Geophysical Limitations on the Erosion History within Arabia … · Geophysical Limitations on the Erosion History within Arabia Terra, Mars-need reference for crustal thickness model

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,

Geophysical Limitations on the Erosion History within ArabiaTerra, Mars-need reference for crustal thickness modelA. J. Evans, J.C. Andrews-Hanna*† , and M.T. Zuber

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

Abstract. The Arabia Terra region, an area of ∼1×107 km2 lying south of the hemisphericdichotomy boundary and centered at (25E, 5N), is a unique physiographic province with to-pography and crustal thickness intermediate between those of the southern highlands and north-ern lowlands. Previous workers have identified numerous morphological indicators suggestiveof erosion. Using altimetry data returned by the Mars Orbiter Laser Altimeter (MOLA) on theMars Global Surveyor (MGS) along with gravity data from the Mars Reconnaissance Orbiter(MRO), we place geophysical constraints on the amount of erosion permitted within ArabiaTerra. Admittance estimates using a multi-taper, spatiospectral localization approach providea best-fit to the observations through degree 50 at a lithosphere thickness of 15 km. The el-evation difference between Arabia Terra and the highlands would require as much as 5 kmof erosion in certain areas to yield the current topography, neglecting the effects of subsequentflexure. However, incorporating flexural rebound requires substantially more erosion, up to 25km, in order to reproduce the elevation and crustal thickness deficit of Arabia Terra. Such alarge amount of erosion would result in exterior flexural uplift exceeding 1 km and gravityanomalies exceeding observations by ∼80 mGal. Consequently, it is unlikely that Arabia Terrawas formed from surface erosion alone. We determine that no more than 3×107 km3 of ma-terial could have been eroded within Arabia Terra, while 1.7 × 108 km3 of erosion is requiredto explain the observed crustal thickness.

1. Introduction

Arabia Terra, with an area of 1×107 km2 centered at (25E, 5N),is an anomalous region along the Martian dichotomy. Tradition-ally considered part of the ancient southern highlands [e.g. Scott &Tanaka 1986 [@]; Greeley & Guest 1987 [@]; McGill & Squyres1991 [@]; Frey et al. 1998 [@]], Arabia Terra provides a moregradual transition from the southern highlands to the northern low-lands in both topography [Smith et al. 1999 [@]; Smith et al. 2001[@]] and crustal thickness [Zuber et al. 2000 [@]; Neumann etal. 2004 [@]]. While the geological processes leading to the for-mation of the region have not been clearly identified [e.g. Kiefer2005 [@]], Arabia Terra contains morphological evidence indica-tive of surface erosion including isolated mesas [Hynek & Phillips2001 [@]; Malin & Edgett 2000 [@]] and partially degraded craters[Craddock et al. 1997 [@]]. Though surface modification hasbeen suggested for the entirety of the highlands [e.g. Craddock& Maxwell 1993 [@]], the anomalous nature of Arabia Terra andits geomorphology may indicate preferential erosion of the region.The amount of erosion may have generated a significant volume ofsediment, possibly contributing to the resurfacing of the northernlowlands.Though previous workers have attempted to constrain the amountof erosion for Arabia Terra and the southern highlands, in general;

*Now at Department of Geophysics, Colorado School of Mines,Golden, Colorado, USA.

†Also at Southwest Research Institute, Boulder, Colorado,USA.

Copyright 2009 by the American Geophysical Union.

0148-0227/09/$9.00

much of the analysis has been based on crater degradation withanywhere between 200 m to 2300 m of material being eroded, asput forth by Craddock & Maxwell 1993 [@]. Hynek & Phillips2001 [@] approached the problem from an alternative geomorphicperspective: using the height of local elevation maxima (isolatedmesas) in concert with the mapping of geological units. Their anal-ysis indicates that a minimum of 1000 m of material was removedfrom the Arabia Terra region in the late Noachian. Recent analysisof data from the Mars Exploration Rover landing site at MeridianiPlanum within Arabia Terra suggests smaller amounts of erosionhave occurred since ∼3.0 Ga, though evidence for this erosion isfound on sedimentary deposits that lie above the original surfaceand thus does not constitute net loss [Golombek et al. 2006 [@]]. Ithas generally been suggested that erosion during the Noachian andearly-mid Hesperian may have been greater due to a warmer andwetter environment [Craddock & Maxwell 1993 [@]; Golombek etal. 2006 [@]]. However, widespread layered deposits across the re-gion suggest an early period of deposition as well [Fassett & Head2007 [@]; Moore 1990 [@]].Prior analyses of erosion in Arabia Terra [Hynek & Phillips 2001[@]] relied on the geomorphology of the terrain and craters. In thispaper, we present our constraints for the erosion of Arabia Terrabased on geodynamical modeling coupled with limitations estab-lished from topography and gravity data returned by the Mar Or-biter Laser Altimeter (MOLA) [Zuber et al. 1992 [@]; Smith et al.1999 [@]] on the Mars Global Surveyor (MGS) [Albee et al. 2001[@]] and the gravity field investigation on the Mars Reconnais-sance Orbiter (MRO) [Zurek & Smrekar 2007 [@]], respectively.By comparing the expected flexural response and gravitational sig-nature [Turcotte et al. 1981 [@]] of various erosional loads to theobservational data, we establish an upper limit on the amount ofmaterial that could have been removed from within Arabia Terra.We employ a lithospheric flexure model [Turcotte et al. 1981 [@]]to attain the flexural rebound and gravitational signature associatedwith a given erosional load. Exploiting recent advances in spher-ical harmonic localization techniques [Simons, Dahlen, & Wiec-zorek 2006 [@]; Wieczorek & Simons 2005 [@]; Wieczorek 2006

1

X - 2 EVANS ET AL.: GEOPHYSICAL LIMITATIONS ON EROSION WITHIN ARABIA TERRA

[@]], we better constrain the elastic lithosphere thickness [McGov-ern et al. 2002 [@]] – a crucial parameter in resolving the flexuralresponse to erosion. Our flexure model, based upon the thin elas-tic shell method of Turcotte et al. 1981 [@], estimates the mem-brane and bending stresses for a load supported by an elastic litho-sphere underlain by a fluid-like medium. We test the viability ofseveral erosional scenarios, including loads capable of reproducingthe unique topography and crustal structure of Arabia Terra froman initial highlands-like topography.

2. Methodology2.1. Spherical Harmonic Localization

Any square-integrable function defined on a spherical surface canbe expanded as a linear combination of spherical harmonics [Wiec-zorek 2007 [@]] by

f(Ω) =

∞Xl=0

lXm=−l

flmYlm(Ω), (1)

and

flm =

ZΩ

f(Ω)Ylm(Ω)dΩ, (2)

where Ω is the solid angle, and Ylm is the spherical harmonic basisfunction of degree l and order m.We apply a method for spatio-spectral localization on a sphere, inwhich data is localized to an arbitrarily-shaped region of interestby applying a family of orthogonal spherical harmonic tapers [Si-mons 2006 [@]; Simons, Dahlen, & Wieczorek 2006 [@]] . Ul-timately, we apply this localized spectral analysis within ArabiaTerra to attain the regional elastic thickness at the time of forma-tion. To spatially concentrate a bandlimited function, f(Ω), withinan arbitrarily-shaped region, R, we maximize the energy concen-tration, λ, according to

λ =

RRf(Ω)2dΩR

Ωf(Ω)2dΩ

= maximum, (3)

within the region, R where 0 ≤ λ ≤ 1. By use of Eq. (2), we canrewrite (3) as

λ =

LwinXl=0

lXm=−l

flm

LwinXl′=0

l′Xm′=−l′

Dlm,l′m′fl′m′

LwinXl=0

lXm=−l

f2lm

, (4)

where

Dlm,l′m′ =

ZR

Y′m(Ω)Yl′m′(Ω) dΩ, (5)

and Lwin is the bandwidth of the localization (window). Each de-gree, l, receives contributions from across the range l − Lwin ≤l ≤ l + Lwin. Hence, our choice for the window bandwidth re-stricts the resulting localization, such that the following inequalityholds for all degrees, lloc, of the windowed field, Lwin ≤ lloc ≤Lobs−Lwin, where Lobs is the maximum expansion degree of thedata set being considered.As shown by Simons, Dahlen, & Wieczorek 2006 [@], Equation(4) reduces to a matrix eigenvalue equation where the eigenfunc-tions of a kernel given by Dlm,l′m′ are spherical harmonic coeffi-cents of the space concentrated tapers [e.g. Wieczorek & Simons

Wieczorek & Simons 2005 [@]]. The result of this reduction in fullindex notation is,

LwinXl′=0

l′Xm′=−l′

Dlm,l′m′fl′m′ = λflm. (6)

The number of eigenfunctions optimally-concentrated within theregion of interest can be obtained by calculating the Shannon num-ber, N ,

N =

(Lwin+1)2Xn=1

λn = (Lwin + 1)2 A

4π. (7)

We use theN optimally-concentrated eigenfunctions to localize theregion, similarly to the method prescribed by Wieczorek & Simons2005 [@].

2.2. Loading Model2.2.1. Thin Elastic Shell AdaptationIn order to represent the effects of erosion in Arabia Terra, we ac-count for the resultant flexure and gravity signature of the erosionalload. We establish limits on the extent of regional erosion by an-alyzing these resultant signatures and comparing to observationaldata.We employ an adapted version [Johnson et al. 2000 [@]] of the thinelastic lithosphere (shell) model outlined by Turcotte et al. 1981[@]. Following Turcotte et al. 1981 [@], we introduce the dimen-sionless parameters,

τ =ETeR2g∆ρ

, (8)

and

σ =D

R4g∆ρ, (9)

whereE is Young’s modulus, Te is the elastic lithosphere thicknessat the time of loading, R is the mean radius of the shell, g is theMartian gravitational acceleration, and ∆ρ is the density contrastbetween continua below and above the shell. The mean shell radius,R, and flexural rigidity, D, can be represented as R = Rp − Te/2and D = ET 3

e /12(1 − ν2), where ν is Poisson’s ratio and Rp isthe equatorial planetary radius. The independent parameters thatwe use for the loading model are listed in Table 1.We use spherical harmonic representations of the load thicknessh, the resulting deflection w, the Martian geoid offset h, and theequipotentially-referenced, final topography bh. Relating the loadthickness and flexure in the spectral domain yields the relation-ship,

wlm = − ρL∆ρ

αlhlm, (10)

where ρL is the load (crustal) density and the transfer function,αl,

αl =

»1− 3ρm

(2l + 1)ρ

– »1

ζl− 3ρm

(2l + 1)ρ

–−1

, (11)

with ρ as the mean Martian density and

ζl=−[l(l+1)−(1−ν)]

σ[−l3(l+1)3+4l2(l+1)2−4l(l+1)]+τ[−l(l+1)+2]+−l(l+1)+(1−ν)].(12)

This formalism allows us to solve for a final topography wherebh = h + w; additionally, by substituting bh for h in Equation 10

EVANS ET AL.: GEOPHYSICAL LIMITATIONS ON EROSION WITHIN ARABIA TERRA X - 3

with the density contrast applied between the mantle and crust, wecan solve for the associated erosional load via h = bh−w.2.2.2. Geoid SolutionWe define a spherical harmonic representation of topography, H ,similarly to McGovern et al. 2002 [@] as

H(Ω) = S(Ω)−A(Ω), (13)

where S is the planetary shape and A is the Martian referencegeoid. We choose the mean planetary radius, 3389.5 km [Smithet al. 2001 [@]] as the first term of a spherical harmonic expansionof the radius similar to McGovern et al. 2004 [@] and approx-imate the deviation of the geoid from the mean planetary radiusas,

A(Ω) = 0.95S2,0. (14)

For our erosional model, a degree-1 term is included in Eq. (14) toaccount for the center-of-mass offset resulting from the erosionalload. Referencing the topography with respect to the geopotentialaccounts for the self-gravitation of Turcotte et al. 1981 [@] [e.g.McGovern et al. 2002 [@]], allowing us to apply the gravity calcu-lation demonstrated by Wieczorek & Philips 1998 [@]. Through-out our computational analysis, we consider both the shape andthe topography to ensure an accurate representation of the resultingflexure and gravity field.2.2.3. Gravity SolutionWe calculate the gravity anomalies resulting from the erosionalload and flexural deformation using the finite amplitude formula-tion of Wieczorek & Philips 1998 [@]. The gravity amomaly canbe expressed as,

∆g =GM

r2

„Rpr

«l(Csurflm + Cmoholm )Ylm, (15)

where Csurflm and Cmoholm represent the topography along the sur-face and base of the crust, respectively. However, we slightly mod-ify the solution, as described by McGovern et al. 2002 [@] forClm,

Clm =4π∆ρr3

M(2l + 1)

l+3Xn=1

nSlmrnn!

Qnj=1(l + 4− j)

(l + 3). (16)

where r is the reference radius of the Martian geoid along the den-sity interface, nSlm is the spherical harmonic representation of theplanetary shape along the interface raised to the nth power, and∆ρ is the change in density across the interface. The first term inthe above expansion represents a first-order (mass-sheet) approxi-mation of the gravity anomaly by representing the mass variationsdue to topography along the surface and Moho as an infinitesimallythin sheet. The higher order terms take into account the effectof the finite amplitude relief along two-dimensional density inter-faces. Though the first-order treatment is generally adequate, forcases of large or varying relief along a density interface, the massdistribution with depth becomes increasingly important and is ac-counted for by the summation of terms beyond n = 1. For thesurface, r = Rp and ∆ρ = ρL, whereas r = Rp − Tcrust and∆ρ = ρm − ρL along the mantle interface. Here, Tcrust repre-sents the mean crustal thickness. We list parameter values for eachinterface in Table 1.

3. Erosional Constraints within ArabiaTerra

Using altimetry data returned by the Mars Orbiter Laser Altime-ter (MOLA) [Zuber et al. 1992 [@]; Smith et al. 1999 [@]] onthe Mars Global Surveyor (MGS) [Albee et al. 2001 [@]] along

with gravity data from the Mars Reconnaissance Orbiter (MRO)[Zurek & Smrekar 2007 [@]], we place geophysical constraints onthe maximum amount of erosion for Arabia Terra. We analyze thetopography [Smith et al. 2001 [@]] and gravity [Konopliv et al.2009, in preparation [@]] in a 1resolution grid in the spatial do-main. Unless otherwise noted, we expand our spherical harmonicsfields to l = 75. We define and restrict our investigation of Ara-bia Terra to the region outlined by Figure 1. Here, we examine theunique structure of Arabia Terra and key evidence interpreted aserosional indicators.

3.1. Terrain and Crustal Thickness

The elevation [Smith et al. 1999 [@]; Smith et al. 2001 [@]] andcrustal thickness [Zuber et al. 2000 [@]; Neumann et al. 2004[@]] profiles within Arabia Terra decrease gradually to the north,in between more discrete transitions at the northern and southernboundaries of the province [Andrews-Hanna et al. 2008 [@]]. Thetopography decreases by∼5 km over a distance of 4000 km acrossArabia Terra between the northern and southern boundaries (Figure2), while the crustal thickness decreases by ∼25 km. Unlike otherareas along the Martian dichotomy, Arabia Terra is afforded a moregentle transition from the highlands to the northern lowlands in el-evation and crustal thickness as shown in Figure 3 [Smith et al.1999 [@]; Smith et al. 2001 [@]]. Though the region possessestopography and crustal thickness that are arguably more similar tothe northern lowlands [Zuber et al. 2000 [@]], recent analysis byAndrews-Hanna et al. 2008 [@] reveals the northern edge of Ara-bia Terra is continuous with the crustal dichotomy boundary, sug-gesting that Arabia Terra is, in a physiographic sense, part of thehighlands.Arabia Terra contains many inliers (local elevation maxima) andisolated mesas (fretted terrain) that have been interpreted as evi-dence for a prior, more elevated surface [e.g. Hynek & Phillips2001 [@]; Carr 2001 [@]]. In order to gauge the minimal amountof eroded material, Hynek & Phillips 2001 [@] use the local eleva-tion maxima to establish a lower bound on regional erosion. Hynek& Phillips 2001 [@] restricted their investigation to western Ara-bia Terra and Margaritifer Sinus and estimated a minimum of 4.5×106 km3 of eroded material. If distributed across Arabia Terra, thistotal amount of erosion is equivalent to a uniform erosional load of450 m.As a result of the prominence of partially degraded craters [Crad-dock & Maxwell 1993 [@]], infilled craters [Forsberg-Taylor etal. 2004 [@]] and ancient valley networks [Carr 1987 [@]], sur-face modification processes, namely erosion and deposition, havebeen proposed to have acted across the whole of the highlands[McGill 2000 [@]; Craddock & Maxwell 1993 [@]]. While par-tially degraded craters are inherent to Arabia Terra as part of thehighlands, Arabia Terra lacks a widespread presence of the ancientvalley networks characteristic of highlands terrain [Phillips et al.2001 [@]]. The absence of the valley networks and an apparentdeficit in the large surface crater population [McGill 2000 [@]],both of which are physiographic indicators of the southern high-lands, have been interpreted as increased activity of erosion anddeposition within Arabia Terra in early Martian history [Hynek &Phillips 2001 [@]]. The abundant geomorphologic evidence indi-cates a complex, yet ambiguous erosional history [Forsberg-Tayloret al. 2004 [@]; McGill 2000 [@]; Craddock & Maxwell 1993[@]; Golombek et al. 2006 [@]]. Given that it is difficult to placefirm constraints on the net volume of material eroded and removedfrom the region, we focus on the geodynamic response to evaluatethe maximum volume of eroded material that is consistent with thegravity and topography.

3.2. Gravity

Notwithstanding the geomorphic evidence for surface erosion, thegravity anomalies expected within a region of massive denudation


are not observed. However, the gravity anomalies over Arabia Terraare dominated by Tharsis’ antipodal bulge [Phillips et al. 2001[@]]. By virtue of its long-wavelength nature, we can approximatethis Arabia bulge by incorporating a degree-1 offset into our grav-ity anomaly as shown in Figure 3. Though we acknowledge thisapproximation is insufficient to remove the entirety of the gravi-tational signature associated with the Tharsis rise and its flexuralresponse, this correction more satisfactorily removes the Tharsis-induced gravity anomalies in Arabia Terra than does the applicationof high-pass filters.With the Arabia bulge correction, we can evaluate the viability ofdifferent erosional scenarios by comparing the modeled and ob-served gravity anomalies. Unless explicitly stated, we assumeArabia Terra was initially devoid of any gravity anomaly differ-ences across its boundaries beyond the isostatic signature asso-ciated with the Martian dichotomy. We expect the gravitationalsignature resulting from erosion interior to Arabia Terra to be ob-servable as a change across the northern and southern provincialboundaries. We define this gravity anomaly difference between theexterior and interior of Arabia Terra as the relative gravity anomaly(RGA).Accordingly, we focus our comparison on analyzing the relativegravity anomaly across the boundaries. We use the standard erroron the mean (noise measurement) and average gravity anomaly oneither side of the boundary to establish a limit of 4±2 milligals(mGal) for the relative gravity anomaly along the southern bound-ary of Arabia Terra. Exterior to northern Arabia Terra, we observea strong negative gravity anomaly immediately north of the bound-ary. Relative to Arabia Terra, this highly localized signal providesfor a negative relative gravity anomaly across the northern low-lands boundary, whereas an erosional load within Arabia Terra willgenerate a positive relative gravity anomaly. This anomaly couldnot have been generated by an erosional load interior to ArabiaTerra and could conceivably be a result of crustal flow along thedichotomy Nimmo & Stevenson 2001 [@]. This negative gravityanomaly was interpreted by Andrews-Hanna et al. 2008 [@] asthe signature of inwards lower crustal flow during the formation ofArabia Terra as a multi-ring structure around the Borealis impactbasin. As a result, we contrast the interior gravity anomaly with itsexterior counterpart beyond this highly localized signature to attaina 16±4-mGal relative gravity anomaly along the northern bound-ary.We use the values of 6 mGal and 20 mGal for the maximum rela-tive gravity anomalies for the southern highlands and northern low-lands, respectively.

3.3. Estimating Regional Elastic Thickness3.3.1. Admittance & CoherenceIn order to model the geophysical response to erosion within Ara-bia Terra, we must first constrain the elastic thickness at the time ofthe erosion. The free-air admittance relation is used to place limitson the effective elastic thickness for a given region [Crosby 2007[@]]. Over geologic timescales, the effective response of the Mar-tian lithosphere to a surface load can be well approximated by anelastic plate with a specified thickness, Te. For thin elastic shellloading, Equations (8 -15) provide a linear mapping between theapplied load and the gravity anomaly [Johnson et al. 2000 [@]],neglecting finite amplitude effects. The transfer function relatingthe final topography to the gravity anomaly is primarily sensitive tothe elastic thickness and not the magnitude of the load.In order to estimate the elastic thickness at the time Arabia Terraformed, we compute the localized admittance spectrum over the re-gion and compare with similarly localized admittance spectra fromthe thin elastic shell model. The admittance spectrum [Wieczorek& Simons 2005 [@]], Z, is defined as

Z(l) =Sgt(l)

Stt(l), (17)

where Sgt is the cross-power spectrum of the free-air gravity andtopography and Stt is the power spectrum of the topography. Theobserved topography, relative to a mean highlands’ elevation of 2.1

km, is used to determine the associated gravity anomaly by Eq. (15)for an elastic thickness estimate; admittance spectra are calculatedfor a range of elastic thicknesses.The associated coherence represents the correlation between thesurface topography and the gravity field. The associated coherencefunction, γ, is given by

γ(l) =Sgt(l)p

Stt(l)Sgg(l), (18)

where Sgg is the power spectrum of the gravity field. A mismatchbetween the modeled and observed coherence may be indicative ofloads that have not been represented. Modification processes suchas un-modeled surface and subsurface loading may be primary fac-tors in reducing the correlation between the gravity field and thesurface topography [McKenzie 2003 [@]]. A satisfactory elasticthickness estimate, requires an admittance fit over a significant por-tion of wavelengths as well as a strong coherence.For our analysis, all power spectra have been localized to the re-gion of interest prior to admittance and coherence computation. In-voking this formalism assumes that surface and subsurface load-ing are statistically independent process [Forsyth 1985 [@]]. Thelocalization of the model and observational data averts the up-ward bias (inflated admittance values) as described by Crosby 2007[@].3.3.2. ResultsSince elastic thickness in Eqns. (8) and (9) is a sensitive parameterwith respect to the permissible erosional load and is poorly con-strained for Arabia Terra, we utilize the free-air gravity admittanceto attain a better estimate for Te. We identify the best-fit lithospherethickness of Te=15 km by minimizing the misfit (Figure 4) betweenmodeled and observed admittances. As we choose Lwin=15, thelocalized admittance can only be computed for degrees 15-60, lim-ited by the finite bandwidth of our spatio-spectral localization. Asshown in Figure 4, this provides a reasonable fit between degrees20 and 50, though the observed admittance takes a downturn be-yond degree 50. The local maximum at degree 18 is a distortion bythe long-wavelength effects of the rotational flattening and Tharsis,since degree 18 in the localized data includes contributions fromas low as degree 3 in the global data fields. Notwithstanding thisaberration in the admittance, an elastic thickness of 15 km providesa best fit between degrees 20 and 50.For any region with accurately modeled loads, we expect a coher-ence near unity for all degrees [McKenzie 2003 [@]]. In the pres-ence of noise, un-modeled surface loads, or sub-surface loading,the coherence may decrease. Though we restrict our investigationto only surface loading, the lesser values in the observed coherencealso suggest that other processes – subsurface erosion or genera-tion of crustal density anomalies – may have acted within ArabiaTerra. Even so, the coherence (Figure 4) remains relatively high forthe localized region which indicates that if subsurface erosion didoccur, it is not a signficant influence on the regional gravitationalanomalies.

4. Erosional Scenarios

We focus on four main erosional scenarios for the province of Ara-bia Terra:

1. Highlands’ Elevation Load – an erosional load of thespatially-varying elevation difference between the mean southernhighlands’ elevation and the Arabia Terra elevation.

2. Highlands’ Flexural Fit – an erosional load yielding the cur-rent surface elevation of Arabia Terra after flexural adjustment.

3. Uniform Erosion – a uniformly thick layer of erosion appliedto the whole of Arabia Terra.


4. Bounded Erosion – a linearly-interpolated load with ero-sional constraints at the northern and southern provincial bound-aries.We employ a forward modeling approach to thoroughly examineeach of the aforementioned loading scenarios for Arabia Terra. Foreach scenario, the erosion is represented as a removal of a surfaceload with a uniform density of 2900 kg m−3 [Zuber et al. 2000[@]; McGovern et al. 2002 [@]]. Though we acknowledge thatother cases which partially erode a sub-region of Arabia Terra maybe equally valid, for simplicity, we constrain our study to scenar-ios which erode the whole of Arabia Terra. The material eroded inthese scenarios is assumed to have been removed entirely from theregion.

4.1. Highlands’ Elevation Load

The Highlands’ Elevation Load represents the elevation differenceof Arabia Terra from the mean highlands’ elevation of 2100 mas shown in Figure 5. In this scenario, we investigate the viabil-ity of forming Arabia Terra from highlands-like terrain and crustalthickness by removing a load representative of the elevation differ-ence. The erosional load ranges from 0 to 5100 m in thickness. Wecontrast this scenario with the Highlands’ Flexural Fit to quantifythe importance of flexure. Along with the assumption of an initial2100-m elevation for Arabia Terra, we assume that the basic phys-ical properties of the highlands are the same as those within ArabiaTerra.Applying the Highlands’ Elevation Load to the thin elastic shellmodel results in a final topography that does not match the currentArabia Terra, as shown in Figure 5. We disregard the sharp tran-sition at the northern and southern edges as a result of sphericalharmonic ringing inherent in such a model.The flexural rebound (deflection) generates significant uplift, yield-ing a region with an elevation that decreases by 700 m from thesouthern to the northern edge of Arabia Terra. This produces a fi-nal topography with an elevation trend shallower than the currentArabia Terra and deviates from the observed elevation at the north-ern boundary by over 4 km. As illustrated in Figure 5, the flexu-ral rebound also generates 500 m of uplift exterior to the northernboundary. This 500-m uplift exterior to northern Arabia Terra liesoutside of one standard deviation of the regional elevation profile(Figure 2). Additionally, the amount of erosion does not achievethe deficit required to match the observed crustal thickness (Fig-ure 3). Thus, the crustal thickness and the topography, interior andexterior to Arabia Terra, fail to match the observations.Although the relative gravity anomaly along the southern boundaryis small at 8 mGal, it still exceeds the 6-mGal limit imposed by theobservations. Larger amounts of erosion at the northern boundaryresults in a greater relative gravity anomaly of 20 mGal, consistentwith the maximum allowable RGA identified for northern ArabiaTerra.While this erosional scenario is nearly consistent with the observedgravity anomalies, it cannot reproduce the present-day topographyor crustal thickness of the region. The inability of this scenario toyield an elevation consistent with the current state of Arabia Terrademonstrates the importance of flexure. The topography of ArabiaTerra cannot be reproduced without significantly more erosion thancalculated by the elevation difference alone. Hence, this erosionalload cannot be singularly responsible for the formation of ArabiaTerra.

4.2. Highlands’ Flexural Fit

Incorporating flexure into the reconstruction of the original surfacerequires erosion of a significantly greater amount than the prior sce-nario. We employ the Turcotte et al. 1981 [@] model as describedby Section 2.2 with ∆ρ = ρm − ρL. This adaptation effectivelypermits an implicit calculation of the amount of additional erosionrequired to produce the observed topography. The supposition oferosion as the primary mechanism responsible for the current phys-iographic state of Arabia Terra requires the initial (pre-erosion) el-evation to be coincident with the southern highlands elevation of2100 m.The erosional load required to form the topography of Arabia Terrafrom an initial state similar to the southern highlands is shown

in Figure 6. The amount of erosion is equivalent to a 750-mlayer of sediment spread across the whole of the northern low-lands. With a 15-km elastic thickness, this scenario erodes up to22 km at the northern extremity yielding a total eroded volumeof 1.7 × 108 km3. This erosional load more closely reproducesthe crustal thickness deficit of Arabia Terra relative to the southernhighlands.As a consequence of erosional amounts in excess of the elastic(lithosphere) thickness, we invoke the caveat that the erosion musttranspire on a timescale sufficiently long to allow for thermal dif-fusion to maintain a minimal elastic thickness of 15 km. Using thethermal diffusion timescale, the erosion must occur on a timescaleof greater than 2.4 My or at a rate less than 9.2 mm/yr. This rateis orders of magnitude greater than the average erosion rates es-timated for Mars Craddock & Maxwell 1993 [@], justifying theassumption of a minimal elastic thickness during the erosionalevent.Though the erosional load is designed to reproduce the topographicexpression of Arabia Terra, the scenario fails to reproduce the el-evation exterior to Arabia Terra and an allowable relative gravityanomaly. In eroding nearly 22 km at the northern extremity, theresultant flexural rebound produces uplift of over 1 km immedi-ately exterior to Arabia Terra. This substantial elevation rise iscontradictory to the observations and is too large to be masked bymeasurement noise. While this 1-km exterior uplift alone is suffi-cient to deem this scenario implausible, the resultant gravitationalanomaly further diminishes the viability of this scenario. The grav-ity anomaly map in Figure 6 contains an 80-mGal relative gravityanomaly across the northern boundary, substantially greater thanallowable for northern Arabia Terra. Furthermore, this scenarioestablishes a strong gradient in the gravity anomaly interior to Ara-bia Terra, contradictory to observations of a nearly uniform gravityanomaly. The relative gravity anomaly on the southern boundaryof 40 mGal also exceeds the allowable RGA.Though the relative gravity anomalies are too large to be accom-modated by the observations, the resulting crustal thickness trendmore closely resembles crustal thickness models than the prior sce-nario. While the discrepancy in crustal thickness in the erosionalmodel is small, the overcompensated, excess crustal thickness issufficient to produce large negative gravity anomalies over ArabiaTerra, in conflict with the observations.This scenario is designed to reproduce the topography of ArabiaTerra via erosion from an initial state similar to the southern high-lands. Using this scenario, we produce an overcompensated ArabiaTerra crustal thickness estimate with a gravity anomaly trend in-terior to Arabia Terra and relative gravity anomalies on the north-ern and southern boundaries that exceed the observations. Theseresults demonstrate that erosion cannot be solely responsible forthe formation of the current Arabia Terra from the southern high-lands.

4.3. Uniform Erosion

This scenario diverges from the notion of a pre-erosional Ara-bia Terra commensurate with the southern highlands and insteaderodes a uniformly thick layer from Arabia Terra. In order toprovide a final elevation and crustal thickness consistent with thecurrent state of Arabia Terra, the pre-erosional state includes iso-static crustal thickness variations specific to the applied erosionalload.As the gravity anomalies arising from isostatically-compensatedtopography are small relative to those arising from flexurallly-supported loads, the uniform erosion scenario will produce a simi-lar relative gravity anomaly across all boundaries. We first consideran amount of erosion consistent with Hynek & Phillips 2001 [@],a uniform erosional load of 450 m. This erosional load producesa 3-mGal relative gravity anomaly on the northern and southernboundaries. The amount of flexural rebound immediately exterior


to Arabia Terra is minimal. Accordingly, this amount of erosion isallowable based on the observations.Using an iterative, forward-modeling approach to minimize themisfit between the modeled and observed relative gravity anoma-lies, we can determine the maximum amount of uniform erosionconsistent with the observations. The 6-mGal relative gravityanomaly on the southern boundary is the primary constraint, al-lowing for a maximum uniform erosional load of approximately1300 m. Neglecting contributions to the southern relative gravityanomaly from noise/error, Table 3, a best-fit uniform erosional loadcan also be determined: 750 m.

4.4. Bounded Erosion

The difference in the observed northern and southern RGA upperlimit suggests that a relatively larger amount of erosion is allow-able along the northern boundary. In this scenario, we consider aload with assigned erosional amounts on each boundary; betweenthe boundaries, the erosion is linearly interpolated to attain the ero-sional load.Through an iterative forward-modeling scheme similar to the priorscenario, we determine the maximum bounded erosional load –erosion linearly increases from 300 m in the south and culmi-nates at 5000 m in the north. As shown in Figure 7, this maxi-mum erosional load attains the 6-mGal and 20-mgal relative gravityanomaly upper limit along the northern and southern boundaries,respectively. Thus, this bounded erosional load is able to reproducethe difference between the respective relative gravity anomalies onthe boundaries. This maximum erosional load amounts to 3.1 ×107 km3 of material that could have conceivably been removedfrom Arabia Terra. Additionally, we calculate a best-fit boundederosional load (Figure 8) designed to match the observed north-ern and southern RGA without error. The best-fit bounded ero-sional load increases from no erosion in the south to 4000 m in thenorth.

5. Discussion

The thin elastic shell loading model applied here provides con-straints on the maximum volume of erosion which can reproducethe observed gravity anomalies (Table 3). In addressing erosionfrom the vantage of geophysics, we eliminate uncertainty in the in-terpretation of geological units and employ a model independent ofspecific fluvial or aeolian processes.Any significant alteration of Arabia Terra would have likely oc-curred prior to the onset of the Hesperian epoch in order to main-tain current estimates for the terrain age [Craddock et al. 1997 [@]]and to be consistent with the thin elastic thickness. It is likely thatif erosion did occur within Arabia Terra, it may have occurred overa period of time [Golombek et al. 2006 [@]; Hynek & Phillips2001 [@]; Craddock & Maxwell 1993 [@]] rather than in a sin-gular event. As our admittance analysis indicates Arabia Terrawas formed in the presence of a 15-km elastic lithosphere, anysubsequent surface modification would have occurred at a greaterelastic thickness. Since the lithosphere becomes more rigid overtime, a given erosional load will result in a relatively larger gravityanomaly. By modeling erosion with a 15-km elastic lithosphere,the erosional load calculated is an upper limit for erosion withinArabia Terra.As illustrated by the highlands’ elevation load, the Arabia Terratopography cannot be reproduced by the removal of a load repre-sentative of the elevation difference as a result of subsequent flexu-ral rebound. Although we can reproduce the topography of ArabiaTerra via the highlands’ flexural fit scenario, the erosion requiredproduces large gravity anomalies and uplift exterior to the regionin conflict with the observations.Although the current physiographic expression of Arabia Terra can-not be explained by erosion, lesser amounts of erosion are allow-able within the region from the geodynamical constraints. Em-ploying a fit to the relative gravity anomaly of Arabia Terra, uni-form erosion of material, no greater than 1300 m could have oc-curred; beyond 1300 m, the relative gravity anomaly along thesouthern boundary of the province is exceeded. However, the

larger, relative gravity anomaly in northern Arabia Terra allows fora greater amount of material to have been removed. Accordingly,our bounded erosional load can reproduce the difference betweenthe observed relative gravity anomalies. The erosional load linearlyincreases with distance from the southern boundary of Arabia Terrawith 300 m of erosion in the south and up to 5000 m in the north.The load represents the maximum amount of erosion that can beremoved from Arabia Terra: 3×107 km3 of material.Given the constraint on the surface age from crater statistics, amajority of the erosion from the Highlands Flexural Fit scenariowould have had to occur no later than ∼3.8 Ga. Though lateralcrustal flow may have diminished the resultant gravity anomaliesobserved on present-day Mars, the persistence of the north-southcrustal dichotomy through the early Noachian provides a constrainton crustal relaxation[?, Zhong and Zuber, 2000; Nimmo & Steven-son 2001 [@]; ?]. On the basis of thermal models that includeconsideration of crustal heat production and the role of hydrother-mal circulation in the crust, relaxation rates ¡10−17 s−1 are re-quired to maintain crustal thickness variations [Parmentier and Zu-ber, 2007]. This constraint is easily met for plausible thermal struc-tures in the Noachian, and limits vertical perturbation of the crust-mantle boundary to be on the order of 1 km within Arabia Terra.Thus, while crustal flow within Arabia Terra would affect our esti-mate on the maximum amount of erosion, erosion with crustal flowstill cannot explain the formation of Arabia Terra from the south-ern highlands. Additionally, it is likely crustal-thinning resultingfrom erosion would increase the effective viscosity allowing forgreater preservation of the Arabia Terra crustal profile [Nimmo &Stevenson 2001 [@]; ?]. Ultimately, given the assumption of a pre-erosional Arabia Terra similar to the highlands, the preservation ofthe large-scale Noachian crustal thickness variations on Mars (i.e.crustal dichotomy, Hellas) [see Nimmo & Stevenson 2001 [@]]suggests that lower crustal flow would not have been substantialwithin Arabia Terra.

6. Conclusions

In order for erosion to be a viable candidate for the formationof Arabia Terra from the southern highlands, an erosional modelmust reproduce the topography and gravity anomaly both withinand exterior to the region. Appropriately reproducing the topogra-phy entails the consideration of flexure; without the considerationof flexure the load itself cannot properly be determined or evalu-ated.Our admittance analysis demonstrates that the present-day topog-raphy of Arabia Terra was established in the presence of a 15-kmthick elastic lithosphere. This lithosphere thickness determines theflexural response of Arabia Terra to any large-scale loading event.In order to generate the observed topography of Arabia Terra viaerosion from the highlands alone, 1.7 × 108 km3 of material mustbe eroded from the region. However, this erosion would result ina substantial flexural uplift of the lithosphere immediately exteriorto Arabia Terra and resultant gravity anomalies that exceed obser-vations.This work demonstrates the maximum amount of erosion that couldhave occurred in Arabia Terra is 3×107 km3, consistent with thegeological minimum established by Hynek & Phillips 2001 [@].Further, we conclude erosion cannot explain the observed topog-raphy and crustal thickness deficit of Arabia Terra. If the uniquephysiography of this region is a result of erosion, it must havebeen accompanied significant viscous relaxtion [Nimmo & Steven-son 2001 [@]] or alternatively must have possessed large isostaticcrustal thickness variations prior to an erosional event.

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(a) Mars Global Topography (km).

(b) Regional Topography (km).

(c) Regional Terrain (km).

Figure 1. Mars Topography in kilometers. (a) Solid line outlines the region of Arabia Terra. The dashed box repre-sents (b) in the global topography. (b) Shaded relief elevation map of the Arabia Terra region. Over a 4000-km span,the topography of Arabia decreases by 5-km. The dashed box represents (c) in the regional topography. (c) A viewof the isolated mesas within Arabia Terra.



AVERAGE 1-STD. DEVIATION

Figure 2. Mean surface elevation across Arabia Terra. The black line represents the average elevation and the greylines represent one standard deviation about the mean. From Andrews-Hanna et al. 2008 [@].


(a) Mars Global Crustal Thickness (km).

(b) Mars Global Gravity Anomaly (mGal).

Tharsis-

influenced

gradient

Southern

RGA

(c) Arabia Terra Regional Gravity Anomaly (mGal).

Figure 3. Mars Crustal Thickness and Gravity (a) Global Crustal Thickness (km). Within the region of Arabia Terra,the crustal thickness decreases from 53-km to 28-km near the northern border, yielding a total crustal thickness reduc-tion of 25-km.Th region enclosed by the solid line is Arabia Terra. (b) Martian Gravity in mGal. Solid line outlinesthe region of Arabia Terra. The Arabia Terra region is dominated by the antipodal signature associated with Thar-sis. (c) A regional gravity anomaly map with a center-of-mass offset incorporated to remove the antipodal signatureassociated with Tharsis.


15 Te

(a) Model and Observation Admittance. (b) Admittance Misfit.

(c) Coherence.

Figure 4. (a) Model and Observation Admittance. The model admittance is shown above for an elastic lithospherethickness of 5, 15, 25, 40, 50 kilometers. The dark solid line represents the actual free-air admittance for Arabia Terra.The peak in admittance near degree 18 is likely due to Tharsis. (b) Admittance Minimum Misfit. The admittance forArabia Terra is best fit by a model with an elastic thickness of 15-km, denoted in the misfit by the asterisk. The misfitis applied between degrees 20 through 50. The minimum misfit is at a 15-km elastic lithosphere. (c) Coherence. Thethick solid line represents the coherence for Arabia Terra and the thin solid line represents the coherence for an elasticlithosphere of 15-km.


(a) Erosional Load (m). (b) Deflection (m).

(c) Final Elevation (m.) (d) Gravity Anomaly (mGal).

Figure 5. Highlands’ Elevation Load. (a) Load applied to Arabia Terra region. The erosional load is the spatially-varying elevation difference between the mean southern highlands’ elevation and the Arabia Terra elevation. (b)Resultant flexure from erosional load. (c) The final elevation of terrain after the erosional load is applied. Final eleva-tion is a summation of the erosional load (a) and the resultant flexure (b). (d) The resultant gravity anomaly includesthe finite amplitude effect resulting from topography on the surface and along the crust-mantle boundary.


(a) Erosional Load (km). (b) Deflection (km).

(c) Final Elevation (km). (d) Gravity Anomaly (mGal).

Figure 6. Highlands’ Flexural Fit Scenario. (a) Load applied to Arabia Terra region. The erosional load is designedto match the observed elevation of Arabia Terra.(b) Resultant flexure from erosional load. (c) The final elevation ofterrain after the erosional load is applied. Final elevation is a summation of the erosional load (a) and the resultantflexure (b). (d) The resultant gravity anomaly includes the finite amplitude effect resulting from topography on thesurface and along the crust-mantle boundary.




Figure 7. Maximum, Bounded Load Scenario. (a) Load applied to Arabia Terra region. The erosional load is formedfrom a linear interpolation between erosional amounts assigned to the northern and southern provincial boundaries,respectively. The erosional load is designed to match the maximum allowable RGA. (b) Resultant flexure from ero-sional load. (c) The final elevation of terrain after the erosional load is applied. Final elevation is a summation of theerosional load (a) and the resultant flexure (b). (d) The resultant gravity anomaly includes the finite amplitude effectresulting from topography on the surface and along the crust-mantle boundary.

7. tables




Figure 8. Best-Fit, Bounded Load Scenario. (a) Load applied to Arabia Terra region. The erosional load is formedfrom a linear interpolation between erosional amounts assigned to the northern and southern provincial boundaries,respectively. The erosional load is designed to best-fit the RGA. (b) Resultant flexure from erosional load. (c) Thefinal elevation of terrain after the erosional load is applied. Final elevation is a summation of the erosional load (a)and the resultant flexure (b). (d) The resultant gravity anomaly includes the finite amplitude effect resulting fromtopography on the surface and along the crust-mantle boundary.


Table 1. Parameter Values for the Thin Elastic Shell Loading Model

Parameter ValueCrustal Density, ρc 2900 kg m−3

Load Density, ρL 2900 kg m−3

Mantle Density, ρm 3500 kg m−3

Mean Density, ρ 3940 kg m−3

Gravity, g 3.72 m s−2

Equatorial Radius, Req 3396 kmMean Planetary Radius, Rp 3389.5 kmPoisson’s Ratio, ν 0.25Shell Thickness, Te 15 kmYoung’s Modulus, E 1011 N m−2

Table 2. Parameter Values for the Density Interfaces

Parameter Surface Interface Mantle InterfaceDensity Change, ∆ρ ρc ρm − ρcReference Radius, r R R− TcrShape, Slm hlm +Alm wlm +Alm


Table 3. Erosion Scenario Summary)

Scenario Relative Gravity Anomaly (mGal) Erosional Load (m)North South North South

Actual 16 ± 4 4 ± 2 - -

Highlands’ Elevation Load 20 8 X XHighlands’ Flexural Fit 80 40 X X

Uniform Erosion (450 m)* 3 2 450 450

Uniform Erosion: Maximum* 7 6 1300 1300Bounded Erosion: Maximum 20 6 5000 300

Uniform Erosion: Best-fit* 5 4 753 753Bounded Erosion: Best-fit 16 4 3900 0

Documents

Geophysical Limitations on the Erosion History within Arabia … · Geophysical Limitations on the Erosion History within Arabia Terra, Mars-need reference for crustal thickness model