [1993], andfold-and-thrust belts [e.g., Morellato et al., 2003] applied tothe rest of the Earth, we might expect that in tectonicallyactive regions, small fractures would become inactive asstrain became increasingly concentrated on only a fewmajor faults. Studies of seismicity seem to be inadequateto test whether small earthquakes also occur more rarelythan the Gutenberg-Richter recurrence relationship in (5)suggests. The transfer of strain from developing partly byslip on small faults to almost entirely by slip only on largefaults, however, need not affect the existence of small

blocks; the creation of many small faults that bound small blocks in the initial stages of deformation before strainincreases beyond a few percent, should still leave the regionriddled with fractures (Figure 2).

[34] Although fractures and small blocks of rock charac-terize the Earths surface in many regions, tectonic fractur-ing of rock occurs at depth, before those fractures andfragments are exhumed and below which direct observationis difficult. Nevertheless, small faults are particularly of


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interest to some communities. Sibson [2001] pointed outthat meshes of small faults are crucial for the fluid flow thatoccurs both when ores are deposited and in settings whereearthquakes occur on faults with orientations such that inthe absence of fluid pressure friction would prevent slip.Citing literature from the early 20th century, Sibson[2001] stressed that ore deposits are commonly associatedwith faults with small displacements, not with majorfaults. Exhumed mineral belts show that the fracturing

of crust at depth, necessarily of tectonic origin, is not arare phenomenon.

2.4. Flaw-Free Rocks

[35] Here we speculate that a corollary to the argumentsgiven above about the role of tectonics as a crusher of rockis that in those places where rock has dodged the rockcrusher, it may be stronger and less easily removed byerosive agents. Granitic intrusions in arc settings are oneexample. Such rock has not been subjected to thrust fault-ing. In fact, the intrusive mechanisms now envisaged forsuch rock [e.g., Coleman et al., 2004; Glazner et al., 2004]may allow repeated annealing of incipient cooling joints,

producing yet fewer flaws for erosion to gain purchase. In

Yosemite National Park, the walls of El Capitan and othermajor climbing targets are particularly flaw-free. Anothergeomorphic feature may require flaw-free rock: domes,whose occurrence in strong or massive rocks has been longrecognized. It has been pointed out since yet another ofGilberts [1904] publications that these features are charac-terized by sheet joints that form parallel to the localtopographic surface. Although the mechanics of sheet jointformation has long been an enigma, recent work of Martel[2006] calls upon a combination of regional horizontalstresses and local topographic curvature to generate openingmode cracks. It is unlikely that these joints would form, ifthe rock were already riddled with fractures that could

accommodate the horizontal stresses. The occurrence ofsimilar domes in both the Sierran arc granite and theArchean deep crustal rock of the Western Ghats in India(Figure 9) can be explained by lack of significant tectonic(faulting) activity since they cooled sufficiently to lie in the

brittle regime.

3. Summary

[36

] Tectonics can affect erosion rates both by elevatingterrain so that erosive agents gain potential energy and byfracturing rock. The latter effect increases the likelihood oftransport by solution, by a variety of hillslope processes,and by rivers and glaciers. Recognition of either role played

by tectonics is not new. We contend, however, that theformer has been overly emphasized, and that the latterseems to be less well appreciated than it deserves.

[37] Tectonic processes that operate in the brittle part ofthe crust facilitate erosion by fracturing rock. First, slip onfaults that are not planar requires deformation of one or bothof the blocks that slide past one another; with finite amountsof slip on major faults, the adjacent blocks must deformwith permanent strain. Moreover, earthquakes within conti-

nental regions occur not just on major faults, but also onwidely distributed, smaller faults. Both seismic moments ofthese earthquakes and dimensions of the faults that ruptureobey power law frequency-magnitude distributions, whichsuggest self-similarity. Thus small earthquakes and smallfaults differ from large ones only in size, and we shouldexpect much of the crust in tectonically active areas to be

pervasively fractured to depths of$1020 km. We contendthat it is difficult to imagine tectonic deformation of the

brittle upper crust that does not include pervasive fracturing.[38] Fracturing of the crust contributes to erosion in a

number of ways. In the logic of Gilbert and Dutton,fractured rock has already undergone disintegration, the

Figure 9. Comparison of two domes of similar scale in massive rock. (left) North dome in YosemiteNational Park, formed in Half Dome granodiorite, the westernmost unit of the Tuolumne Intrusive Series,and (right) dome in Archean rocks of the Periyar drainage in Kerala state, western Ghats, India.


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first stage of erosion. The erosion rates we measure intectonically active regions are increased because the rock has

been through this initial step before reaching depths accessedby surface processes. The creation of fragments amenable totransport down hillslopes or by rivers and glaciers eases the

burden of rivers and glaciers. Processes such as landsliding,themselves facilitated by fractured rock at the surface, inturn, tend to break fragments into smaller pieces, making

them yet easier to transport by rivers and glaciers below[e.g., Crosta et al., 2007]. The creation of fractures alsoincreases the surface area of rock that can be attackedchemically, and hence enhances the rate of chemical erosion.Enhanced chemical erosion, in turn, contributes to thedisintegration of rock into fragments easily transported byrivers, glaciers, and hillslopes. Correlations of chemical and

physical erosion testify to the importance of enhancedsurface area for both [e.g., Gaillardet et al., 1999].

[39] The association of rapid erosion where rock has beentectonically fractured gains support from the opposite case.High relief in tectonically quiescent regions, like the WesternGhats (Sahyadri) of India [Gunnell et al., 2003], the high-lands of Sri Lanka [von Blanckenburg et al., 2004], and the

Guyana Shield [ Brown et al., 1992; Edmond et al., 1995;Stallard, 1985, 1988], does not lead to rapid erosion, despitehigh rainfall in all of these areas. As these authors recognized,the resistant intact rock of these regions retards its erosion. Inthese regions, tectonic activity has been mild, if present at all,since the high-grade rock was deformed by largely ductile

processes in Precambrian time and later was exhumed. Thisrock may never have been extensively fractured. We havenoted that a similar case may be made for the resistance toerosion of igneous rocks injected into the upper crustafter thecrust has undergone most of its strain. Some exhumedgranitic plutons that form the cores of high mountain rangesmay be massive (unfractured), and therefore sufficientlystrong to stand in high local relief above the adjacent valleys

because they have escaped the tectonic rock crusher thatprepared the surrounding country rock for erosion.

[40] All surely agree that geodynamic processes play avital role in shaping the Earths surface, but not only by

building mountains. At a small scale, these same processesthat build mountains also sow the seeds of their destruction.If we are to benefit fully from the insights of our forbearers,Dutton and Gilbert, we must understand what they recog-nized as the first step in erosion: disintegration.

[41] Acknowledgments. The writing of this paper was stimulated byfield trips led by A. C. Narayana to the Western Ghats and by K. S. Kelloggto Colorados Front Range. One of us (P.M.) also discussed some aspects oftectonic fracturing with S. Willett in 2003. D. Hatzfeld helped with the

preparation of Figures 4, 5, and 7. We thank J. D. Stock for two especiallythorough, prompt, constructive reviews and S. Gupta, P. O. Koons, and K. XWhipple for additional helpful suggestions. R.S.A. acknowledges financialsupport of the NSF through grant EAR-0126253. Molnar thanks the MillerFoundation at the University of California in Berkeley for support duringthe final preparation of the manuscript. Our travel to the Western Ghats wassupported in part by a University of Colorados Council on Research andCreative Works seed grant to S.P.A.

ReferencesAbercrombie, R. E. (1995), Earthquake source scaling relationships from

1 to 5 ML using seismograms recorded at 2.5-km depth, J. Geophys.Res., 100, 24,015 24,036.

Abercrombie, R. E., T. H. Webb, R. Robinson, P. J. McGinty, J. J. Mori,and R. J. Beavan (2000), The enigma of the Arthurs Pass, New Zealand,

earthquake: 1. Reconciling a variety of data for an unusual earthquake,J. Geophys. Res., 105, 16,11916,137.

Abercrombie, R. E., S. Bannister, A. Pancha, T. H. Webb, and J. J. Mori(2001), Determination of fault planes in a complex aftershock sequenceusing two-dimensional slip inversion, Geophys. J. Int., 146, 134 142.

Aki, K. (1966), Generation and propagation of G waves from the Niigataearthquake of June 16, 1964, 2, Estimation of the earthquake moment,released energy, and stress-strain drop from G wave spectrum, Bull.

Earthquake Res. Inst. Tokyo, 44, 7388.Attal, M., and J. Lave (2006), Changes in bedload characteristics along the

Marsyandi River (central Nepal): Implications for understanding hillslopesediment supply, sediment load evolution along fluvial networks, anddenudation in active orogenic belts, Spec. Pap. Geol. Soc. Am., 398,143171.

Beaumont, C., P. Fullsack, and J. Hamilton (1992), Erosional control ofactive compressional orogens, in Thrust Tectonics, edited by K. R.McClay, pp. 118, Chapman and Hall, New York.

Bird, P. (2003), An updated digital model of plate boundaries, Geochem.Geophys. Geosyst., 4(3), 1027, doi:10.1029/2001GC000252.

Bodin, P., and S. Horton (2004), Source parameters and tectonic implica-tions of aftershocks of the Mw 7.6 Bhuj earthquake of 26 January 2001,

Bull. Seismol. Soc. Am., 94, 818 827.Boulton, G. S., and R. Vivian (1973), Underneath the glaciers, Geogr.

Mag., 45, 311 319.Briner, J. P., and T. W. Swanson (1998), Using inherited cosmogenic 36Cl to

constrain glacial erosion rates of the Cordilleran ice sheet, Geology, 26,36.

Brown, E. T., R. F. Stallard, G. M. Raisbeck, and F. Yiou (1992), Determi-

nation of the denudation rate of Mount Roraima, Venezuela using cos-mogenic 10Be and 26Al, Eos Trans. AGU, 73(43), 170.Burbank, D. W. (2005), Cracking the Himalaya, Nature, 434, 963 964.Burbank, D. W., J. Leland, E. Fielding, R. S. Anderson, N. Brozovic, M. R.

Reid, and C. Duncan (1996), Bedrock incision, rock uplift, and thresholdhillslopes in the northwestern Himalayas, Nature, 379, 505 510.

Butler, R. (2003), The Hawaii-2 Observatory: Observation of nanoearth-quakes, Seismol. Res. Lett., 74, 290 297.

Chen, W.-P., and P. Molnar (1977), Seismic moments of major earthquakesand the average rate of slip in Central Asia, J. Geophys. Res., 82, 29452969.

Coleman, D. S., W. Gray, and A. F. Glazner (2004), Rethinking the empla-cement and evolution of zoned plutons: Geochronologic evidence forincremental assembly of the Tuolumne Intrusive Suite, California,Geology, 32, 433 436.

Cowie, P. A., and C. H. Scholz (1992), Displacement-length scaling rela-tionship for faults: Data synthesis and discussion, J. Struct. Geol., 14,11491156.

Cowie, P. A., C. H. Scholz, M. Edwards, and A. Malinvero (1993), Faultstrain and seismic coupling on mid-ocean ridges, J. Geophys. Res., 98,17,91117,920.

Cox, S. C., D. Craw, and C. P. Chamberlain (1997), Structure and fluidmigration in a late Cenozoic duplex system forming the Main Divide inthe central Southern Alps, New Zealand, N. Z. J. Geol. Geophys., 40,359373.

Crosta, G. B., P. Frattini, and N. Fusi (2007), Fragmentation in the Val Polarock avalanche, Italian Alps, J. Geophys. Res., 112, F01006, doi:10.1029/2005JF000455.

Dahlen, F. A., and J. Suppe (1988), Mechanics, growth, and erosion ofmountain belts, Spec. Pap. Geol. Soc. Am., 218, 161 178.

Das, S., and C. Henry (2003), Spatial relation between main earthquake slipand its aftershock distribution, Rev. Geophys., 41(3), 1013, doi:10.1029/2002RG000119.

Dutton, C. E. (1882), The Tertiary History of the Grand Canyon, U.S. Geol.Surv. Monogr., vol. 2, U.S. Gov. Print. Office, Washington, D. C.

Eaton, J. P., M. E. ONeill, and J. N. Murdock (1970), Aftershocks of the

1966 Parkfield-Cholame, California, earthquakes: A detailed study, Bull.Seismol. Soc. Am., 60, 11511197.Edmond, J. M., M. R. Palmer, C. I. Measures, B. Grant, and R. F. Stallard

(1995), The fluvial geochemistry and denudation rate of the GuyanaShield in Venezuela, Colombia, and Brazil, Geochim. Cosmochim. Acta,59, 33013325.

Eshelby, J. D. (1957), The determination of the elastic field of an ellipsoidalinclusion and related problems, Proc. R. Soc. London, Ser. A, 241, 376396.

Fedotov, S. A. (1965), Regularities of the distribution of strong earthquakesin Kamchatka, the Kurile Islands, and northeastern Japan (in Russian),Trans. Inst. Fiz. Zemli Akad. Nauk SSSR, 36, 66 93.

Fischer, M. P., and A. Polansky (2006), Influence of flaws on joint spacingand saturation: Results of one-dimensional mechanical modeling,

J. Geophys. Res., 111, B07403, doi:10.1029/2005JB004115.


10 of 12

F03014


11/12

Gaillardet, J., B. Dupre, P. Louvat, and C. J. Allegre (1999), Global silicateweathering and CO2 consumption rates deduced from the chemistry oflarge rivers, Chem. Geol., 159, 3 30.

Gibowicz, S. J., R. P. Young, S. Talebi, and D. J. Rawlence (1991), Sourceparameters of seismic events at the Underground Research Laboratory inManitoba, Canada: Scaling relations for events with moment magnitudesmaller than 2, Bull. Seismol. Soc. Am., 81, 11571182.

Gilbert, G. K. (1877), Land sculpture, in Report on the Geology of theHenry Mountains: Geographical and Geological Survey of the Rocky Mountain Region, pp. 93144, U.S. Gov. Print. Office, Washington,

D. C.Gilbert, G. K. (1904), Dome and dome structures of the High Sierra, Geol.Soc. Am. Bull., 15, 2936.

Gillespie, P. A., J. J. Walsh, and J. Watterson (1992), Limitations of dimen-sion and displacement data from single faults and the consequences fordata analysis and interpretation, J. Struct. Geol., 14, 11571172.

Glazner, A. F., J. M. Bartley, D. S. Coleman, W. Gray, and R. Z. Taylor(2004), Are plutons assembled over millions of years by amalgamationfrom small magma chambers?, GSA Today, 14, 4 11.

Gunnell, Y., K. Gallagher, A. Carter, M. Widdowson, and A. J. Hurford(2003), Denudation history of the continental margin of western penin-sular India since the early MesozoicReconciling apatite fission-trackdata with geomorphology, Earth Planet. Sci. Lett., 215, 187 201.

Gupta, S., P. A. Cowie, N. H. Dawers, and J. R. Underhill (1998), Amechanism to explain rift-basin subsidence and stratigraphic patternsthrough fault-array evolution, Geology, 26, 595 598.

Hack, J. T. (1957), Studies of longitudinal stream profiles in Virginia andMaryland, U.S. Geol. Surv. Prof. Pap., 294B, 4597.

Hack, J. T. (1973), Stream-profile analysis and stream-gradient index,J. Res. U.S. Geol. Surv., 1, 421 429.

Hamilton, R. M., and J. H. Healy (1969), Aftershocks of the Benhamnuclear explosion, Bull. Seismol. Soc. Am., 59, 22712281.

Hamilton, R. M., B. E. Smith, F. G. Fischer, and P. J. Papanek (1972),Earthquakes caused by underground nuclear explosions on Pahute Mesa,

Nevada Test Site, Bull. Seismol. Soc. Am., 62, 13191341.Hancock, G. S., R. S. Anderson, and K. X. Whipple (1998), Beyond power:

Bedrock river incision process and form, in Rivers Over Rock: FluvialProcesses in Bedrock Channels, Geophys. Monogr. Ser., vol. 107, editedby K. J. Tinkler and E. E. Wohl, pp. 3560, AGU, Washington, D. C.

Hanks, T. C. (1977), Earthquake stress drops, ambient tectonic stresses, andstresses that drive plate motions, Pure Appl. Geophys., 115, 441 458.

Hanks, T. C. (1992), Small earthquakes, tectonic forces, Science, 256,14301432.

Hanks, T. C., and H. Kanamori (1979), A moment magnitude scale,J. Geophys. Res., 84, 23482351.

Hardebeck, J. L., et al. (2004), Preliminary report on the 22 December 2003M6.5 San Simeon, California, earthquake, Seismol. Res. Lett., 75, 155172.

Hatzfeld, D., A. A. Christodoulou, E. M. Scordilis, D. Papagiotopoulos,and P. M. Hatzidimitriou (1986), A microearthquake study of the Myg-donian graben (northern Greece), Earth Planet. Sci. Lett., 81, 379 396.

Hatzfeld, D., et al. (1997), The Kozani-Grevena (Greece) earthquake ofMay 13, 1995 revisited from a detailed seismological study, Bull. Seis-mol. Soc. Am., 87, 463 473.

Hatzfeld, D., V. Karakostas, M. Ziazia, I. Kassaras, E. Papadimitriou,K. Makropoulos, N. Voulgaris, and C. Papaioannou (2000), Microseismi-city and faulting geometry in the Gulf of Corinth (Greece), Geophys. J.

Int., 141, 438 456.Hauksson, E., L. M. Jones, K. Hutton, and D. Eberhart-Phillips (1993), The

1992 Landers earthquake sequence: Seismological observations,J. Geophys. Res., 98, 19,835 19,858.

Hirata, T. (1989), Fractal dimension of fault systems in Japan: Fractalstructure in rock fracture geometry at various scales, Pure Appl.Geophys., 131, 157 170.

Holmes, A. (1944), Principles of Physical Geology, 532 pp., ThomasNelson, London.

Holmes, A. (1965), Principles of Physical Geology, 2nd ed., 1288 pp.,Ronald Press, New York.

Ide, S., and G. C. Beroza (2001), Does apparent stress vary with earthquakesize?, Geophys. Res. Lett., 28, 33493352.

Ishiyama, T., K. Mueller, M. Togo, A. Okada, and K. Takemura (2004),Geomorphology, kinematic history, and earthquake behavior of the activeKuwana wedge thrust anticline, central Japan, J. Geophys. Res., 109,B12408, doi:10.1029/2003JB002547.

Kautz, S. A., and J. G. Sclater (1988), Internal deformation in clay modelsof extension by block faulting, Tectonics, 7, 823 832.

Kelleher, J., L. R. Sykes, and J. Oliver (1973), Possible criteria for predict-ing earthquake locations and their application to major plate boundariesof the Pacific and Caribbean, J. Geophys. Res., 78, 25472585.

Kellogg, K. S. (2001), Tectonic controls on a large landslide complex:Williams Fork Mountains near Dillon, Colorado, Geomorphology, 41,355368.

King, G. (1983), The accommodation of large strains in the upper litho-sphere of the Earth and other solids by self-similar fault systems: Thegeometrical origin of b-value, Pure Appl. Geophys., 121, 761 815.

King, G. C. P., Z. X. Ouyang,P.Papadimitriou,A. Deschamps, J. Gagnepain,G. Houseman, J. A. Jackson, C. Soufleris, and J. Virieux (1985), Theevolution of the Gulf of Corinth (Greece): An aftershock study of the1981 earthquakes, Geophys. J. R. Astron. Soc., 80, 677 693.

King, G. C. P., R. S. Stein, and J. Lin (1994), Static stress changes and thetriggering of earthquakes, Bull. Seismol. Soc. Am., 84, 935 953.Koons, P. O. (1989), The topographic evolution of collisional mountain

belts: A numerical look at the Southern Alps of New Zealand, Am. J.Sci., 289, 10411069.

Koons, P. O. (1990), Two-sided orogen: Collision and erosion from thesandbox to Southern Alps, New Zealand, Geology, 18, 679 682.

Koons, P. O., and D. Craw (2002), Beyond steady state in three-dimensional orogens, Eos Trans. AGU, 83(47), Fall Meet. Suppl.,Abstract T72B-06.

Little, T. A., R. J. Holcombe, and B. R. Ilg (2002), Kinematics of obliquecollision and ramping inferred from microstructures and strain in middlecrustal rocks, central Southern Alps, New Zealand, J. Struct. Geol., 24,219239.

Lliboutry, L. (1994), Monolithologic erosion of hard beds by temperateglaciers, J. Glaciol., 40, 433 450.

Loveless, J. P., G. D. Hoke, R. W. Allmendinger, G. Gonzalez, B. L. Isacks,and D. A. Carrizo (2005), Pervasive cracking of the northern ChileanCoastal Cordillera: New evidence for forearc extension, Geology, 33,973976.

Marrett, R., and R. W. Allmendinger (1990), Kinematic analysis of fault-slip data, J. Struct. Geol., 12, 973 986.

Marrett, R., and R. W. Allmendinger (1991), Estimates of strain due tobrittle faulting: Sampling the fault populations, J. Struct. Geol., 13,735738.

Marrett, R., and R. W. Allmendinger (1992), Amount of extension onsmall faults: An example from the Viking Graben, Geology, 20, 4750.

Martel, S. J. (2006), Effect of topographic curvature on near-surface stressesand application to sheeting joints, Geophys. Res. Lett., 33, L01308,doi:10.1029/2005GL024710.

McGarr, A., and R. W. E. Green (1978), Microtremor sequences and tiltingin a deep mine, Bull. Seismol. Soc. Am., 68, 16791697.

McGarr, A., S. M. Spottiswoode, and N. C. Gay (1975), Relationship ofmine tremors to induced stresses and rock properties in the focal region,

Bull. Seismol. Soc. Am., 65, 981 993.McGarr, A., R. W. E. Green, and S. M. Spottiswoode (1981), Strong ground

motion of mine tremors: Some implications for near-source groundmotion parameters, Bull. Seismol. Soc. Am., 71, 295 319.

McKeown, F. A., and D. D. Dickey (1969), Fault displacements andmotions related to nuclear explosions, Bull. Seismol. Soc. Am., 59,22532269.

Molnar, P. (1979), Earthquake recurrence intervals and plate tectonics, Bull.Seismol. Soc. Am., 69, 115133.

Molnar, P. (1987), Inversion of profiles of uplift rates for the geometry ofdip-slip faults at depth, with examples from the Alps and the Himalaya,

Ann. Geophys., 5B, 663 670.Morellato, C., F. Redini, and C. Doglioni (2003), On the number and

spacing of faults, Terra Nova, 15, 315 321.Nadeau, R. M., and L. R. Johnson (1994), Seismological studies at Park-

field VI: Moment release rates and estimates of source parameters forsmall repeating earthquakes, Bull. Seismol. Soc. Am., 88, 790 814.

Nadeau, R., M. Antolik, P. A. Johnson, W. Foxall, and T. V. McEvilly(1994), Seismological studies at Parkfield III: Microearthquake clustersin the study of fault-zone dynamics, Bull. Seismol. Soc. Am., 84, 247263.

Negishi, H., J. Mori, T. Sato, R. Singh, S. Kumar, and N. Hirata (2002),Size and orientation of the fault plane for the 2001 Gujarat, India earth-quake (Mw7.7) from aftershock observations: A high stress drop event,Geophys. Res. Lett., 29(20), 1949, doi:10.1029/2002GL015280.

Olson, J. E. (2004), Predicting fracture swarmsThe influence of subcri-tical crack growth and the crack-tip process zone on joint spacing in rock,Spec. Publ. Geol. Soc., 231, 73 87.

Ouyed, M., G. Yielding, D. Hatzfeld, and G. C. P. King (1983), An after-shock study of the El Asnam (Algeria) earthquake of 1980 October 10,Geophys. J. R. Astron. Soc., 73, 605 639.

Pandey, M. R., R. P. Tandukar, J. P. Avouac, J. Lave, and J. P. Massot(1995), Interseismic strain accumulation on the Himalayan crustal ramp(Nepal), Geophys. Res. Lett., 22, 751 754.


11 of 12

F03014


12/12

Pettifer, G. S., and P. G. Fookes (1994), A revision of the graphical methodfor assessing the excavatability of rock, Q. J. Eng. Geol., 27, 145 164.

Pollard, D. D., and P. Segall (1987), Theoretical displacements and stressesnear fractures in rock: With applications to faults, joints, veins, dikes, andsolution surfaces, in Fracture Mechanics of Rock, edited by B. K.Atkinson, pp. 277349, Elsevier, New York.

Resor, P. G., D. D. Pollard, T. J. Wright, and G. C. Beroza (2005), Integrat-ing high-precision aftershock locations and geodetic observations tomodel coseismic deformation associated with the 1995 Kozani-Grevenaearthquake, Greece, J. Geophys. Res., 110, B09402, doi:10.1029/

2004JB003263.Robinson, R., and P. J. McGinty (2000), The enigma of the Arthurs Pass,New Zealand, earthquake: 2. The aftershock distribution and its relationto regional and induced stress fields, J. Geophys. Res., 105, 16,13916,150.

Sammis, C. G., and G. C. P. King (2007), Mechanical origin of power lawscaling in fault zone rock, Geophys. Res. Lett., 34, L04312, doi:10.1029/2006GL028548.

Schmidt, K. M., and D. R. Montgomery (1995), Limits to relief, Science,270, 617 620.

Scholz, C. H. (1968),The frequency-magnituderelationof microfracturing inrock and its relation to earthquakes, Bull. Seismol. Soc. Am., 58, 399415.

Scholz, C. H., and P. A. Cowie (1990), Determination of total strain fromfaulting using slip measurements, Nature, 346, 837 839.

Scholz, C. H., N. H. Dawers, J.-Z. Xu, M. H. Anders, and P. A. Cowie(1993), Fault growth and fault scaling laws: Preliminary results,

J. Geophys. Res., 98, 21,951 21,961.Schulte-Pelkum, V., G. Monsalve, A. Sheehan, M. R. Pandey, S. Sapkota,

R. Bilham, and F. Wu (2005), Imaging the Indian subcontinent beneaththe Himalaya, Nature, 435, 12221225.

Segall, P. (1984), Formation and growth of extensional fracture sets, Geol.Soc. Am. Bull., 95, 454 462.

Selby, M. J. (1980), A rock mass strength classification for geomorphicpurposes: With tests from Antarctica and New Zealand, Z. Geomorphol.,24, 3151.

Shaw, J. H., and J. Suppe (1994), Active faulting and growth folding in theeastern Santa Barbara Channel, California, Geol. Soc. Am. Bull., 106,607626.

Shearer, P. M., J. L. Hardebeck, L. Astiz, and K. B. Richards-Dinger(2003), Analysis of similar event clusters in aftershocks of the 1994

Northridge, California, earthquake, J. Geophys. Res., 108(B1), 2035,doi:10.1029/2001JB000685.

Sibson, R. H. (2001), Seismogenic framework for hydrothermal transportand ore deposition, Soc. Econ. Geol. Rev., 14, 2550.

Sklar, L., and W. E. Dietrich (2001), Sediment and rock strength controls onriver incision into bedrock, Geology, 29, 10871090.

Sklar, L. S., and W. E. Dietrich (2004), A mechanistic model for riverincision into bedrock by saltating bed load, Water Resour. Res., 40,W06301, doi:10.1029/2003WR002496.

Sleep, N. H. (1971), Thermal effects of the formation of Atlantic continentalmargin by continental break up, Geophys. J. R. Astron. Soc., 24, 325350.

Sornette, D., and V. Pisarenko (2003), Fractal plate tectonics, Geophys. Res.Lett., 30(3), 1105, doi:10.1029/2002GL015043.

Soufleris, C., J. A. Jackson, G. C. P. King, C. P. Spencer, and C. H. Scholz(1982), The 1978 earthquake sequence near Thessaloniki (northernGreece), Geophys. J. R. Astron. Soc., 68, 429 458.

Spottiswoode, S. M., and A. McGarr (1975), Source parameters of tremorsin a deep-level gold mine, Bull. Seismol. Soc. Am., 65, 93 112.

Spyropoulos, C., W. J. Griffith, C. H. Scholz, and B. E. Shaw (1999),Experimental evidence for different strain regimes of crack populationsin a clay model, Geophys. Res. Lett., 26, 10811084.

Spyropoulos, C., C. H. Scholz, and B. E. Shaw (2002), Transition regimesfor growing crack populations, Phys. Rev. Lett., 65, 056105, doi:10.1103/PhysRevE.65.05610584.

Stallard, R. F. (1985), River chemistry, geology, geomorphology, and soilsin the Amazon and Orinoco basins, in The Chemistry of Weathering,edited by J. I. Drever, pp. 293316, Springer, New York.

Stallard, R. F. (1988), Weathering and erosion in the humid tropics, in Physical and Chemical Weathering in Geochemical Cycles, edited byA. Lerman and M. Meybeck, pp. 225246, Springer, New York.

Stein, R. S., and M. Lisowski (1983), The 1979 Homestead Valley earth-quake sequence, California: Control of aftershocks and postseismic de-formation, J. Geophys. Res., 88, 64776490.

Stock, J. D., and W. E. Dietrich (2006), Erosion of steepland valleys bydebris flows, Geol. Soc. Am. Bull., 118, 11251148.

Stock, J. D., D. R. Montgomery, B. D. Collins, W. E. Dietrich, and L. Sklar(2005), Field measurements of incision rates following bedrock exposure:Implications for process controls on the long profiles of valleys cut byrivers and debris flows, Geol. Soc. Am. Bull., 117, 174 194.

Suppe, J. (1983), Geometry and kinematics of fault-bend folding, Am. J.

Sci., 90, 648 721.Suppe, J. (1985), Principles of Structural Geology, 537 pp., Prentice-Hall,Englewood Cliffs, N. J.

Sykes, L. R. (1971), Aftershock zones of great earthquakes, seismicitygaps, and earthquake prediction for Alaska and the Aleutians, J. Geophys.

Res., 76, 80218041.Teng, T. L., and T. H. Henyey (1981), The detection of nanoearthquakes, in

Earthquake Prediction: An International Review, Maurice Ewing Ser.,vol. 4, edited by D. W. Simpson and P. G. Richards, pp. 533542,AGU, Washington, D. C.

Thuro, K. (1997), Drillability prediction: Geological influences in hard rockdrill and blast tunneling, Geol. Rundsch., 86, 426 438.

Turcotte, D. L. (1986), A fractal model for crustal deformation, Tectono-physics, 132, 261 269.

Vanacker, V., F. von Blanckenburg, T. Hewawasam, and P. W. Kubik(2007), Constraining landscape development of the Sri Lankan escarp-ment with cosmogenic nuclides in river sediment, Earth Planet. Sci. Lett.,253, 402 414.

Vervoort, A., and K. De Wit (1997), Correlation between dredgeability andmechanical properties of rock, Eng. Geol., 47, 259 267.

von Blanckenburg, F., T. Hewawasam, and P. W. Kubik (2004), Cosmo-genic nuclide evidence for low weathering and denudation in the wet,tropical highlands of Sri Lanka, J. Geophys. Res., 109 , F03008,doi:10.1029/2003JF000049.

Wager, L. R. (1937), The Arun River drainage pattern and the rise of theHimalaya, Geogr. J., 89, 239 250.

Walsh, J. J., and J. Watterson (1987), Distributions of cumulative displace-ment and seismic slip on a single normal fault surface, J. Struct. Geol., 9,10391046.

Walsh, J. J., and J. Watterson (1992), Populations of faults and fault dis-placement and their effects on estimates of fault-related regional exten-sion, J. Struct. Geol., 14, 701 712.

Walsh, J., J. Watterson, and G. Yielding (1991), The importance of small-scale faulting in regional extension, Nature, 391, 381 393.

Weissel, J. K., and M. A. Seidl (1997), Influence of rock strength propertieson escarpment retreat across passive continental margins, Geology, 25,631634.

Wilson, B., T. Dewers, Z. Reches, and J. Brune (2005), Particle size andenergetics of gouge from earthquake rupture zones, Nature, 434, 749752.

Wobus, C., A. Heimsath, K. Whipple, and K. Hodges (2005), Active out-of-sequence thrust faulting in the central Nepal Himalaya, Nature, 434,10081011.

Wu, H.-Q., and D. D. Pollard (1995), An experimental study of the relation-ship between joint spacing and layer thickness, J. Struct. Geol., 17, 887905.

Yamada, T., J. J. Mori, S. Ide, R. E. Abercrombie, H. Kawakata,M. Nakatani, Y. Iio, and H. Ogasawara (2007), Stress drops and radiatedseismic energies of microearthquakes in a South African gold mine,

J. Geophys. Res., 112, B03305, doi:10.1029/2006JB004553.Yielding, G., J. A. Jackson, G. C. P. King, H. Sinvhal, C. Vita-Finzi, and

R. M. Wood (1981), Relations between surface deformation, fault geome-try, seismicity, and rupture characteristics during the El Asnam (Algeria)earthquake of 10 October 1980, Earth Planet. Sci. Lett., 56, 287304.

R. S. Anderson and S. P. Anderson, Institute of Arctic and Alpine

Research, University of Colorado, Boulder, CO 80309-0450, USA.P. Molnar, Department of Geological Sciences, University of Colorado,

Boulder, CO 80309-0399, USA. ([email protected])


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Tectonics, Fracturing of Rock, And Erosion