Density variations within the south polar layered deposits ...Density variations within the south polar layered deposits of Mars Junlun Li,1 Jeffrey C. Andrews-Hanna,1,2 Youshun Sun,1

Density variations within the south polar layered deposits of Mars

Junlun Li,1 Jeffrey C. Andrews-Hanna,1,2 Youshun Sun,1 Roger J. Phillips,3

Jeffrey J. Plaut,4 and Maria T. Zuber1

Received 19 August 2011; revised 1 March 2012; accepted 5 March 2012; published 20 April 2012.

[1] The south polar layered deposits (SPLD) constitute the largest known reservoir ofwater on Mars. Previous studies solved for the best fit uniform density of the depositsusing a forward approach. Here we invert for the lateral density variations in the layereddeposit using gravity data from radio tracking of Mars Reconnaissance Orbiter,topography from MOLA on board Mars Global Surveyor, and radar sounding data fromMARSIS on board Mars Express. We use the gravity anomalies outside the SPLD toconstruct a Wiener filter, which is applied to the gravitational signature of the SPLD toremove the short-wavelength anomalies over the SPLD that are spectrally consistentwith an origin in the crust or mantle. We then use a constrained inversion for thevertically averaged density within the SPLD as a function of position. The resultssuggest significant density variations within the SPLD. An inverse relationship between thedensity and thickness of the SPLD suggests that thicker portions of the cap contain lessdust. Alternatively, the Dorsa Argentea Formation may extend beneath the SPLD andresult in the observed high gravity anomaly in the marginal area of the SPLD. We findthese conclusions to be robust against the choice of inversion constraint and perturbationsto the applied filter. A synthetic test is also performed to verify the recoverability of thedensity variation in our approach.

Citation: Li, J., J. C. Andrews-Hanna, Y. Sun, R. J. Phillips, J. J. Plaut, and M. T. Zuber (2012), Density variations within thesouth polar layered deposits of Mars, J. Geophys. Res., 117, E04006, doi:10.1029/2011JE003937.

1. Introduction

[2] Today, the surface and near-surface water on Mars isprimarily in the form of ice. It is estimated that volume ofwater in the polar caps and polar layered deposits is equiv-alent to a global layer about 20 m in depth [Smith et al.,2001; Plaut et al., 2007; Selvans et al., 2010]. Also, a vastquantity of water has been found within the topmost 1 m ofthe Martian surface at high latitudes [Boynton et al., 2002;Feldman et al., 2002, 2004; Mitrofanov et al., 2002], andimpact crater morphologies suggest more water existedwithin the upper few kilometers of the crust over large areasof the planet in the past [Barlow and Perez, 2003].[3] Both the south and north polar layered deposits of

Mars are geologically young (<100 Ma) compared to othersurface features. They have been a topic of great interestsince they were first observed, as they could contain therecord of relatively recent climate change [Carr, 2006]. The

south polar layered deposits (SPLD) are highly asymmetricwith a volume estimated to be 1.6 ! 106 km3 and thethickest part about 3.7 km [Plaut et al., 2007]. Many pre-vious researchers suggested that the SPLD is primarilycomposed of water-ice, with central, thin CO2 cover [Byrneand Ingersoll, 2003; Titus et al., 2003; Bibring et al., 2004;Plaut et al., 2007], though more recent work has uncoveredevidence for massive CO2 ice deposits within some portionsof the SPLD [Phillips et al., 2011]. By examining the stra-tigraphy exposed on scarp walls from THEMIS (ThermalEmission Imaging System on board Mars Odyssey) visibleimages, Milkovich and Plaut [2008] inferred that the SPLDis composed of three main sequences of deposit layers,corresponding to three different geologic periods. Wieczorek[2008] used gravity data from radio tracking of Mars GlobalSurveyor and Mars Odyssey [Konopliv et al., 2006], andestimated the best fit constant density to be 1271 kg/m3. Healso estimated the concentration of dust content to bebetween 14 and 28% by volume if they were completely freeof solid CO2, depending on the assumed dust density.Alternatively, 55% CO2 ice could be sequestrated by volumeif there was no dust deposited. The effects of the CO2 ice willbe discussed in detail later in our paper. Using the data fromradio tracking of Mars Reconnaissance Orbiter, Zuber et al.[2007a] assumed that the density across the SPLD is con-stant and found the best fit density to be 1220 kg/m3. Theyalso suggested that this density can be explained by water icemixed with 15% dust.

1Department of Earth, Atmospheric and Planetary Sciences,Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

2Now at Department of Geophysics and Center for Space Resources,Colorado School of Mines, Golden, Colorado, USA.

3Planetary Science Directorate, Southwest Research Institute, Boulder,Colorado, USA.

4Jet Propulsion Laboratory, California Institute of Technology, Pasadena,California, USA.

Copyright 2012 by the American Geophysical Union.0148-0227/12/2011JE003937

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, E04006, doi:10.1029/2011JE003937, 2012

E04006 1 of 13

[4] In this work, we inverted for the density variationwithin the SPLD with constraints on the density smoothnessand deviation. We first use the gravity anomalies outside theSPLD to construct a Wiener filter, which is applied to thegravitational signature of the SPLD to remove the short-wavelength anomalies over the SPLD that are spectrallyconsistent with an origin in the crust or mantle. We also per-form a synthetic test to verify the recoverability of ourapproach. The robustness of our inversion approach is exten-sively examined by setting the parameters in the inversionwith different values and comparing the corresponding results.The influence of the silicate dust on the estimated permittivityof the SPLD on the inversion results is also studied. Aninverse relationship between the density and thickness of theSPLD suggests that thicker portions of the cap contain lessdust.

2. Methods and Results

2.1. Data Preparation[5] The gravity data from Mars Reconnaissance Orbiter

tracking is in the form of spherical harmonics, extending upto degree 100, with a corresponding spatial resolution of107 km (mromgm0020g) [Zuber et al., 2007b; Konoplivet al., 2011]. However, because the highest degrees arenoisy, degrees beyond 85 are cosine tapered to reduce thenoise, yielding an effective (full wavelength) spatial resolu-tion of 125 km. Additionally, the spherical harmonic degree2 order 0 associated with flattening is removed, as well asthe rest of degrees 2 and 3, which are primarily dominatedby the effects of Tharsis loading.[6] The topography and gravity anomalies for the south

polar layered deposits are shown in Figure 1. Here we haveremoved very long wavelength residual gravity anomaliesassociated with the global signature of the Tharsis province.From Figures 1a and 1c we see a strong correlation betweentopographic features and gravity anomalies outside theSPLD. We first remove these correlated anomalies beforefocusing on the anomalies within the SPLD.

2.2. Removing Gravity Anomalies ArisingFrom the Topography[7] The gravity anomalies shown in Figure 1 could arise

from a combination of origins: 1) vertical relief along thedensity interface between crust and mantle (i.e., the Moho);2) vertical relief along the density interface between the crustand the atmosphere; 3) lateral density variations arising fromcrustal and mantle heterogeneity; 4) vertical relief along theinterface between the SPLD and the crust; 5) vertical reliefalong the density interface between the SPLD and theatmosphere; 6) lateral density variations arising from het-erogeneity within the SPLD in terms of dust content, con-trasting ice compositions and porosity; and 7) errors in themeasured gravity field. In this paper, we attempt to isolate theeffects of density variations within the SPLD by removingthe effects of the other contributions to the gravity fieldthrough either direct observation or carefully chosen filteringof the data.[8] First, we remove anomalies originating from the Moho

and crust topography. The mean crustal thickness is assumedto be 56 km [Zuber et al., 2007a]. It is not possible to solveuniquely for both the relief along the Moho and the densityvariations within the SPLD using the observed gravity andtopography alone. To circumvent this issue, we use theobserved gravity and topography outside of the SPLD tomodel the Moho relief there, and calculate the best fit degreeof compensation. The result is then applied to the entireregion both inside and outside of the SPLD in order to cal-culate the Moho relief. The best fit degree of compensationoutside the SPLD in this region is found to be 91% [Zuberet al., 2007a]. The Moho compensation depth hc can becalculated from:

rcghl ! 0:91 " rm # rc$ %ghc! hc "

rchlrm # rc

! 0:91 $1%

where rc is the density of the crust (2900 kg/m3); rm is thedensity of the mantle (3500 kg/m3); hl is the topography ofthe crust (SPLD excluded). Assuming Airy compensationand applying the observed degree of compensation outside

Figure 1. (a) Surface topography (m); (b) basal topography (m) from MARSIS [Plaut et al., 2007];(c) gravity anomaly (mGal) over the SPLD (red outline in Figure 1b). The radial free air anomaly is cal-culated at the reference radius R = 3396 km. The figures are oriented with 0 longitude located at the top,and the study area is about 2400 km across.

LI ET AL.: DENSITY VARIATIONS IN THE SPLD OF MARS E04006E04006

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of the SPLD to the MARSIS-derived crustal topographybeneath the SPLD, we can infer the Moho topography bothbeneath and around the SPLD region. Zuber et al. [2007a]addressed the uncertainty in Moho topography, and con-cluded that the mean SPLD density is not sensitive to thiserror source. The lithosphere flexure due to the polar loadshould have a negligible effect on the density determination:Zuber et al. [2007a] investigated the possible range of thebasal unit deformation under SPLD and concluded thatflexure would have a small effect on the mean density (anincrease in mean density of 70 kg/m3 if there is a 100 mflexural depression beneath the SPLD); also, Phillips et al.[2008] concluded that the flexure under the NPLD issmall (&100 m), possibly due to a very thick lithosphere(>300 km). Wieczorek [2008] also reached a similar con-clusion that the mean density of the SPLD is not sensitive tothe elastic thickness of the lithosphere.[9] To forward-model the gravity anomalies arising from

the different sources, we performed analyses in both Carte-sian and Fourier space. The spatial scale of the SPLD issmall relative to the planet and the use of global gravity andtopography combined with spherical harmonic localization

would not improve the model results. To compute thegravity anomalies originating from surface topography andMoho relief, the forward modeling method of Parker [1973]in Fourier space is applied:

F g' ( " #2pG exp # k"!!!!!!z0

" #X"

n!

"k!!!!!!n#1

n!F rchl

n x; y$ %'

# rm # rc$ %hcn x; y$ %( $2%

where (x,y) is the horizontal location; G is the universalgravitational constant; rc and rm are the densities of the crust

and mantle, respectively;"k!!!!!! "

$$$$$$$$$$$$$$$kx2 ) ky2

pis the amplitude

of the horizontal wave number; hl and hc are the topographyat the top of the crust (without the SPLD) and Moho relief,respectively; and F denotes the Fourier transform. Thetopography at the top of the crust (hl) is taken from MOLAtopography outside of the SPLD [Smith et al., 2001], andfrom the relief of the base of the SPLD derived fromMARSIS radar [Plaut et al., 2007]. The relief along theMoho is calculated from the topography using best fit degreeof compensation as described above.[10] By removing the gravity anomalies arising from these

two sources, we obtain residual gravity anomalies. Theresidual anomalies, shown in Figure 2, are dominated by theSPLD, but they also include contributions from densityheterogeneities within the crust and mantle, from departuresfrom the best fit degree of compensation, and from errors inthe measured gravity field.

2.3. Inversion for SPLD Density Anomalies[11] To invert for the density anomaly distribution, we

first divide the SPLD region into many rectangular prisms.After the contribution from each individual prism is isolated,sophisticated constraints on the inversion can be applied.The gravity originating from each prism is first calculated asa function of its location and the observation point, and thenthe modeled gravity at any particular observation point(x0, y0, z0) is simply the summation of the contributions fromall prisms, each of which is 30 km by 30 km in our study. Asensitivity matrix, which characterizes the contribution fromall the prisms to all the observation points by mapping thedensity model space to the gravity data space, is constructed.For example, an entry in the sensitivity matrix characterizinghow the gravity observation at a point (x0, y0, z0) is affectedby a prism located at (x, y) is calculated with the followingequation [e.g., Rama Rao et al., 1999]:

g x0; y0; z0; x; y$ % " # !U x0; y0; z0$ %!z0

" # !!z0

ZZZGr$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

x# x0$ %2 ) y# y0$ %2 ) z# z0$ %2q dxdydz

" #Gr z# z0$ %atan x# x0$ % y# y0$ %

z# z0$ %$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$x# x0$ %2 ) y# y0$ %2 ) z# z0$ %2

q

0

B@

1

CA) y# y0$ % ln x# x0 )$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$x# x0$ %2 ) y# y0$ %2 ) z# z0$ %2

q% &8><

>:

) x# x0$ % ln y# y0 )$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$x# x0$ %2 ) y# y0$ %2 ) z# z0$ %2

q% &9=

;x2x1

y2y1

z2z1 $3%!!!

!!!!!!

Figure 2. Radial gravity anomalies associated with thecrust and mantle heterogeneity, as well as the SPLD (mGal).


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where the prism is bound by x1, x2, y1, y2, z1, z2. Each row inthe sensitivity matrix, also called a sensitivity kernel, char-acterizes how the gravity at an observation point is affectedby all the prisms. Figure 3 shows an example of the kernel.We can see that the gravity anomaly is most sensitive to themass beneath it, and the sensitivity decreases rapidly topoints that are displaced laterally from the vertical projectionof the observation point. The calculation indicates that for anobservation point about 4 km above the SPLD the sensitivityhas decreased to around 1/50 of the maximum value at ahorizontal distance less than 100 km away from the sourceof the anomaly. Therefore, the gravity anomalies that origi-nate from the SPLD have localized origins horizontally.[12] The inversion will be affected by errors in the

observed gravity data, errors in the basal topography of theSPLD, and errors in the modeled Moho topography, as wellas density anomalies within the crust or mantle. Therefore,we need to implement smoothness and deviation constraintsin our inversion. The inverse problem can now be written byminimizing the following expression:

min Am# dk k) a2 Lmk k) b2 m# m0k k' (

: $4%

The first term above is the L-2 norm between the syntheticand observed data, where A is the sensitivity matrix calcu-lated by equation (3), m is the model density distributionwithin SPLD for which we invert, and d is the gravityanomaly observation. The second term is the modelsmoothing term, where a2 is the weighting factor and L is afive-point Laplacian operator matrix, which calculates thesecond derivative using four neighboring points: left-center,right-center, up-center, and down-center. The second termpenalizes the density roughness of neighboring points,leading to a smoother model and more realistic representa-tion of the density variations within the SPLD than wouldotherwise result. The last term controls the deviation of ourmodeled density from a reference model m0 of uniformdensity, where b2 is a weighting term. Here m, d and m0 arevectors. The constant density model of 1200 kg/m3 [Zuberet al., 2007a] for SPLD is chosen as our reference model.We first choose a2 = 1 ! 10#4 and b2 = 1 ! 10#3 for theinversion here, and the influence of the parameter choice onthe inversion result will be discussed later in the paper. Inleast squares sense, equation (4) can be rewritten:

ATA) a2LTL) b2I) *

m " ATd ) b2I m0; $5%

where I is the identity matrix. We then invert for the densityanomaly using equation (5). The residual gravity anomaliesafter correcting for the topography along the crust and Mohoconsist of two parts: gravity anomalies from the SPLD andgravity anomalies from crust and mantle heterogeneities.Neglecting the effects of crustal and mantle heterogeneity,the results of this inversion are shown in Figure 4. InFigure 4a we see that the variation of density in SPLD isquite large, ranging from about 500 to about 2400 kg/m3.The high and low extremes in this density distribution areunlikely for a deposit composed primarily of water ice, andwould require portions of the deposits to have column-averaged porosities approaching 40% or to be composedpredominantly of rock, respectively.[13] This large variation in density results in part from the

neglect of the contribution of crust and mantle hetero-geneities to the residual gravity anomalies. Figure 4b showsthe residual gravity anomalies after the hypothesized con-tribution from the SPLD has been removed. In Figure 4b we

Figure 3. Sensitivity kernel of the inversion for an obser-vation point above the SPLD. The area size shown in thisfigure is the same as in Figure 1. The full width at half max-imum (FWHM) is about 70 km.

Figure 4. Inverted density distribution without removing anomalies arising from crust and mantle hetero-geneities. (a) Inverted density distribution of the SPLD (kg/m3); (b) residual gravity anomalies after theSPLD removed (mGal); (c) correlation between the SPLD thickness and density.


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find that residual gravity anomalies within the SPLD are“over-removed” so that the anomalies originating from crustand mantle heterogeneities or errors in the measured gravityfield are inconsistent in magnitude inside and outside theSPLD. Assuming that the gravity anomalies from the crustand mantle or from errors in the data exist and are similar inmagnitude throughout this area, this suggests that gravityanomalies arising from non-SPLD sources are considered asanomalies arising from within the SPLD, and are mistakenlyused to invert for the density variations of the SPLD. In otherwords, gravity anomalies that actually result from heteroge-neity in the crust and mantle are modeled as arising fromdensity variations within the SPLD. The non-SPLD anoma-lies could bias the density distribution from our inversion.Figure 4c shows the correlation between the SPLD thicknessand SPLD density. The correlation coefficient is quite small(#0.1176), suggesting that the modeled density variationsdo not correlate with the observed properties of the SPLDthough this is in part a result of the large scatter in densitiesdiscussed above.

2.4. Removing Anomalies Originating From Crustand Mantle Heterogeneities[14] As discussed in the previous section, the gravity

anomalies over the SPLD may originate in part from densityvariations within the crust and mantle, departures from thebest fit degree of compensation, or errors in the gravity data,and we must remove these contributions before the trueSPLD density can be recovered. Here we use the gravityresiduals outside the SPLD to construct a Wiener filter tocharacterize the spectral nature of the residual gravityanomalies outside the SPLD that likely have a source in thecrust or mantle. We adapted the approach of Pawlowski andHansen [1990], and briefly describe our procedures asfollows.[15] There are two assumptions in the processing: 1) the

spectral features of anomalies originating from the SPLD aredifferent from those originating from the crust and mantle;and 2) the crust and mantle heterogeneities are consistentand uniform across the region of study, inside and outsidethe SPLD. The Wiener’s optimum filter theory in theapplication of gravity anomaly separation is to find a filterthat minimizes the mean square error between the desiredanomaly and actual output anomaly. The optimal Wienerfilter is found by:

minimize < gs x; y$ % # g x; y$ %#h x; y$ %j j2 > $6%

where gs is the desired anomaly (in our case the gravityanomalies from the crust and mantle heterogeneities), g isthe gravity observation, (the combined anomalies from crustand mantle heterogeneities as well as the SPLD), and h is theoptimum Wiener filter. The “*” here denotes the spatialconvolution. The angular bracket denotes the mathematicalexpectation value of the contained function.[16] The optimum filter h that satisfies equation (6) can be

rewritten in the wave number domain as:

H$u; v% " < Gs u; v$ %G* u; v$ % >< G u; v$ %G* u; v$ % >

$7%

where G(u,v) is the Fourier transform of g(x,y), Gs(u,v) is theFourier transform of gs(x,y), and H(u,v) is the Fouriertransform of h(x,y). The asterisk denotes the complex con-jugate. Assuming that the gravity anomalies from the SPLDare not correlated with the anomalies arising from crustaland mantle heterogeneities, and the gravity field is stationary(the spectral features remain unchanged from one area toanother) and ergodic (in spite of the fact that we only haveone measurement of the gravity field, we can estimate itsmathematical expectation), equation (7) can be simplified as:

H$u; v% $ Gs u; v$ %j j2

G u; v$ %j j2: $8%

To stabilize the signal separation, we further assume theanomaly is radially isotropic, and now the Wiener filter iswritten as:

H$u; v% $ Gs f$ %j j2

G f$ %j j2; where f "

$$$$$$$$$$$$$$$u2 ) v2

p: $9%

To obtain Gs, we assume crustal and mantle heterogeneityexist similarly across the whole region both beneath andaround the SPLD. Under this assumption, we use the gravityanomalies around the SPLD to construct Gs. Therefore, theWiener optimum filter is calculated in terms of gravityanomalies surrounding the SPLD (Gsurrouding), and thecombined gravity anomalies from both the crust and mantleheterogeneities and the SPLD (G). Additionally, an areacorrection factor Ac, which accounts for the area ratio of thesurrounding area and the whole area of interest, is incorpo-rated to correct the amplitude of the filter. The filter then canbe expressed as:

H$u; v% $Gsurrounding f$ %!! !!2!Ac

G f$ %j j2: $10%

[17] Before applying this to the data, we first use a syn-thetic test to demonstrate the necessity of regularization andfiltering. Amodel SPLDwith an average density of 1200 kg/m3

is used to generate the synthetic gravity. The topography andbasal relief here is the same as the real SPLD. Within thismodel SPLD, a high-density anomaly block of 1450 kg/m3 issurrounded by materials with a density of 1100 kg/m3

(Figure 5a). Its gravity signal is shown in Figure 5b. A radi-ally isotropic background noise (Figure 5c) with amplitudeabout 50 mGal and correlation length close to the observednoise originating from the crustal and mantle heterogeneitiesis added to generate a synthetic gravity model (Figure 5d).Comparing Figure 5d with Figure 4a, we consider that thissynthetic test has similar noise amplitude and pattern as inthe real case.[18] The inverted density model without filtering short

wavelength gravity signals is shown in Figure 5e. Thismodel is heavily biased due to the background noise, and wecannot draw any firm conclusion regarding the density dis-tribution from the inverted model. The inverted densitymodel using the Wiener filtered gravity signal is shown inFigure 5f. It is clear that the majority of the background noisehas been successfully removed, and the reconstructed modelshows a quite similar pattern of density variation as the truedensity model (Figure 5a). In comparison, an inversion


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without regularization and filtering easily yields a densityroot mean square error (RMSE) exceeding 500 kg/m3; aninversion with regularization but without filtering yields adensity RMSE of &180 kg/m3; an inversion with both reg-ularization and filtering yields a density RMSE of only&100 kg/m3. A test inversion of synthetic data representinga uniform density SPLD with the same regularization shows

a density RMSE of &50 kg/m3. This means that certain biasin density inversion is inevitable with regularization assmoothing and damping (from the mean density constraint)are enforced. Still, we need to use regularization in theinversion, or much larger RMSE in density would otherwiseoccur. The conclusion from the synthetic test is that using aregularized inversion subsequent to Wiener filtering, we can

Figure 5. Synthetic test for regularized inversion with Wiener filtering. (a) Model SPLD with averagedensity of 1200 kg/m3. The density ranges from 1100 kg/m3 to 1450 kg/m3; (b) gravity signal (mGal) asso-ciated with the model SPLD; (c) background gravity noise (mGal) with a peak amplitude &50 mGal andcorrelation length similar to the real case; (d) noisy synthetic gravity signal (mGal) by combing Figures 5band 5c; (e) regularized inversion without filtering first to remove short wavelength signals (kg/m3);(f) regularized inversion with Wiener filtered gravity signal (kg/m3).


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reliably extract the density distribution from the data withstrong noise.

3. Results

3.1. Density Inversions for the SPLD[19] We then apply this methodology to the real data. The

Wiener filter is shown in Figure 6a. Applying the Wiener

filter to the gravity anomalies in Figure 4a, we can separatethe anomalies originating from crustal and mantle hetero-geneities, which are shown in Figure 6b. Here we see that, aswe assumed, the anomalies due to crust and mantle hetero-geneities are present throughout this entire region. Thecontinuity of anomalies across the border of the SPLD sug-gests that the Wiener filter has successfully predictedanomalies from crust and mantle sources within the SPLD

Figure 6. Inversion results from Wiener filtered gravity anomalies. (a) Wiener filter in wave numberdomain; (b) Wiener filter output of gravity anomalies originating from crust and mantle heterogeneities(mGal); (c) gravity anomalies from the SPLD, after anomalies from the crust and mantle heterogeneitiesare removed (mGal); (d) density distribution of the SPLD (kg/m3); (e) Residual anomalies (mGal);(f) correlation between the SPLD thickness and density.


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that are consistent in magnitude and distribution with thoseoutside the SPLD. Figure 6c shows the separated gravityanomalies originating from the SPLD. It should be noticedthat there are some long wavelength features remainingoutside the SPLD. These result because in constructing theWiener filter, we assumed that the distribution of the crustaland mantle anomalies are uniform and radially isotropic,which is only an approximation. Therefore, the removal ofanomalies from crust and mantle heterogeneities is actuallyan averaged removal. After the filtering, the signature of theSPLD dominates the residual anomaly, and we are then ableto invert for the density distribution within the SPLD.[20] Figure 6d shows the density distribution within

SPLD. The density ranges from &600 to &1350 kg/m3,which is much narrower range than that without removal ofcrust and mantle anomalies (&500 to 2400 kg/ m3) with thesame constraint parameters. The reason for the lower densityin this solution (&600 kg/m3) will be discussed in detaillater. We note that the density around the marginal area ofthe SPLD appears higher than the density in the central area.It should be noted that the high density anomaly is notcaused by our inversion method, as the synthetic test hasdemonstrated the absence of such an anomaly if the densityis not indeed higher. After plotting the density as a functionof the SPLD thickness, we find a significant inverse corre-lation (P value #0.75, Figure 6f). This suggests that thickerregions of the SPLD may contain less dust, a lower fractionof CO2 ice relative to H2O ice, or a greater porosity. Incomparison, Grima et al. [2009] found that the marginalareas of Gemina Lingula in the NPLD have higher real andimaginary values of dielectric constant in radar soundingdata, implying higher dust content in the PLD ice at themargins than in the thicker interior sections.[21] We also note that densities are higher in the vicinity

of 270* longitude (toward the left of the SPLD in Figure 6),and also the gravity residuals are higher in that directionoutside of the SPLD (Figures 6d and 7e). The correlation ofthese residuals outside the SPLD with the Dorsa Argenteaformation (DAF) [Carr, 2006] suggests that the higherSPLD densities may also be explained in part by the possibleextension of the DAF beneath the SPLD. Carr [2006] sug-gests that the DAF is actually an ancient, ice-rich polardeposit, analogous to the deposits that are at the pole today,and the numerous pits on the DAF are interpreted as evi-dence of basal melting of the ground ice [Head and Pratt,2001; Ghatan et al., 2003; Ghatan and Head, 2002, 2004;Milkovich et al., 2002]. A higher silicate fraction within thismore ancient deposit is likely, which would contribute to thelarger gravity and density anomalies in this portion of theSPLD if the DAF was penetrated by the radar and includedwith the SPLD in the inversion. These studies also recog-nized the presence of small volcanoes in that area. Anothersmall volcano at 73*S, 342*E with radially elongate pits onits flanks and irregular pits provides additional direct evi-dence of a connection between volcanism and the pits in theDAF. Volcanic loading in this area would contribute to thepositive gravity anomalies beyond the typical backgroundvariability that could be erroneously interpreted by theinversion as greater density ice in the overlying SPLD.Alternatively, the DAF is young relative to the ancientNoachian crust, and therefore likely has a significant com-ponent of flexural support. If DAF spreads extensively

beneath the SPLD, its thickness may vary with location, withthe thickest part close to 270* longitude. Also, if this mate-rial was not penetrated by the radar, then this state of litho-spheric support would result in higher residual anomalies inthis area after applying the best fit degree of compensation[Zuber et al., 2007a] to calculate the Moho relief and sub-tracting the anomalies arising from the surface topographyand Moho.[22] We also note that some parts within the SPLD are

predicted to have anomalously low densities (&600 kg/m3).This might result from short wavelength positive gravityanomalies within the SPLD region that actually come fromthe SPLD itself (e.g., arising from thickness variations of theSPLD), but were treated as originating from the crust ormantle by the Wiener filter and therefore removed. In otherwords, the gravity signal originating from the crust andmantle is not totally separable from the signal from theSPLD (e.g., the synthetic test in Figure 5). It is also possiblethat the pattern of the crust and mantle heterogeneityunderneath the SPLD does not match the overall radiallyaveraged anomaly spectrum in this region (e.g., the hetero-geneity may not be radially isotropic, or there exist real andunpredictable differences between the crust beneath theSPLD and that outside of it). In either of these two cases, thefilter cannot work perfectly, and may result in some errors inthe short wavelength gravity signal separation. Nevertheless,the remaining long wavelength gravity signal (Figure 6c)and the large-scale structure and density distribution of theSPLD (Figure 6d) should be reliable.

3.2. Robustness of Inversion and Filtering[23] We now address the influence on the results of the

choice of inversion parameters a2 and b2 in equation (4).Here, a small a2 results in weak spatial coherence in density,i.e., more roughness in the density model, while a larger a2

results in greater smoothness in the inverted model. Simi-larly, a small b2 allows large deviations from the referenceconstant density model, while larger b2 results in a strongerresemblance between the inverted result and the referencemodel. Figure 7 shows the influence of a2 and b2 on severalkey descriptors of the model output. All the computationshere are performed assuming the reference density m0 is1200 kg/m3 [Zuber et al., 2007a]. The root mean square(RMS) of gravity anomaly residuals within SPLD(Figure 7a) is small when the constraints are loose (i.e., a2

and b2 are small). However, this choice of parameters causesthe inversion to over-fit the gravity anomalies, and makesthe RMS within the SPLD much smaller than the RMSoutside the SPLD (&13 mGal, mainly consisting of longwavelength features). Also, the inversion then yields theunphysical result of negative minimum densities (Figure 7c),and very large maximum density (Figure 7d). In general, weprefer to use a larger b2(&10#3) in the inversion for thefollowing reasons: 1) smaller b2 results in a negative mini-mum density, which means the inversion is still overlyaffected by the remaining noise; and 2) the mean density(&750 to 1000 kg/ m3) for smaller b2 models is contradic-tory the previous studies [Zuber et al., 2007a; Wieczorek,2008]. We conclude that smaller b2 inversions are not geo-logically realistic, as the predicted large density variationsare not supported by the fact that the SPLD is mainly com-posed of layered deposits and the density changes from one


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Figure 7. Dependence of RMS of gravity residuals, mean, minimum and maximum density and the cor-relation coefficient on inversion constraint parameters a2 and b2. The white star indicates the defaultvalues for a2 and b2 in the real data inversion. (a) RMS of the residual gravity anomalies (mGal); (b) meandensity (kg/m3) of the SPLD; the contour line “917” indicates the density of the pure water ice, and thecontour line “1095” indicates the density of the water ice with 10% dust content; (c) minimum density(kg/m3) of SPLD; the contour line “0” indicate zero density; (d) maximum density (kg/m3) of SPLD;(e) correlation coefficient of SPLD; (f) correlation coefficient under the constraints a2 = 1 ! 10#5 andb2 = 1 ! 10#2.


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place to another should be more moderate. The upper-half ofthe a2-b2 descriptor space is more meaningful and thereforepreferred in the inversion.[24] Figure 7e shows that the correlation between the

SPLD thickness and density becomes stronger when b2becomes larger. Significantly, the correlation coefficient isnegative over the vast majority of the parameter space con-sidered, demonstrating that the inverse relationship betweenSPLD thickness and density is a robust result. We showanother correlation plot in Figure 7f where a2 equals to 1 !10#5 and b2 equals to 1 ! 10#2. The correlation coefficientis #0.78, indicating a strong inverse relationship betweenthe SPLD thickness and its density distribution.[25] We also study the dependence of the several afore-

mentioned parameters on the initial reference density m0.The results are shown in Figure 8. Figure 8a shows thedependence of the RMS of gravity anomaly residuals withinthe SPLD on m0. There is a positive correlation betweenthese two parameters, but the variation of RMS is not

significant. Figure 8b shows that the maximum, minimumand mean densities also have a positive correlation with m0,as would be expected. We note that the variation of the meandensity is small compared to that of the reference density,e.g., the mean density varies from&870 kg/m3 to 1300 kg/m3

when m0 changes from 900 kg/m3 to 1500 kg/m3. Thisindicates that the mean density converges to a small rangeeven if our reference model could have a larger range ofplausible values. Figure 8c shows the correlation coefficienthas a negative dependence on m0, and it is sensitive to thevalue of m0. However, negative correlation coefficients arecalculated from all cases. Figure 8d shows the correlationbetween the SPLD thickness and its density when m0 =1600 kg/m3.[26] We next study how the Wiener filter approximation

for representing the gravity anomalies within the SPLDarising from crustal and mantle heterogeneity would affectthe final inversion result. We perturb the amplitudes of ourfilter by multiplying it with a Gaussian noise function that

Figure 8. Dependence of RMS of gravity anomaly residuals, mean, minimum, and maximum density,and correlation coefficient on reference density m0. (a) RMS of residual gravity anomalies on m0 (mGal);(b) mean, minimum, and maximum density on m0 (kg/m

3); (c) correlation coefficient on m0; (d) correla-tion at m0 = 1600 kg/m3

.


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has a standard deviation of 1/10 the magnitude of the coef-ficients. These inversions assume a2 = 1 ! 10#4 andb2 = 3 ! 10#3 and m0 = 1200 kg/m3. We performed 1000inversions using the perturbed filter to obtain a viable sta-tistical sample. The RMS of the gravity anomaly residualswithin the SPLD has a mean of 9.7 mGal, and a standarddeviation of 0.20 mGal. The mean density has a mean valueof 1138.2 kg/m3, and a small standard deviation of 4.7 kg/m3.The maximum and minimum densities have mean values of1384.2 + 37.0 kg/m3, and 591 + 14.2 kg/m3, respectively.The correlation coefficient also has a weak dependence onthe inaccuracy of coefficients of the filter. We find a verysmall standard deviation of 0.03 and a mean value of #0.74.This indicates that a strong inverse correlation between theSPLD thickness and density will still hold even if we cannotconstruct a completely accurate filter to remove the gravityanomalies originating from the crust and mantle hetero-geneities. In general, we find that the dependence of thedensity and its correlation coefficient on the Wiener filter isnot particularly strong. That is to say, even if we introducedsome errors in constructing the Wiener filter by assumingradial average or assuming there is no spectral correlationbetween the gravity anomalies arising from the SPLD andthe crust and mantle heterogeneities, the inversion result isstill robust and reliable.

4. Discussions and Conclusions

[27] In this paper, we investigate the density distributionwithin the south polar layered deposits of Mars. We find aninverse correlation between the thickness of the SPLD andits density, which suggests higher dust concentration in themarginal areas of the deposits. This phenomenon might beexplained by the fact that the marginal area is located atlower latitude and thus has experienced more sunlight and ahigher ambient temperature, which may result in more icesublimation and higher residual dust. Katabatic winds couldalso conceivably contribute to volatile erosion in these areas.Our result agrees with that of Grima et al. [2009], whichimplied higher dust content at the margins of the NPLD. Wealso find that there exist positive gravity anomaly residualsassociated with the Dorsa Argentea formation (DAF). Theseanomalies could arise due to either flexural support of theDAF, or magma intrusions within the crust in this region, assuggested by melting pits and small volcanoes on top ofsome pits. The high density of magma compared to thesurrounding crust material may explain the positive gravityanomalies we have observed. We also test the influence ofthe inversion parameters as well as some possible inaccuracyof the filter coefficients on the inverted model, and find theconclusions to be robust.[28] We have noted that in the Ultimi Lingula region

(150*E, 73*S) the inverted densities are relatively lower.When we compared the regularized inversion results with(Figure 6) and without (Figure 4) the filtering, we find thatthis region always has relatively lower densities. Excessiveporosity of SPLD in this region or disproportional anomaliesarising from the crust or mantle underneath that cannot becompletely removed by filtering may be reasonable expla-nations, but there are also some artifacts in our processingthat may lead to this anomalous result: 1) The removal ofthe gravity anomalies associated with crust and Moho

topography by equation (2) introduced some unwantednoises, as we assumed constant density for the crust andmantle, as well as the uncertainties in the radar imaging ofthe basal unit and the estimated Moho relief [Zuber et al.,2007a]; 2) our filter assumes the gravity signal from theSPLD and other sources are largely spectrally separable, butfor some regions this may not be the case and the filterincidentally removed the gravity feature associated with theSPLD (e.g., Ultimi Lingula has very outstanding thicknesscompared to other surrounding SPLD areas and thereforemay raise spectrally similar gravity signals compared to thegravity anomalies arising from crust and mantle).[29] Recent work [Phillips et al., 2011] demonstrated the

existence of a large CO2 reservoir within the SPLD, asso-ciated with a reflection free zone observed by the SHARADradar sounder. This CO2 ice layer has a maximum thicknessof &672 m, with a mean of &200 m (rco2 = 1589 kg/m3).The maximum CO2 thickness approximately coincides withthe maximum SPLD thickness and the minimum densitypredicted by our inversion. The presence of this CO2 ice hasthe effect of increasing the depth to the base of the SPLDrelative to the model of Plaut et al. [2007], which assumed ahigher dielectric constant appropriate for water ice. Thiswould increase thickness of the SPLD by up to 200 m[Phillips et al., 2011], which would decrease the predicteddensity from the inversion model by &10%. The change inbasal topography would also impact the modeled gravityanomalies arising from the crust and mantle, increasing thegravity anomalies attributed to the SPLD and the resultingdensity by a lesser amount. The net effect of accounting forthe presence of this CO2 ice in the inversion would be theprediction of a lower density in this region, which alreadylies in a predicted density low. This is counter to ourexpectations, as CO2 ice has a greater density than water ice.However, a CO2 ice thickness of 500 m within a 2500 mthick section of the SPLD would increase the density byonly &100 kg/m3 relative to a pure ice cap. By comparison,contamination of water ice with 10% dust at a density of2500 kg/m3 would increase the density by 160 kg/m3, whilea 10% porosity would decrease the density by 90 kg/m3. Thepredicted inverse correlation of density with SPLD thicknessin our results suggests that the increased dust content towardthe margins of the SPLD has a greater effect on the meandensity distribution than the CO2 ice within the SHARADreflection free zone.[30] In addition to being the largest surface reservoir of

water on Mars [Zuber et al., 2007a], the south polar layereddeposits provide an important record of the recent climate ofMars. The density variations and inferred variation in dustcontent derived from this geophysical inversion of gravity,topography, and radar data provide important information onthe composition of the deposits. This added information canbe used in conjunction with the stratigraphy of the depositsfrom both surface and subsurface mapping [Fishbaugh andHead, 2000; Carr, 2006; Seu et al., 2007; Phillips et al.,2008; Byrne, 2009] in trying to reconstruct the recent cli-mate and volatile history of Mars.

Appendix A: Influence From Permittivity Variation

[31] On the basis of our inversion, the density distributionof the SPLD is consistent with a mixture of water ice and a


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denser material that is likely to be silicate dust. The per-mittivity of the SPLD is affected by the dust content as wellas the permittivity of the dust grains, which in turn affectsthe thickness of the SPLD calculated from MARSIS. In aprevious study of the structure of the SPLD using MARSISdata [Plaut et al., 2007], a constant permittivity ! = 3 wasassumed to convert the time delay in radar sounding todepth. As indicated in our results, the SPLD is not pure ice,thus a constant permittivity of ice (! = 3) may not yield thecorrect thickness of the SPLD. Here we performed asequential inversion to determine jointly the best fit density,permittivity, and thickness correction for the SPLD. Theinversion process is as follows:[32] 1) Invert for the best fit SPLD density distribution

using the methodology developed in this work;[33] 2) Calculate the equivalent permittivity for the dusty

ice as a function of the spatially varying density. The per-mittivity is calculated using a mixing model [Phillips et al.,2008], assuming a mixture of ice with either silicate dust orair, for densities above and below that of pure water ice,respectively.[34] 3) Correct the SPLD basal topography and thickness

with the updated equivalent permittivity and then correct theMoho relief;[35] 4) With the updated SPLD thickness model, repeat

from 1) until the sequential inversion converges.[36] We tested three different values for the permittivity of

the dust, namely 5, 7 or 9, representing a likely range for thesilicate inclusions [Nunes and Phillips, 2006]. Note if the

density is less than that of the pure ice (917 kg/m3) porousice with vacuum inclusion is assumed [cf. Phillips et al.,2008].[37] Figure A1 shows the density, equivalent permittivity

and basal relief uplift of the SPLD after the sequentialinversion. It is found that the influence of the permittivityvariation on the SPLD density is small, mainly because weassumed the crust is in partial Airy compensation (equation (1))and the gravity anomaly arising from the basal topographyhas been compensated at the Moho. The uncertainty in SPLDthickness due to variation in permittivity has been previouslydiscussed by Plaut et al. [2007], who estimated this uncer-tainty to be less than 10%. In this joint inversion of thegravity and radar data, with the change of the basal reliefgenerally being less than 150 m, the full range of change inbasal relief of &500 m for the !dust = 9 case corresponds to afew to few 10 s of percent of the SPLD thickness. For the!dust = 7 case, the mean and standard deviation of the SPLDpermittivity are 3.48 and 0.27, and the RMS change in den-sity relative to the baseline model is less than 5%. Our esti-mates of uncertainty are generally consistent with those ofPlaut et al. [2007]. In all models, the same patterns of highand low density hold. Therefore, our previous discussions arestill valid in spite of the permittivity variation in the dusty ice.

[38] Acknowledgments. We thank Sue Smrekar and Shane Byrne forreviewing and giving constructive comments to improve our paper. We alsothank Editor Mark Wieczorek for providing helpful comments on our paper.The work was supported by the NASA Mars Reconnaissance Orbiter RadioScience Gravity investigation.

Figure A1. Final distributions of density, permittivity and basal relief correction of the SPLD after thesequential inversion. The three columns are the results when the permittivity of the silicate inclusion is5, 7, and 9, respectively. The first row is the density (kg/m3); the second row is the equivalent permittivity;the third row is the uplift of the basal topography of the SPLD (m) due to the permittivity correction(positive value means upward lifting).


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Density variations within the south polar layered deposits ...Density variations within the south polar layered deposits of Mars Junlun Li,1 Jeffrey C. Andrews-Hanna,1,2 Youshun Sun,1