lithospheric loading by the northern polar cap on …lithospheric loading by the northern polar cap...
TRANSCRIPT
Icarus144, 313–328 (2000)
doi:10.1006/icar.1999.6310, available online at http://www.idealibrary.com on
Lithospheric Loading by the Northern Polar Cap on Mars
Catherine L. Johnson and Sean C. Solomon
Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road, N.W., Washington, DC 20015E-mail: [email protected]
James W. Head III
Department of Geological Sciences, Brown University, Providence, Rhode Island 02912
Roger J. Phillips
Department of Earth and Planetary Sciences, Washington University, St. Louis, Missouri 63130
David E. Smith
Geodynamics Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771
and
Maria T. Zuber
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Received March 24, 1999; revised December 9, 1999
New topography data for the northern polar region on Mars, re-turned by the the Mars Orbiter Laser Altimeter (MOLA) during theaerobraking hiatus and science phasing orbits, allow characteriza-tion of the topography of the present northern polar cap and itsenvirons. Models for loading of an elastic shell by an axisymmetricload approximating the present polar cap geometry indicate thatthe maximum deflection of the subice basement is in the range 1200to 400 m for an elastic lithosphere of thickness 40 to 200 km over-lain by a cap of pure H2O ice. Corresponding model cap volumesincrease from 1.5 to 1.8× 106 km3, as elastic lithosphere thicknessdecreases from 200 to 40 km. The presence of sediments in the polarcap increases the depth to basement and resulting cap volume for agiven value of elastic lithosphere thickness. One-dimensional heatflow calculations indicate that the temperature at the base of thecap may approach the melting point of cap material if the litho-sphere underlying the cap is thin. The basal temperature is 170 Kfor a 200-km-thick lithosphere overlain by pure ice but is as greatas 234 K for a 40-km-thick lithosphere overlain by a cap with ahigh sediment/ice ratio. Constraints on elastic lithosphere thick-ness are weak, but geologic mapping and MOLA data suggest thata flexurally derived circumpolar depression filled with sedimentsis consistent with elastic lithosphere thickness values in the range60–120 km. Gravity and topography over the whole cap are poorlycorrelated, possibly due to viscous relaxation of long-wavelengthtopography, but gravity and topography over the western portionof the main cap are consistent with an elastic lithosphere thicknessof 120 km, for a crustal thickness of 50 km. Both MOLA data and
geological information suggest a formerly larger northern polar cap.The relationship of time scales for changes in the polar cap volumeand extent to time scales for viscous relaxation of topography hasimportant implications for investigations of even present polar captopography. Viscoelastic calculations show that the Maxwell timefor an Earth-like mantle viscosity for Mars (1021 Pa-s) is 105 yr. TheMaxwell time scales directly with the martian mantle viscosity sothat values as high as 107 yr are possible. Time scales for changesin polar cap volume are poorly constrained, but major changes incap volume over periods of 106–108 yr are consistent with currentunderstanding of polar cap processes. c© 2000 Academic Press
Key Words: Mars; ices; geophysics; Mars, climate; Mars, interior.
1. INTRODUCTION
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313
The northern polar cap of Mars is an important volatile revoir for that planet. The partitioning of volatiles among the pocaps, the atmosphere, and the regolith has changed througha consequence of climate changes driven by variations in petary obliquity (Kieffer and Zent 1992). In particular, the pocaps have likely undergone episodic changes in mass and sextent, producing a temporally varying load on the underlylithosphere. It is difficult to determine the detailed time evotion of the polar caps because of complex feedbacks amonmate variations, resulting changes in polar cap volumes, aninfluence of the polar caps on planetary dynamics (Rubin
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1990, 1993; Spada and Alfonsi 1998; Bills 1999). Howevnew topography and gravity data from the Mars Global Sveyor (MGS) mission (Smithet al.1998; Zuberet al.1998a,b),together with geological information derived from Mariner aViking images, enable a significant advance in the characzation of the spatial extent, volume, and surface morphologthe present-day northern cap. This information in turn proviconstraints for elastic and viscoelastic compensation modelthe northern polar cap (this study, Zhong and Zuber 2000), mels for the dynamics and recent temporal variations in the(Zuberet al.1998a), and investigations of the effect of the currcap on the planet’s mass distribution and solid-body dynam(Zuber and Smith 1999). Further, in combination with climamodels (Touma and Wisdom 1993, Bills 1999), the charactzation of the present cap and suggestions from topographyimage data of a formerly larger cap provide foundations forture studies of the interactions among climate, cap volume,planetary dynamics over time.
Prior to the MGS mission, knowledge of the topographythe northern polar cap and surrounding regions was derfrom regional digital elevation models based on photoclinoetry, stereo imaging, and three Mariner 9 occultation measments (Dzurisin and Blasius 1975, Blasiuset al.1982, Espositoet al.1992, Batson and Eliason 1995). These models indicathat the polar deposits are described by a broad topograhigh at latitudes northward of 80◦N. The thickness of the polar deposits was estimated to average 2 km and to be as gre5 km (Thomaset al.1992). Wide curvilinear reentrants knownchasmata, some with steep scarps, modify the long-wavelecap topography. While heights derived from stereo imagyield high-spatial-resolution information on relative topogrphy within the region defined by the images, long-wavelentopography is not constrained and elevations derived from sinformation cannot be tied to an absolute global reference fraGlobal digital elevation models for Mars (Wu 1989, 1991) asuffer from poor long-wavelength control. Because of the laspatial extent of the cap, long-wavelength information is critito an accurate estimation of the surface topography of the capsurrounding regions. Prior to MGS, a degree and order 8 (equlent to wavelengths of 2700 km and greater) spherical harmglobal topography model derived from radio occultation dand Viking lander sites (Smith and Zuber 1996) providedbest estimate of the long-wavelength shape of Mars.
Polar deposits include the residual or permanent polarseasonal ices, and the polar layered deposits that surrounmay underlie the perennial caps. Viking Orbiter Infrared Thmal Mapper data indicate that the composition of the residnorthern polar cap is primarily H2O ice; measurements of the icalbedo suggest that small amounts of dust or sediments arepresent (Thomaset al. 1992). Seasonal ices are composed pmarily of CO2, with H2O and dust abundances probably refleing their relative atmospheric abundances. The layered depo
first observed in Mariner 9 images (see review by Thomaset al.1992 and references therein), are well exposed in trough wN ET AL.
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and at the cap margins. The layers appear to be approximhorizontal, to extend for tens of kilometers, and to be on the oof meters thick. Poorly known properties of the layered deporelevant to assessing the magnitude of the load of the north pcap on the martian lithosphere include the total volume oflayered deposits (their lateral extent and thickness beneatresidual polar ices are unknown) and their bulk compositionparticular the ice/sediment ratio. Although the layered depoclearly reflect climatic effects, improved characterization oflayers would be necessary to establish links with climate cyc
Investigations of how the mass anomaly associated withpolar cap is compensated require information on the grafield. Pre-MGS spherical harmonic gravity field descriptionsMars (Smithet al.1993, Konopliv and Sjogren 1995) extenddegree and order 50 (wavelengths as short as 430 km), buhighest resolution is achieved only in a low-to-mid-latitude baResolution at high latitudes is substantially poorer. Malin (19estimated the density of the polar deposits to be 1± 0.5 kg m−3
using line-of-site accelerations from seven Viking spacecorbits and a volume estimate for the polar cap derived from aanalysis of the digital elevation model of Dzurisin and Blas(1975). New high-resolution gravity (Smithet al. 1999) andtopography data collected by the MGS spacecraft enable mconfident analyses of compensation of polar cap topograph
Mars Orbiter Laser Altimeter (MOLA) elevation profiles obtained during a three-week period in fall 1997 and duringperiod March–September 1998 have yielded high-resolutionpography for the northern polar cap and surrounding reg(Smith et al. 1998; Zuberet al. 1998a,b). The improved topography provides new insights into the relief and extentpreviously defined geologic units. Here we summarize thepography and geologic setting of the polar cap and its envirWe employ elastic and viscoelastic models in order to invegate lithospheric loading and the consequent deflection ofunderlying surface. We discuss the implications of lithosphthickness for polar cap volume and heat flow into the base opolar cap, and we explore time scales for relaxation of topophy and the temporal evolution of the degree of compensaOur modeling provides a context for investigations of modcap dynamics and the influence of the cap on the momeninertia and planetary dynamics of Mars. Finally we presentidence for a formerly larger northern polar cap and highligsuch open issues as the time frame over which this largermay have persisted, the time scales for climate variationsdifficulties inherent to determining the past climate history, athe nature of interactions among climate history, cap evolutand planetary dynamics.
2. PRESENT ICE CAP TOPOGRAPHY
MOLA data for the northern hemisphere, as of this writinconsist of 18 profiles from the aerobraking hiatus orbits (199
alls188 profiles from the science phasing orbits (1998) prior to(SPO-1) and following (SPO-2) Mars solar conjunction, and
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LITHOSPHERIC LOADING BY
more than 720 profiles collected during the the first two monof the ongoing mapping phase of the MGS mission. Becaof the inclination of the MGS orbit, the generally nadir-pointialtimeter normally yields topographic measurements only soward of 86.3◦N. Ten altimetry profiles were collected north86.3◦N, however, by pointing the spacecraft approximately◦
off-nadir to enable the maximum height of the ice cap to be msured (Fig. 1a). Along-track resolution is 300–400 m, andmaximum vertical resolution is about 30 cm (Smithet al.1998,Zuberet al.1998b). Topography data presented in this papermeasurements of surface height relative to the geoid, whiccomputed from Mars gravity field model mgm0883 (Lemoet al. 1999, Rowlandset al. 1999) and constrained to matcthe mean equatorial radius of 3396.0± 0.3 km (Zuberet al.1998a).
The MOLA profile data have been used to construc2-km-resolution grid of the northern hemisphere topographylatitudes north of 55◦N (Zuberet al. 1998b). Figure 1a showa representation of the gridded topography northward of 60◦N.The residual polar cap is asymmetric about the north pole,tending as far south as 78◦N at longitudes near 0◦E but extendingsouthward only to 85◦N in the region 140◦ to 220◦E. However, ifthe dunes of Olympia Planitia (Fig. 1b) are underlain by residice, as suggested by Zuberet al. (1998b), then to first order thpolar cap is symmetric about the north pole and has a radiuabout 10◦ in latitude. Chasma Borealis, the largest reentrant (gitudes 330◦ to 10◦E) into the polar cap, is clearly seen, and tMOLA data provide high-resolution profiles across many otchasmata and troughs. The surface of the ice cap is smoohorizontal scales of less than a meter over baselines of hundof meters to kilometers and is smooth at the 10-m level obaselines of tens of kilometers (Zuberet al. 1998b). On aver-age, the ice cap increases in height from its edge toward theThe highest point on the ice cap is at−1950 m± 50 m and iswithin a few kilometers of the rotation pole.
Exterior to the ice cap the martian surface slopes downwtoward the pole at all longitudes, with the greatest polewslopes occurring over longitudes 220◦–270◦E at the northernperiphery of the Tharsis Rise. The martian surface near thecap edge lies between−4800 m and−5200 m relative to themean elevation of the equator. The relief of the ice cap is t2950± 200 m (Zuberet al.1998b).
MOLA profiles across the region surrounding the residualprovide additional important information on polar cap procesDeposits immediately exterior to the residual cap have varitopographic signatures. In the longitude band 0◦–60◦E, the cir-cumpolar plains deposits appear to be very smooth. In contthe plains deposits in the region 140◦–255◦E are interrupted byresidual ice deposits (outliers, see below) of significant posrelief. Impact craters within 100 km of the permanent ice cexhibit crater floor depths that are too shallow to be explaiby impact-related structural uplift or interior wall collapse (J.
Garvin, personal communication, 1999). The floors of seveof these craters exhibit asymmetric topographic profiles. BoORTHERN POLAR CAP, MARS 315
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viscous relaxation and infilling of the crater cavities by icedust could account for the reduced relief. Asymmetric crafloor topography could result from viscous relaxation if lateheterogeneities in rheology, related to changes in the depthcomposition of the permafrost layer, are present.
3. GEOLOGIC SETTING
Geological mapping of the northern polar region has led toindentification of several major units related to the presentcap and possibly to an earlier, different cap geometry (Fig.The north polar cap and its circumpolar deposits are situin the central part of the northern lowlands. Tanaka and S(1987) mapped the Hesperian-aged Vastitas Borealis Form(Hv) over the majority of the northern lowlands. (A reviewmartian stratigraphy and associated nomenclature is provby Tanakaet al. 1992.) On this older deposit are superposthe Amazonian-aged polar ice deposits (Api) and the cloassociated polar layered deposits (Apl). The polar ice depcorrelate well with the topographic high of the present cap.
Surrounding the polar deposits in an annulus from apprmately 70◦ to 80◦N are circumpolar deposits of Amazonian agincluding mantle material (Am) and two types of dune marial, crescentic (Adc) and linear (Adl). Most of these depoappear to be superposed on the Vastitas Borealis formationscuring or obliterating the topography characteristic of mof its members. Sources for the sediments composing thecumpolar units may include erosion of polar layered depoemplacement in association with some channel deposits, anlian redistribution of regolith and other material. The thickneof the circumpolar deposits may vary substantially (Fishbaand Head 1999), forming thick units close to the polar capperhaps only a thin veneer at lower latitudes. Where thecumpolar deposits are thin, the regional slope will follow thof the underlying Vastitas Borealis formation. MOLA topogrphy profiles extending across the Vastitas Borealis Formanorthward toward the pole show breaks in slope in the latitrange 70◦–78◦N (Fig. 2, also Fishbaugh and Head 1999). Ttopography northward of the arrows indicated on each proin Fig. 2, but southward of the polar deposits, is more nehorizontal on average than topography southward of the arwhich displays the regional poleward slope typical of the Vatas Borealis Formation. Exceptions are in the area of the NPolar Basin (Headet al.1998), where the topography is very fland distinctive breaks in slope are less readily identified (Figprofiles from orbits 242 and 255). The break in slope appeacoincide with the margins of the circumpolar deposits mapby Dial (1984) and Tanaka and Scott (1987) in the longitudegion from 270◦ counterclockwise to 90◦E (Fishbaugh and Hea1999, and profiles from orbits 255, 242, 210, and 252 in FigThe slope break does not correlate with the mapped HespeAmazonian contact (Fig. 1b) in the longitude band 90◦–270◦E
ralth(Fig. 2, profiles from orbits 230, 224, and 256) but may reflecta change in thickness of the circumpolar deposits from thin,
ce
316 JOHNSON ET AL.
FIG. 1. (a) Gridded topography for the region 60◦–90◦N (Zuberet al.1998b) obtained from MOLA data collected during the aerobraking hiatus and scienphasing orbits. Color scale in kilometers is shown. MOLA orbit tracks marked in black indicate locations of off-nadir pole-crossing profiles shown inFig. 4. MOLAorbit tracks marked in red indicate locations of profiles shown in Fig. 2. (b) Geologic map, simplified from Tanaka and Scott (1987). Units related to polar processesinclude: Api (white), residual polar deposits; Adl (orange), linear dunes; Apl (black), polar layered terrain; Am (blue), polar mantle material; Adc (dark yellow),crescentic dune material; Hv (green), subpolar plains deposits; and c (gray), cratered terrain. (b) also shows some units distant from the pole that are unrelated
◦ ◦
to polar processes. The lighter yellow and turquoise at longitudes 240–270 E denote flows and sediments related to Alba Patera. A finger of ancient (Noachian)highland material (dark brown) is also seen at longitudes 210◦–250◦E.
for orbit
LITHOSPHERIC LOADING BY NORTHERN POLAR CAP, MARS 317
FIG. 2. MOLA topographic profiles for the ground tracks shown in red in Fig. 1a. Orbit numbers are given at the left of the profiles. Elevations shown
255 correspond to values indicated by the vertical axis; other profiles are of- haverealem-fea-opo-d to
sh-been
the
by Fishbaugh and Head (1999).
mantling deposits southward of 75◦N to thicker deposits northward of 75◦N toward the polar cap. Circumpolar deposits mform thin veneers in other regions as well. For example, Zuet al. (1998b) suggest that residual ice may underlie the lindunes of Olympia Planitia on the basis of MOLA profile daacross the dunes.
Outliers mapped as residual polar cap deposits are contrated in a band from 70◦ to 80◦N (Dial 1984, Tanaka andScott 1987). MOLA data show that many of these outliers
the region from 140◦ to 255◦E have significant relief (tens ofmeters to over 700 m relative to the surrounding regions),fset vertically for clarity. Arrows indicate breaks in long-wavelengthslope as identified
ayberearta
cen-
in
tens of kilometers across (Fishbaugh and Head 1999), andan albedo similar to that of the residual polar ices. The aextent, relief, and albedo of the outliers suggest they are rnants of a formerly larger polar cap rather than seasonaltures. This hypothesis is also supported by observations of tgraphic depressions (similar to terrestrial kettle holes relateglacier retreat) in the vicinity of the residual cap outliers (Fibaugh and Head 1999). Residual polar cap material hasmapped in the cavities of some larger craters, such as in
◦ ◦
arecrater centered at 73N, 165 E (Tanaka and Scott 1987). Thesoutherly latitudinal extent of the outliers correlates in general
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318 JOHNSO
with the locations of the break in slope identified in the pfiles shown in Fig. 2. This correspondence suggests thacircumpolar deposits in the regions northward of the mararrows in Fig. 2 could be derived, at least in part, from sements once part of a formerly larger cap. While these obvations are consistent with an increased cap size in thethe spatial extent and timing of a larger polar cap are poconstrained.
On the basis of impact crater densities, the polar mate(Api, Adl, Apl, Am, Adc) are inferred to be among the youngedeposits on the surface of Mars. The circumpolar depositsclearly less heavily cratered than the underlying Hesperian-aVastitas Borealis formation. Although the polar layered depounderlie the residual ice, their composite age is uncertain. Wgeologic mapping allows local stratigraphic relations to betablished, the low impact crater densities on the polar unitsnot permit distinction among these units on the basis of avesurface ages (Thomaset al.1992).
4. ELASTIC LITHOSPHERIC LOADING MODELS
MOLA data provide high-resolution information on the tpography of the upper surface of the polar cap. The degrewhich the cap is compensated has implications for the depthe basement underlying the cap and thus for the volume ocap. We employ loading models for a thin spherical elastic sas a means to investigate basement deflections and topogrsignatures characteristic of flexural compensation of the capoutline of the model formulation is given in Section 4.1 beloand its application to the northern polar cap and assumptinvoked are described in Section 4.2.
4.1. Model Formulation
The deflectionw due to an arbitrarily distributed load onthin elastic lithospheric shell satisfies the differential equati[
D∇6+ 4D∇4+ 4D∇2+ETeR2∇2+ 2ETeR2]w
= R4(∇2+ 1− ν)q (1)
(Kraus 1967, Willemann and Turcotte 1981).D= ET3e /
12(1− ν2) is the flexural rigidity, whereTe is the elastic shelthickness,E is Young’s modulus,ν is Poisson’s ratio,R is themean radius of the shell (R= Rp− Te/2, whereRp is the plan-etary radius), andq is the effective local normal stress on tshell.∇2 is the Laplacian operator defined in a spherical codinate system and evaluated at the mean radius of the shelw is positive radially outward. Contributions toq (positive out-ward) come from the applied load corresponding to the origice cap topography and from the restoring force due to thesity contrast at the depressed crust–mantle boundary bethe load. In this formulation shear stresses are assumed
insignificant in magnitude in comparison with normal stressAs we are primarily interested in the long-wavelength deflectiN ET AL.
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of the subice basement this is a reasonable assumption (Ban1986). We shall see later that gravity field predictions frommodel that includes shear stresses (Banerdt 1986, Phillipset al.1999) are very similar to those predicted using the formulatiodescribed above. For loads with a wavelength on the order ofplanetary radius, there is an additional term due to the (upwadisplacement of the geoid and so
q = −(ρicegh− ρmghg−1ρgw), (2)
whereg is the gravitational acceleration,ρm and1ρ are the man-tle density and the density contrast responsible for the restornormal stresses, respectively,ρice is the load density,h is thetopography of the load, andhg is the deflection of the geoid re-sulting from the additional mass of the topography. Substituti(2) into (1) gives[
D∇6+ 4D∇4+ 4D∇2+ ETeR2∇2+ 2ETeR2
−1ρg(∇2+ 1− ν)]w = −ρiceg(∇2+ 1− ν)h̄, (3)
whereh̄ is the modified load given byh−(ρm/ρice)hg. Assumingno flexural moat infill or cap flow,1ρ= ρm. For loads of awavelength small compared with the planetary radius,h̄ ≈ h.
This formulation includes both membrane and bendinstresses. For loads having a wavelength small compared wR, (3) reduces to a simpler form [see, e.g., Eq. (1) of Brotchand Sylvester (1969) and Eq. (5) of Turcotteet al. (1981)]. Thepresent lateral extent of the northern polar cap on Mars is snificant and, as discussed above, may have been greater inpast, so we solve (3) explicitly.
As in Turcotteet al. (1981) we introduce the dimensionlesparametersτ andσ given by
τ = ETe
R2g1ρ(4)
and
σ = D
R4g1ρ. (5)
τ is a measure of the rigidity of the spherical shell if bendinresistance is neglected, andσ is a measure of the resistance of thshell to bending. The topography of the loadh, the modified loadh̄, the displacement of the geoidhg, and the resulting deflectionw can be expressed as spherical harmonic expansions
h(θ, φ)= Rp
∞∑l=2
l∑m=0
Pml (cosθ )
(Cm
l cosmφ+ Dml sinmφ
)(6)
∞∑ l∑m
(m m
)
es.onh̄(θ, φ)= Rpl=2 m=0
Pl (cosθ ) C̄l cosmφ+ D̄l sinmφ (7)
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LITHOSPHERIC LOADING BY
hg(θ, φ)= Rp
∞∑l=2
l∑m=0
Pml (cosθ )
(Cm
gl cosmφ+ Dmgl sinmφ
)(8)
w(θ, φ)= Rp
∞∑l=2
l∑m=0
Pml (cosθ )
(Am
l cosmφ+ Bml sinmφ
)(9)
whereθ andφ are colatitude and longitude, respectively,Pml are
the associated Legendre polynomials of degreel and orderm,and the coefficients of the sine and cosine terms are conssatisfying full normalization of each spherical harmonic. Subtuting (4), (5), (7), and (9) into (3) and solving (3) in the spectdomain yields the relationship
(Am
l
Bml
)= −ρice
1ραl
(C̄m
l
D̄ml
), (10)
whereαl is given by
αl =−[l (l + 1)− (1− ν)]
σ [−l 3(l + 1)3+ 4l 2(l + 1)2− 4l (l + 1)]+ τ [−l (l + 1)+ 2]+ [− l (l + 1)+ (1− ν)].
(11)
The spherical harmonic coefficients in the expansions ofhg, h,andw are related by
(Cm
gl
Cmgl
)= 3
(2l + 1)ρ̄
[ρice
(Cm
l
Dml
)−1ρ
(Am
l
Bml
)], (12)
where ¯ρ is the mean density of the planet. Thus
(Am
l
Bml
)= −ρice
1ργl
(Cm
l
Dml
)(13)
with
γl =[1− 3ρm
(2l + 1)ρ̄
][1
αl− 3ρm
(2l + 1)ρ̄
]−1
. (14)
(Aml , Bm
l ) and (Cml , Dm
l ) are the fully normalized coefficientof the spherical harmonic expansions of the topographyh anddeflectionw, respectively. For loads of wavelengths much lethanR, αl ≈ γl .
The elastic response of the lithosphere to an arbitrary tographic loadh can be modeled by expanding the load in spherharmonics and computingαl , γl , and hencew from Eqs. (6)–(14). The resulting topographyh′ is given byh′ = h+w.
Finally, this approach can also be used to compute the gra
anomaly over the polar cap. We assume a single crustal laof thicknessTc. If the gravity field is expressed as a sphericORTHERN POLAR CAP, MARS 319
antsti-al
ss
o-al
ity
harmonic expansion
1g(θ, φ) = Rp
∞∑l=2
l∑m=0
Pml (cosθ )
(Sm
l cosmφ + Tml sinmφ
)(15)
then the spherical harmonic coefficients (Sml , T
ml ) are given by(
Sml
Tml
)= −4πGρice
(l + 1
2l + 1
)[1−(
1− Tc
Rp
)l+2
γl
](Cm
l
Dml
),
(16)
whereG is the gravitational constant.
4.2. Polar Ice Cap Loading
On the basis of the above formulation we examine loadinthe martian lithosphere by the northern polar cap. We assthat the surface on which the ice rests would, in the absence opolar cap, be perfectly spherical. Exterior to the cap the lowavelength topography of the northern polar region indicathat the ice cap lies off-center in a broad, shallow-relief sad(superposed on the spherical planetary surface). This sharelief saddle may result in long-wavelength deviations of up200 m of the underlying original (i.e., unloaded) surface fra spherical surface; we examine the implications of such detions from sphericity for the estimates of polar cap volume belThe topography surrounding the northern polar cap is extremsmooth at large and small scales (Smithet al. 1998). While itis impossible to rule out undetectable topographic featuresneath the polar cap, the long- and short-wavelength featurthe topography surrounding the cap suggest a smooth orisurface of low relief.
Key parameters adopted in our modeling are given in TabIn the absence of strong constraints on the density of the pice cap, we use a nominal value of 1000 kg m−3, a figure thatneglects the presence of dust, sediments, and volatiles othewater. Predicted lithospheric deflections scale linearly withcap density, however, so we also examine the implicationthis assumption for such inferences as ice cap volume. A mcomplex issue is that of the temporal evolution of the ice cboth the gross changes in height and extent of the cap antime scales over which such changes have occurred. Initiall
TABLE IParameter Values for Flexural Loading Models
Parameter Value
Young’s modulus, E 1011 N m−2
Poisson’s ratio,ν 0.25Mean density, ¯ρ 3940 kg m−3
Mantle density,ρm 3500 kg m−3
Load density,ρice 1000 kg m−3
Gravitational acceleration,g 3.72 m s−2
yeral
Planetary radius,Rp 3397 km
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mcs
f
1
d
tith
spAp
hatdel10)
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andsesr
ther cap
thee, thel of
ibleriorthe
thanural
en-eldm-
thedel
ero-ted,
atedphy
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320 JOHNSO
FIG. 3. (a) Upper profiles depict the topography of the model ice cap lothe dashed line shows the analytical expression for the load (a cosine of colawith quarter wavelength of 593 km and maximum amplitude 1 km), whilesolid line is the load reconstructed from its spherical harmonic expansion. Loprofiles show the deflection of the original surface, as a function of elastic sthickness, for the model. (b) Final topography for the elastic shell thicknein (a).
investigate a simplified scenario, examining the response oelastic lithosphere over an inviscid interior to a load of extand relief similar to those of the present cap.
The 10 off-nadir MOLA profiles across the polar cap indicathat the cap shape can be approximated to first order by a siaxisymmetric function, which we take to be the first quartercle of a cosine of colatitude. The spherical harmonic expanof this simplified load is calculated and the deflectionw andfinal topographyh′ computed for a range of values for the efective elastic lithosphere thickness. Sample forward modelsshown in Fig. 3 for a unit ice cap relief (1 km), a quarter wavlength of 593 km (corresponding to a polar cap radius of◦
in latitude), and effective elastic thicknessesTe of 40, 120, and200 km. The change in slope of the load topography at atance of approximately 500 km is due to tapering of the loedge to avoid numerical problems. The lithospheric deflecscales linearly with the peak applied (or final) load and withice cap density. We scale the predicted final topographyh′ tomatch the relief of the present ice cap of 2950± 200 m (Zuberet al. 1998b) (Figs. 4 and 5). The 10 off-nadir MOLA profileacross the polar cap are compared with the final topographydicted from our simplified load geometry in Fig. 4. The MOLprofiles show the clear symmetry of the polar cap topogra
◦
about the rotation pole for latitudes above 85N (distances of0–300 km). An excellent match of the model profiles to thET AL.
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MOLA data is seen for three orbits (377, 380, and 415) tcross topographically symmetric regions of the cap. The moprovides a good average fit to orbits (404, 406, 408, and 4that cross the cap over Olympia Planitia and the Chasma Borregions, features which are clearly asymmetric about the rtion axis. The model overestimates the height of the cap fororbits yielding rather short profiles (384 and 385) and for or382.
Basement deflections for the isostatic case (Te= 0 km) and foreffective elastic lithosphere thicknesses of 40, 80, 120, 160,200 km are shown in Fig. 5. For this range of elastic thicknesand a cap density of 1000 kg m−3, the base of the northern polacap could extend from 400 to 1180 m below the level ofcap edge. The total mass of dust and sediments in the polaload is unknown, but reasonable lower and upper bounds oncap density are 1000 and 2000 kg m−3, respectively. Becausthe basement deflection scales linearly with the load densitybase of the polar cap could lie more than 2 km below the levethe cap edge for a cap load of density 2000 kg m−3 supported bya thin elastic lithosphere. There is little evidence for a discernouter-rise signature in the model-predicted topography exteto the ice cap, a result attributed to the distributed nature ofload and to partial support of the load by membrane, ratherflexural, stresses. The extent and depth of the predicted flexmoat varies with elastic thickness.
4.3. Gravity Field Predictions
Identification of the degree to which the polar cap is compsated requires information on the gravity field. The gravity fiarising from a (known) topographic load and its flexural copensation can be computed using Eq. (16). Figure 6 showsresults of such a calculation using our axisymmetric load mofor a range of elastic plate thicknessesTe of 40–200 km and forcrustal thicknessesTc of 10 and 50 km, selected as illustrativvalues. Also shown is the gravity anomaly that would be pduced by uncompensated topography (solid line). As expecthere is a trade-off betweenTc andTe, particularly forTe less thanabout 100 km. The peak gravity anomaly due to uncompenstopography is 129 mGal. Flexural compensation of topogracould result in a relative gravity low of about−20 mGal closeto the edge of the polar cap.
The gravity anomaly predicted using a more detailed repsentation of the topography field and a model for loading othin elastic shell that includes tangential stresses (Banerdt 1is shown in Fig. 7. A total crustal thicknessTc of 50 km, an elas-tic thicknessTe of 120 km, a load density of 1500 kg m−3, anda value for the Young’s modulus of 1011 Nm−2 were assumedWhen considering the difference in model load densities, ovegood agreement is seen between the gravity field predictedthis model (Fig. 7) and that predicted from our simplified mo(Fig. 6) for the appropriate choices ofTe andTc. Figure 7 alsoshows a recent gravity field model for Mars (Smithet al.1999);
eboth the gravity field model (“observed gravity”) and the elasticshell model were expanded from spherical harmonic degrees 2
re shown
LITHOSPHERIC LOADING BY NORTHERN POLAR CAP, MARS 321
FIG. 4. Off-nadir profiles (solid) crossing the polar cap, plotted as a function of distance from the north pole. Ground tracks for these orbits a
in Fig. 1a. Dashed lines are the predicted final topography generated by assuming a cosine load and matching the final relief to the value of 2950 m of Zuberet al. (1998b). The model profiles have been shifted by−5 km to match the MOLA data.
t
t
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ution
322 JOHNSO
FIG. 5. Model ice cap relief and basement deflection, scaled such thaice cap relief matches the 2950 m value given by Zuberet al. (1998b). Regionoutlined by the dashed box is magnified in the inset to show predicted deflecin the vicinity of the ice cap edge.
to 52 (employing a cosine taper from degrees 48 to 52).agreement between the observed and modeled field is goodthe western hemisphere portion of the main cap between a85◦N and the pole, but gravity anomalies over the cap souward of 85◦N and circumcap anomalies are not reproducedthe topographically loaded flexure model.
5. VISCOELASTIC LOADING MODELS
The models described above are based on the responseapplied load of an elastic lithosphere over an inviscid substrParticularly for long-wavelength loads, such as the northernlar cap, it is important to examine the viscous relaxation timetopography and its relationship to the temporal evolution ofload. Here we investigate the viscoelastic response of a sp
ical planet to a temporally invariant load of wavelengthλ. The for loads of wavelengths relevant to this problem is insensitiveand
response is described by the governing equations of mass andto deep structure.) Loads of full wavelength comparable toFIG. 6. Free-air gravity anomaly atr = Rp predicted by the axisymmetricgravity anomaly for uncompensated topography. The predicted gravity ano
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TABLE IIParameter Values for Viscoelastic Loading Models
Parameter Value
Planetary radius,Rp 3400 kmCrustal thickness,Tc 50 kmNominal elastic shell viscosity 1030 Pa-sNominal mantle viscosity 1021 Pa-sShear modulus 1011 PaCrustal density,ρc 2800 kg m−3
Mantle density,ρm 3500 kg m−3
Core density,ρco 6600 kg m−3
Core radius,Rco 0.5 Rp
momentum conservation and the equation of gravitationalturbation
ui,i = 0 (17)
σi j , j + ρ(r )φ,i −1ρgδi j = 0 (18)
φ,i i = 4πG1ρ, (19)
whereui is velocity,σi j is stress,ρ(r ) is density,φ is the pertur-bation of the gravitational potential,g is the gravitational acceleration,1ρ is the density pertubation associated with the loand summation over repeated indices is implied. The rheoof an incompressible Maxwell viscoelastic medium is given
σi j + (η/µ) σi j ,t = −Pδi j + 2ηεi j ,t , (20)
whereη andµ are viscosity and shear modulus respectivelyPis pressure, andσi j ,t andεi j ,t are the time derivatives of stresand strain, respectively.
For a specified load and set of planetary mechanical proties, an analytical solution for the time evolution of stressessurface deflections can be obtained (Zhong and Zuber 2000)adopted model parameters are given in Table II. (Note thatparameters of the planetary core are unimportant, as the sol
cosine load for the elastic thicknesses in Fig. 4. The solid line shows the expectedmalies for crustal thicknesses of 10 and 50 km are shown in (a) and (b), respectively.
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LITHOSPHERIC LOADING BY
smaller than twice the cap diameter (or spherical harmonicgrees 9 and greater) have been investigated.
The relaxation of loads of degree 9, 18, and 36 as a funcof time is shown in Fig. 8 for effective elastic thicknesses0, 50, and 100 km. Relaxation in Fig. 8 is represented bydegree of compensation (Turcotteet al. 1981), defined as thratio of the observed deflection to that which would occurlithosphere having no strength were subjected to the sameSeveral important inferences can be made from the figure. Ffor all values of effective elastic lithosphere thickness shoa portion of the load relaxes over a characteristic time giby the Maxwell timeτm. For an upper mantle viscosity of 1021
Pa-s, a value similar to that of the Earth’s upper mantle,Maxwell time is 105 yr. If the mantle viscosity were as great1023 Pa-s, the Maxwell time would be 107 yr (Zhong and Zuber2000). Second, for models incorporating an elastic lithosphthe shortest wavelengths remain uncompensated, even ovescales of 108 yr. Third, for a given wavelength load, there isasymptotic limit to the compensation state that is controlledthe effective elastic lithosphere thicknessTe. For longer wave-length loads, substantial variation in the asymptotic limit is sfor Te in the range 0–100 km.
6. DISCUSSION
The flexural and viscoelastic lithospheric loading models psented here provide bounds on the volume of the present nern polar cap (under the assumptions specified at the beginof Section 4.2) and predictions for the degree of compensaof polar cap topography given specific lithospheric propertHowever, even with detailed information on the current grity and topography over the polar region, inferences on cpensation mechanism and thus of lithospheric structure reqknowledge of the temporal evolution of the polar cap. If the pocap mass and spatial extent have changed significantly overscales comparable to the Maxwell timeτm, the present gravityand topography will reflect not only the present cap geombut the time-integrated history of the cap.
6.1. Present Cap Geometry: Implicationsfor Lithospheric Loading
We first discuss the implications of our lithospheric loadmodels under the premise that the present cap geometry hasisted over a time period longer thanτm (105 yr for a mantleviscosity of 1021 Pa-s). For this assumption to hold, the timscales associated with processes causing significant chanthe mass and extent of the cap, including cap dynamics andmate variations, operate over time scales longer thanτm. Underthese conditions, the present cap is in quasi-steady state (reto τm) and the models described above provide some insightcompensation of cap topography.
The elastic plate calculations of Section 4.2 show that theume of the northern polar cap depends strongly on the effe
elastic lithosphere thickness and on the average density ofload. Using a lower bound on mean cap density, that of H2O iceORTHERN POLAR CAP, MARS 323
de-
ionofthe
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re,timenby
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v-m-uirelartime
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ol-tive
(1000 kg m−3), our axisymmetric cap model gives volume esmates for the cap that vary by 43% for uncompensated to fcompensated topography. For effective elastic lithosphere thnesses in the range 200 to 40 km, the volume calculated fromaxisymmetric cap model lies in the range 1.5 to 1.8× 106 km3.Because of the unknown ice/sediment ratio in the cap, the aage cap density is uncertain to within about a factor of twoplausible upper bound on mean cap density of 2000 kg m3 cor-responds to volume estimates for our axisymmetric cap mthat lie in the range 1.8 to 2.3× 106 km3. Earlier we noted thathe long-wavelength topography surrounding the northern pcap is consistent with the premise that the cap lies on a brlow-relief saddle. Given that the variation in mean elevatsurrounding the cap is±200 m, we conservatively assumeuncertainty in the depth to basement of 200 m everywhereneath the cap. This assumption yields an uncertainty in thevolume of 0.6× 106 km3.
Lithospheric thickness in the northern polar region not oaffects the subsidence beneath the cap but also constrainheat flow into the base of the ice cap. A thin lithosphereplies high values for lithospheric thermal gradient, heat fland basement subsidence, while a thick lithosphere impliesvalues for these quantities. For a given lithosphere thicknthe maximum temperature at the base of the polar cap cacalculated, as the thickness of the polar cap follows from etic shell calculations (Fig. 4). We assume that the base ofelastic lithosphere corresponds to the 550◦C isotherm and usean average Earth-like value for the thermal conductivity oflithosphere of 3.3 W m−1 K−1 (McNutt 1984). A value of 160 K(Squyreset al. 1992) is used for the annual mean surface teperature at the pole, and the thermal conductivity of ice attemperature is 3.8 W m−1 K−1 (Fletcher 1970). For the following calculations we use the basement deflections showFig. 4 for a pure H2O-ice cap. For a 200 km-thick lithospherthermal gradients are low and the temperature at the basthe polar cap is 170 K, a value close to the mean surfaceperature. In contrast, a 40-km-thick lithosphere results in hthermal gradients and temperatures of up to 215 K at theof the polar cap. The presence of sediments in the polar capincrease the cap density and cause greater subsidence bethe cap, thus increasing the predicted temperature at the bathe cap. The thermal conductivity of the cap will also decresomewhat, further increasing the basal temperature. If thedensity is increased to 2000 kg m−3 and the thermal conductivity decreased to 3.5 W m−1 K−1 (values intermediate betweethe thermal conductivities for ice and rock specified abothe temperature at the base of the polar cap would be 23for a 40-km-thick lithosphere. The pressure dependence omelting point of H2O ice is minor (−7.4× 10−8 K Pa−1, Hobbs1974), and the melting point at the base of even a thick careduced by only a few degrees relative to that at the surfDissolved salts within the ice cap, however, could reducemelting point sufficiently that for a thin lithosphere the temp
theature at the base of the cap may approach the melting point ofthe mixture.
rmonict, andshow a
324 JOHNSON ET AL.
FIG. 7. Free-air gravity anomaly atr = Rp predicted using the spherical elastic shell flexure model of Banerdt (1986) and a band-limited spherical haexpansion of MOLA-derived gridded topography (Zuberet al. 1998b). Elastic lithosphere thickness is 120 km, crustal thickness is 50 km, and load, crusmantle densities are 1500, 2900, and 3300 kg m−3, respectively (see text for details). Color-shaded image shows the model-derived gravity field. Contours
similarly bandpass-filtered Mars gravity field model (Smithet al.1999). Solid c the zeroeoc
nai
me
h
seioi
-ageiongi-edtheuch
theunitsi-
ve a
sionichTheth0 km
lsoed-
contour is shown in red, and the contour interval is 50 mGal.
The inferred temperatures at the base of the polar cap clhave implications for the rheology of the ice and thus for viscflow of the cap. Models in which viscous flow balances acmulation produce a best fit to polar cap topography for outwflow velocities of less than 1 mm per martian year, assumirheology appropriate to H2O ice and a temperature for the cmaterial governed by the mean annual surface temperaturenorthern polar region (Zuberet al.1998b). The above discussioshows that vertical temperature gradients in the polar capbe significant, with enhanced temperatures at the base of thleading to greater basal flow and shear stresses within the(Hooke 1998). The maximum relief of the polar cap may tbe controlled by basal flow.
MOLA data alone provide little information on effective elatic lithosphere thickness because topography exterior to thlar cap is dominated by long-wavelength features unassocwith polar processes that mask any consistent flexural mouter rise signature. However, MOLA data in conjunction wgeologic mapping may provide tentative constraints onTe. One
interpretation for the break in slope identified in the profilshown in Fig. 2 is that it corresponds to the boundary betweontours are positive anomalies, dashed contours are negative anomalies,
arlyusu-
ardg apn then
aycapcapus
-po-
atedat–th
the northward-sloping Hesperian units and the Amazoniancircumpolar deposits that fill a flexural topographic depressimmediately outward of the cap. In some regions (e.g., lontudes 135◦ to 270◦E) the older Hesperian units may be coverwith a mantle of Amazonian-age deposits too thin to modifyregional slope imparted by the underlying Hesperian units. Sa relationship would account for the lack of correlation ofmapped contact between the Amazonian and Hesperianwith the break in slope indentified in Fig. 2 within this longtude band. By this interpretation, the flexural moat would hasoutherly latitudinal limit of 75◦ to 78◦N, or 120 to 300 km fromthe edge of the polar cap. (For the purposes of this discuswe ignore profiles that cross the North Polar Basin, for whthe identified location of the break in slope is less robust.)flexural profiles in Fig. 5 indicate that a flexural moat of wid120–300 km could be generated by the response of a 60–12thick elastic lithosphere to the cap load.
As noted earlier, the breaks in slope identified in Fig. 2 acorrelate with the southerly limit of polar cap outliers. The s
eseniments north of the identified slope breaks could therefore re-flect sediments deposited from a retreating former cap of larger
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LITHOSPHERIC LOADING BY
FIG. 8. Degree of compensation for loads of varying wavelengths anelastic lithosphere of thickness (a) 0 km, (b) 50 km, and (c) 100 km. Sdashed, and dotted lines correspond to loads of degree 9 (twice the poldiameter), 18, and 36. The calculations assume a crustal thickness of 50 ka mantle viscosity of 1021 Pa-s; the latter results in a relaxation time for the loof 105 yr. The slight overcompensation for the degree 36 load on a strengtlithosphere occurs because of the influence of the crust–mantle boundathe stress state. In this case local isostasy is not the asymptotic limit olithospheric response to loading (Zhong 1997).
lateral extent than the present cap. The breaks in slopetified in Fig. 2 and the polar cap outliers would then bothconsistent with an earlier cap extending southward to atapproximately 75◦N over a significant longitudinal range. Bthis reasoning, the circumpolar depression filled by Amazosediments would be related to the extent of the formerly lacap, rather than to the flexural response of the lithosphethe present cap, prohibiting inferences on effective elastic lisphere thickness.
Modeling of the free-air gravity anomaly associated withpolar cap topography and comparisons with current gravity
models indicate that interpretation of gravity anomalies in tnorthern polar region is a difficult problem. The modeling dORTHERN POLAR CAP, MARS 325
anlid,r cap
ands
lessy onthe
en-east
ianerto
o-
eeld
scribed in Section 4.3 suggests that the broad gravity highthe central part of the polar cap may reflect flexural competion of topography. Values for effective elastic lithosphere thiness and crustal thickness of 120 and 50 km, respectivelyconsistent with current gravity fields over the western hesphere portion of the main cap for a cap density of 1500 kg m−3
(Fig. 7), although of course these values are nonunique. Lovalues ofTe, consistent with the range inferred on the basisgeology and meridional slope above, would provide a similato the gravity field for higher load densities (Eq. 16).
The poor correlation of gravity anomalies and topograpover much of the north polar region is puzzling. If the lonwavelength gravity anomaly associated with the whole ofcap (80◦N to the pole at most longitudes) is examined, thenobservation that much of the polar cap has no associated grhigh would lead to an interpretation favoring significant compsation of the long-wavelength polar cap load, through viscrelaxation and/or a thin effective elastic lithosphere thickneThe inference that the longest wavelengths associated witcap have at least partially relaxed is supported by the viscotic calculations shown in Fig. 8, as long as the cap is at leaold as the Maxwell time. Under the alternative interpretatii.e., that the main part of the polar cap is reflected in the grasignal, the shorter wavelength anomalies, uncorrelated withpography, may reflect a combination of such effects as latevarying crustal and lithospheric properties (e.g., lateral vations in upper crustal density related to variable ice/sedimratios, Phillipset al. 1999) and spatial variations in the degrof compensation due to the removal and deposition of matat different spatial scales.
6.2. Temporal Evolution of the Polar Cap: Implicationsfor Lithospheric Loading
The above discussion on polar cap volume and basal temtures and inferred thicknesses of the effective elastic lithospwas based on the assumption that the present cap geometpersisted over time scales longer than the Maxwell time formartian mantle. The temporal evolution of the polar cap iscourse, closely coupled to the climate history of Mars. Climhistory is in turn strongly affected by quasi-periodic variatioin planetary obliquity (the angle between the spin axis andnormal to the orbit plane of Mars), which cause changes inaverage insolation as a function of latitude. These changesto an exchange of volatiles among the atmosphere, polar cand regolith. Exchange of volatiles between the regolith andatmosphere or cap may have been important in the past bethe current atmosphere holds insufficient volatiles to accofor a significantly larger former cap (Kiefferet al. 1992). Dur-ing periods of low obliquity the variation in the average annsurface temperature with latitude is high, perennial ice caps f(Kieffer et al.1992), and atmospheric pressure decreases.
hee-ing periods of high obliquity, in contrast, the perennial ice capdecreases in size (Kiefferet al.1992) and atmospheric pressure
ca
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326 JOHNSO
increases. These temporal changes in the volume of the polacan lead to increases and decreases in loading of the underlithosphere.
Several lines of evidence point to a previously larger northpolar cap. First, the presence of outliers suggests that themay have extended southward at least to latitude 75◦N. Second,as mentioned earlier, models in which viscous flow balanaccumulation produce a best fit to polar cap topography for nligible accumulation rates and outward flow velocities of lethan 1 mm per martian year, assuming a rheology appropriaH2O ice (Zuberet al. 1998b). These models for cap dynamisuggest that the polar cap is either in steady state or decrein size at a very slow rate. Third, sublimation models matchthe current cap shape indicate that the net effect of sublition and condensation (for the present obliquity of Mars) inorthward retreat of the southern edges of the cap and groof the cap at the pole (Ivanov and Muhleman 2000). IvanovMuhleman (2000) suggest that if the planetary obliquity hremained constant, the time scale for formation of the curpolar cap shape is 106 to 108 yr. The effect of obliquity cyclesover this time interval tends to favor the lower bound on the fmation time, because the ice cap recedes rapidly during peof high obliquity, but insufficient water ice is restored during priods of low obliquity (Ivanov and Muhleman 2000). Assumtions in the Ivanov and Muhleman model, however, engencaution against overinterpretation of the absolute time scinferred.
Time scales for obliquity variations on Mars are difficult to ifer, and the complexity of feedbacks between orbital variatiand the solid-body response to climate changes may meanthere is no single “characteristic” time scale for obliquity vaations. Individual obliquity cycles occur over periods of abo105 yr (Touma and Wisdom 1993, Bills 1999). The similar timconstants associated with the precession of the martian spinand precession of the orbit normal can lead to obliquity ronances, however, with time scales of 106 yr (Bills 1999). Inaddition, feedback between the changing polar cap massplanetary dynamics can occur. Unloading and loading oflithosphere due to removal and reaccumulation of the pre(Zuber and Smith 1999), or even a significantly larger (B1999), polar cap in any individual obliquity cycle does notfect the planetary dynamics. However, phase lags in this feback mechanism can result in long-term secular changes inobliquity (Rubincam 1990, 1993; Spada and Alfonsi 1998; B1999). Given all of these uncertainties, robust inferences onlong-term evolution of climate on Mars are not possible.
The above discussion indicates that, although current cstraints on climate change time scales and associated chanthe size of northern polar cap are weak, significant changepolar cap volume over periods of 106 to 108 years may have occurred. From our viscoelastic calculations, but only if the martmantle has an Earth-like viscosity of 1021 Pa-s, the time scale
for viscous response of the mantle to changes in cap loadis short compared with the time scale for producing those loN ET AL.
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7. CONCLUSIONS
We have employed elastic and viscoelastic models antimetry and gravity data returned by the Mars Global Surveaerobraking hiatus and science phasing orbits to investigatnature of isostatic compensation of the northern polar caMars. Viscoelastic modeling suggests that the Maxwell timeτm
scales directly with mantle viscosityη, with τ ranging from 105–107 yr for η in the range 1021 (Earth-like) to 1023 Pa-s. Elasticplate models for compensation of the polar cap are valid iftime scales for climate-driven changes in the polar cap sizesignificantly longer thanτm. Under this premise the thicknessthe effective elastic lithosphere and the density of the ice/mixture of the cap load control the cap thickness and volumethe temperature at the base of the cap. A thin elastic lithospbeneath the polar cap results in greater subsidence beneacap, a larger cap volume, and higher basal temperaturesthose of a thick elastic lithosphere. For a thin lithosphere apolar cap containing a significant fraction of sediments, tematures at the base of the cap may approach the melting pocap material. Constraints on effective elastic lithosphere thness are weak. If the Amazonian-aged circumpolar deposia flexural depression surrounding the present cap, the effeelastic lithosphere thickness is in the range 60–120 km. Cuanalyses of gravity and topography (Phillipset al. 1999) areconsistent with an elastic lithosphere thickness of 120 km fcrustal thickness of 50 km, although trade-offs among effecelastic lithosphere thickness, crustal thickness, and load deare permissive of other values forTe. Interpretation of the gravityfield in the northern polar region is difficult. One interpretatis that there is some correlation of gravity and topographythe central portion of the polar cap, but residual anomaliescorrelated with topography, over the remainder of the cap relateral variations in crustal properties (Phillipset al.1999). Analternative interpretation of the long-wavelength gravity fielthat there has been relaxation of the longest wavelengths anthe remaining residual anomalies are at least in part unrelatpolar cap processes.
Current uncertainties in the viscosity of the martian maand in characteristic time scales for climate-driven changepolar cap geometry allow the possibility that the time scagoverning viscous relaxation and climate forcing are sim
ingadThis similarity would result in a complex and coupled loadinghistory and lithospheric response, even for the modern polar
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LITHOSPHERIC LOADING BY
cap. Future work in many areas, including climate modelipolar cap processes, and mantle dynamics, is needed to adfurther our understanding of the effects of polar cap loadingthe martian lithosphere.
ACKNOWLEDGMENTS
We are grateful to the many instrument, spacecraft, and mission operaengineers who have contributed to the success of MGS and MOLA. Weknowledge thoughtful reviews by B. Bills and J. Weertman. This resehas been supported by NASA Grants NAG5-4620 (C.L.J.), NAG5-4077NAG5-4436 (S.C.S.), NAG5-8263 (J.W.H.), NAG5-4448 (R.J.P.), and NAG4555 (M.T.Z.).
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