and Planetary Science Letters 189 (2001) 75^84 www.elsevier.com/locate/epsl

Degree-1 mantle and the crustal dichotomy on

Shijie Zhong *, Maria T. Zuber

Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA

Received 18 October 2000; received in revised form 26 March 2001; accepted 11 April 2001

Abstract

The surface of Mars consists of an old, heavily cratered and elevated southern hemisphere and younger, resurfaced and depressed northern hemisphere, a feature often termed the crustal dichotomy. The global crustal structure [Zuber et al., 2000] revealed by topography and gravity data from the Mars Global Surveyor spacecraft, and the possible late formation of the boundary zone between the hemispheres [McGill and Dimitriou, 1990], have been proposed to indicate an endogenic origin for the dichotomy. However, degree-1 that is required for any endogenic process to be viable cannot be produced with conventional mantle convection models [Schubert et al., 1990]. We have studied the role of radially stratified viscosity on mantle deformation by using Rayleigh^Taylor instability analyses in a spherical shell geometry. Our analyses reveal that when mantle viscosity is stratified with a weak , deformation at long wavelengths is more efficient than that at short wavelengths. The weaker the asthenosphere, the longer the wavelength at which the deformation is the most efficient. A thicker asthenosphere also favors the deformation at long wavelengths. Both the Rayleigh^Taylor instability analyses and numerical modeling of mantle convection show that degree-1 convection can be produced within the Martian mantle provided that the mantle had a weak asthenosphere (V500 km thick and V102 times weaker than the underlying mantle) early in planetary history. The degree-1 convection causes preferential heating of one hemisphere that may explain the primary features associated with the dichotomy in crustal structure. ß 2001 Elsevier Science B.V. All rights reserved.

Keywords: mantle; convection; Mars; mantle rheology;

1. Introduction cesses include single [7] and multiple [8] hemi- spheric-scale impacts. An impact-related mecha- Since the Martian crustal dichotomy was ¢rst nism implies that the dichotomy is a primordial identi¢ed by the Mariner 9 spacecraft [4], both feature [2] formed when large impactors in - endogenic [5,6] and exogenic [7,8] processes have crossing orbits were still present in the post-accre- been proposed to explain its origin. Exogenic pro- tional . However, an impact origin may be di¤cult to reconcile with recent Mars Global Surveyor (MGS) geophysical observations that indicate pole-to-pole gradual variations in to- * Corresponding author. Present address: Department of Physics, University of Colorado at Boulder, Boulder, CO pography [9] (Fig. 1a) and crustal thickness [1] 80309, USA. Tel.: +1-303-735-5095; Fax: +1-303-492-7935. and a mismatch between the surfacial expression

0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved. PII: S0012-821X(01)00345-4

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart 76 S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84

Fig. 1. (a) Molleweide projection of the topography of Mars updated from Smith et al. [9]. The geological expression of the di- chotomy boundary occurs approximately at the green to blue transition. In the map zero longitude runs down the center of the ¢gure. (b) Pole-to-pole slice of topography and crustal thickness [1] along 0³ longitude illustrating planet-scale (degree-1) struc- ture. The mean crustal thickness in the north is V40 km (left to center) and increases to V75 km at high southern latitudes (right).

of the dichotomy and the crustal structure (Fig. the observed geological and geophysical con- 1b) [1]. In addition, geological mapping suggests straints. An early study suggested on the basis that at least part of the boundary formed later in of qualitative arguments that the thinner crust in Martian history (Late Noachian or Early Hesper- the northern hemisphere could be a consequence ian) [2,10] than would be expected if produced by of sub-crustal caused by unspeci¢ed de- a mega-impact or impacts. gree-1 mantle convection [5]. More recently, Sleep Endogenic processes could conceivably satisfy [6] proposed that the dichotomy boundary may

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84 77 represent relic boundaries associated with plate to degree-1 convection that can explain the gen- in the northern hemisphere. The con¢r- eral characteristics of the global topography and mation of the impact origin of the 1500-km diam- crustal structure. eter Utopia structure [2] in the northern hemi- sphere from the MGS topography [9] and gravity [11] observations suggest that if the hemi- 2. Physical models spheric di¡erence was a consequence of plate tec- tonics, it must have originated early in solar sys- To study the generation of degree-1 structure, tem history. The recent discovery of zones of we have employed two di¡erent approaches: Ray- alternating magnetization in the southern hemi- leigh^Taylor instability analyses and ¢nite ele- sphere [12] has been interpreted as evidence of ment models of thermal convection. We describe spreading of the early Martian crust [13]. How- our model approaches in this section. ever, the crust in this region does not have a structure that is obviously suggestive of plate tec- 2.1. A Rayleigh^Taylor instability analysis tonics [1] and other tectonic processes, such as magmatic intrusion [14], may alternatively explain A Rayleigh^Taylor instability analysis may the magnetic lineations. On the other hand, if the provide important insights into the conditions average crustal thickness is V50 km [1], it is un- under which degree-1 convection may occur [22]. clear whether mantle convection could result in Our analytic methods are based on a recently de- of such a thick crust, given that the veloped model for viscoelastic stress relaxation in ^ phase transition, which aids the a spherical shell geometry [23]. For our Rayleigh^ subduction, does not occur until a depth of Taylor instability analysis, the mantle is consid- V200 km. ered to be purely viscous. In addition, the mantle In order for an endogenic process (such as but is assumed incompressible with two layers of dif- not restricted to ) to be a viable ferent viscosity and density. The dynamics is de- mechanism to explain a global feature like the termined by the equations of continuity and mo- crustal dichotomy, planet-scale (degree-1) mantle tion: convection is necessary [3]. However, mantle con- ! vection models with either isoviscous [3] or tem- 9W u ˆ 0 1† perature-dependent viscosity [15,16] structure do ! T ! ! not produce degree-1 convection. Core formation 39P ‡ 9 W ‰R 9 u ‡ 9 u †Š3bger ˆ 0 2† may result in degree-1 convection [3,17], but if this process produced the dichotomy, then evi- where !u is the velocity, P is the pressure, R is the ! dence for early core formation on Mars [18] viscosity, g is the gravitational acceleration, e r is would also imply a primordial origin for the di- the unit vector in vertical direction, and b is the chotomy. Such a scenario would require addition- density. The surface and core^mantle boundary al mechanisms to explain both the resurfacing of (CMB) are subjected to stress-free boundary con- the northern hemisphere [19] and the relatively ditions. Similar analyses in a Cartesian geometry young age for at least part of the dichotomy are used in studying the structure of salt domes boundary [2,11]. The dynamics of solid-state [24,25]. The density interface is at r = rd . For the phase changes may produce a single thermal up- upper layer with r s rd , b = bu and R = Ru. For 3 welling plume (i.e., approximately degree-1 fea- r 6 rd , b = bl (i.e., 3400 kg m in Table 1) and ture), which has been used to explain the Tharsis R = Rl.Ifbl 6 bu, then the two-layer system is un- -tectonic province on Mars [20,21]. How- stable. If a perturbation at a wavelength or spher- ever, a single upwelling plume can only form after ical harmonic degree is introduced to the topog- 2U109 years [20,21], which may be too late to raphy of the density interface, the topography will explain the formation of dichotomy [2]. In this grow with time as the instability develops. For study we explore endogenic processes that lead our models with three deformable density interfa-

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart 78 S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84 ces including the surface and the CMB, the time Table 1 evolution of the interfacial topography H(l,t) Model parameters at harmonic degree l and at r = rd is controlled Parameter Value 6 by the sum of three exponential functions with Mars radius R0 3.4U10 m 6 di¡erent characteristic time dli (i = 1, 2 and 3) Radius of the CMB 1.65U10 m [23] Density of the mantle 3400 kg m33 a Heat production rate Hb(t) X3 Uranium concentration 25.7 ppb H l; t†ˆ hliexp t=d li† 3† Thermal expansivity 3U1035 K31 iˆ1 Thermal di¡usivity 1036 m2 s31 Thermal conductivity 3.0 W K31 m31 where h is the eigenfunction. The characteristic Surface gravitational acceleration 3.7 m s32 li 31 time d depends on the density and viscosity struc- Adiabatic temperature gradient 0.013 K MPa li Temperature at the CMBb 1950 K tures of the two-layer model [23]. The analytic Activation energy E 1.2U105 J mol31 techniques to determine the characteristic times Activation volume V 2U1036 m3 mol31 and eigenfunctions are given in [23]. For b 6 b , a l u Hb(t) is the bulk mantle heat production rate with appropri- there is one positive characteristic time dlo that ate decay times and concentration for each radioactive ele- corresponds to the unstable mode. The growth ments [24]. rate of the instability q(l) for degree l is: bThis temperature includes adiabatic temperature increase with pressure. q l†ˆhlo=d lo 4† internal heating that results from radioactive de- The assumption of the unstable density strati¢- cay [24]. cation is rather arbitrary and is invoked mainly to In contrast to our Rayleigh^Taylor instability simplify our stability analyses. How the mantle analyses, we assume that the mantle has a homo- evolves to give rise to unstable conditions is ad- geneous intrinsic density and that the only source dressed by our models of thermal convection. of density anomalies is from thermal expan- sion: 2.2. Finite element models of thermal convection Nb ˆ b K T3T † 6† with variable viscosity 0 0

A Rayleigh^Taylor instability analysis assumes which drives the mantle £ow. In Eq. 6, b0 and T0 in¢nitesimal deformation and does not include the are reference density and temperature, and K is energetics. To fully understand the development the thermal expansion coe¤cient. We will use of degree-1 mantle structure, it is important to depth- or/and temperature-dependent viscosity: formulate numerical models of thermal convec- tion. In addition to the conservation equations R ˆ A r†exp‰ E ‡ PV†=RTŠ 7† of mass and momentum, Eqs. 1 and 2, we also include the equation of energy balance in our where E and V are activation energy and volume, models of thermal convection: respectively (Table 1), P is the pressure, R is the gas constant, and A(r) determines the radial de- DT ‡ !u W9T ˆ U 92T ‡ Q 5† pendence of viscosity. Our models include an 80- Dt km thick high viscosity lid that does not change where T is the temperature, U is the coe¤cient of with time. Details of viscosity structure are dis- thermal di¡usion, Q is the rate of internal heat cussed in Section 3. generation. We assume that the Martian mantle The surface and CMB are subjected to free-slip has the same concentration of radioactive ele- and isothermal boundary conditions. With the ments as that for the Earth's mantle (Table 1) Bousinessq approximation, we only consider the [24]. We also consider time dependence for the super-adiabatic temperature in our models. The

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84 79 initial temperature is assumed to be equal to the thickness of 750 km (i.e., rd = 2650 km) for the solidus temperature (1160³C) at a depth of 80 km top layer, a perturbation at harmonic degree l is and to decrease linearly to the surface tempera- introduced as the topography for the density in- ture at the surface. Below the depth of 80 km, the terface (the amplitude of the perturbation is the mantle temperature is initially the same as that at same for all harmonic degrees). The growth rate the depth of 80 km. The super-adiabatic temper- for the instability is calculated for each harmonic ature at the CMB is ¢xed at 1320³C. Superim- and is then normalized by the maximum growth posed on this radial temperature pro¢le is a ran- rate found for all harmonic degrees. The maxi- domly perturbed temperature with very small mum growth rate occurs at a spherical harmonic amplitude ( 6 0.1 K). When the adiabatic temper- degree that decreases with increased viscosity for ature gradient is considered, temperature at the the bottom layer (Fig. 2a). Degree-1 becomes the CMB is 1677³C (or 1950 K). This temperature most unstable wavelength (MUW) when the vis- may be consistent with the estimates of melting cosity contrast is greater than 100 (Fig. 2a). Sim- temperature for the core, which depends on the ilar e¡ects of strati¢ed viscosity on the MUW core sulfur content [26]. For the calculations with were observed previously [25,22,29]. Our results temperature-dependent viscosity, the viscosity is indicate that as the viscosity of the lower layer determined by the total temperature that includes increases deformation is more e¤cient at longer the adiabatic temperature. wavelengths. Our models assume a spherically axisymmetric geometry. We use a ¢nite element approach to solve Eqs. 1, 2, and 5 for time-dependent thermal convection [27]. We use 81 and 181 grid points in the radial and azimuthal directions, respectively. Numerical grids are signi¢cantly re¢ned near the thermal boundary layers. Numerical tests with higher resolution demonstrate that our models are well resolved.

3. Results

3.1. Rayleigh^Taylor instability analyses

In a previous study on the origin of hemispher- ic asymmetry of lunar mare (i.e., a degree- 1 structure), we have demonstrated that hydrody- namic instabilities for a planet with a small core relative to planetary radius (Rcore/Rplanet 6 0.15) can lead to degree-1 mantle convection [22]. How- ever, the relatively large core for Mars (0.4 6 Rcore/Rplanet 6 0.6) as implied from recent measurement of the moment of inertia [28] dic- tates that a di¡erent explanation is required for the Martian degree-1 convection. Here we apply Fig. 2. (a) Dependence of normalized growth rate on spheri- Rayleigh^Taylor instability analyses to a two- cal harmonic degrees for a two-layer mantle with di¡erent layer mantle model to investigate the e¡ects of viscosity contrast Ru/Rl between the upper and lower layers. The radius for the boundary between the upper and lower radially strati¢ed viscosity on £ow structure. layer Rd is 2650 km. (b) Dependence of the MUW in terms With parameters appropriate for Mars and a of spherical harmonic degree on Ru/Rl and Rd .

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Fig. 2b shows the dependence of the MUW on gest that viscosity strati¢cation may be the key the viscosity contrast and layer thickness (or rd ). to producing degree-1 mantle convection (Fig. For an isoviscous mantle, the longest possible 2b). Our thermal convection models are used to MUW is degree-4 and it occurs when the two investigate how degree-1 mantle convection may layers are approximately equal in thickness. This develop in a dynamically self-consistent manner. behavior partially explains why thermal convec- The following observations for the Earth's mantle tion models for isoviscous £ow cannot produce prompt us to focus on models for Mars in which degree-1 structure [3]. For isoviscous £ow, when the mantle viscosity increases with depth. (1) The a layer becomes too thin, the resisting force from viscosity in the asthenosphere may be 300 times either the surface or the CMB tends to promote smaller than that in the , as inferred short-wavelength deformation. As the bottom from studies of the Earth's geoid [30]. The in- layer becomes more viscous, the MUW increases ferred viscosity contrast needs to be V600 if sur- and occurs at degree-1 over a wide parameter face tectonic plates are considered in the geoid space (Fig. 2b). Increasing the viscosity for the models [31]. An even weaker asthenosphere is in- top layer also favors long-wavelength structure, ferred from studies of earthquake cycles and post- and degree-1 may become the MUW when the seismic rebound [32] and remote triggering of top layer is su¤ciently more viscous than the bot- earthquakes [33]. (2) Observations of seismic ani- tom layer (Fig. 2b). These analyses indicate that sotropy in the ( 6 300 km in depth) degree-1 structure may be produced with strati¢ed and studies on silicate rheology suggest that man- viscosity structure over a wide range of model tle deformation at depths smaller than 200 to 300 parameters. km is controlled by dislocation creep [34,35], which can substantially weaken the £ow with 3.2. Time-dependent thermal convection stress. A relatively weak shallow layer may also calculations result from the depth dependence of homologous temperature [24] and . The Rayleigh^Taylor instability analyses sug- We ¢rst present three cases to demonstrate the

Fig. 3. Characteristic thermal structure and £ow ¢eld for Cases 1 (a), 2 (b), and 3 (c) with di¡erent Ru/Rl. Rd is 2650 km. The times in (a), (b) and (c) are 4690, 1710, and 450 Ma, respectively. To highlight the velocities in the more viscous lower layer, the amplitudes of velocities are plotted as their square roots. The viscosity for the 80-km thick lid is 2000Rl .

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84 81 control of strati¢ed viscosity on the development 1.5U109 years are 1790, 1717, and 1651 K, re- of degree-1 convection. All three cases have an spectively. Our results thus not only explain the 80-km thick high viscosity lid, and their mantle degree-1 structure, but may also suggest an im- viscosity structures are assumed to be time-invar- portant role of the length scales of mantle struc- iant and only dependent on the radius. Case 1 has ture on heat transfer. The latter point is particu- an isoviscous mantle with a viscosity of 5U1021 larly interesting given that many parameterized Pa s. The characteristic thermal structure for Case mantle convection models that in general do not 1 has wavelengths comparable to the thickness of explicitly consider the e¡ects of wavelengths of the mantle (Fig. 3a), consistent with previous mantle £ow on heat transfer predict an over- studies [3] and predictions from our Rayleigh^ heated Martian mantle [38]. However, our models Taylor instability analysis for isoviscous mantle with layered viscosity structure do not consider (Fig. 2). In Case 2, the viscosity from the base the thickening of with cooling. of the lid to a depth of 750 km is reduced to Mantle rheology may depend on temperature 1020 Pa s. Considering the di¡erence in gravita- and pressure [34]. The e¡ects of this rheology tional acceleration between Mars and the Earth, are considered in Case 4. A relatively small acti- the depth of 750 km may correspond to the vation energy is used (Table 1), because it is con- depths for the asthenosphere and the proposed sistent with observations of £exural rigidity on change in deformation mechanism from disloca- Earth's £oor [39]. The pre-exponential con- tion creep to di¡usion creep in the Earth's upper stant in the rheological equation (Table 1) is chos- mantle [34,35]. However, our numerical experi- en such that the viscosity at the solidus temper- ments and the Rayleigh^Taylor instability analy- ature and the mid-mantle depth is 1020 Pa s. The sis (Fig. 2b) indicate that our conclusions do not pre-exponential constant is reduced by a factor of depend signi¢cantly on the choice of this depth. 500 from 80-km depth to 750-km depth. The re- The incorporation of a weak layer leads to two sultant averaged viscosity structure after 400 Ma di¡erent scales in thermal structure: a short-wave- is similar to that in Case 3. For Case 4 during the length structure in the weak top layer and a long- early stage, convection mainly occurs in the weak wavelength structure associated with the more vis- upper layer with relatively small horizontal scale cous bottom layer (Fig. 3b). This is consistent and temperature anomalies (Fig. 4a). As the lower with previous studies applied to terrestrial mantle layer heats up, it induces convection throughout £ow with a slightly smaller viscosity contrast the mantle and leads to degree-1 structure at [36,37]. Further reduction in viscosity for the V230 Ma (Fig. 4b). The degree-1 structure can top layer to 1019 Pa s in Case 3 results in a de- be maintained for over 1U109 years (Fig. 4c). In gree-1 £ow and thermal structure with one hemi- Case 4, the heat £ux out of the core is greater sphere that is signi¢cantly hotter than the other than 5 mW m32 only in the ¢rst 100 Ma. As (Fig. 3c). The e¡ect of a weak upper layer on the the mantle temperature increases, the core heat £ow structure is thus generally consistent with our £ux decreases and eventually becomes negative. Rayleigh^Taylor instability analysis. Our numerical experiments show that the for- The viscosity structure a¡ects not only the ther- mation of degree-1 structure is insensitive to ini- mal structure (Fig. 3a^c), but also the mantle tem- tial and boundary conditions. For example, with perature and surface heat £ux. Although Cases 1^ the same viscosity structure as in Case 3, similar 3 have the same high viscosity lid, the averaged degree-1 structure to that in Case 3 is produced heat £ux for the ¢rst 1.5U109 years is larger for for models with either insulated bottom boundary models with a weaker upper layer (for Cases 1, 2, conditions or the initial temperature taken from and 3 the heat £ux are 25, 37, and 41 mW m32, Fig. 3a. Numerical resolution tests con¢rm the respectively). The enhanced cooling in such mod- robustness of the results. Due to the computation- els results in lower mantle temperatures. For al cost for models with large viscosity contrast Cases 1, 2, and 3, averaged temperatures for (e.g., Case 3), fully 3D spherical models have the mantle (including lithosphere) for the ¢rst not been computed. However, based on previous

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart 82 S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84

Fig. 4. Thermal structure and £ow ¢eld for Case 4 at di¡erent times 202 Ma (a), 235 Ma (b), and 470 Ma (c) of Case 4 with a depth- and temperature-dependent rheology. studies of thermal convection in 2D spherically ness lithosphere show that the degree-1 mantle axisymmetric and 3D spherical models [40] and convection enhances the cooling of the Martian our Rayleigh^Taylor instability analyses (Fig. 2), mantle, but the signi¢cant core heat £ux is only we believe that our results will not change signi¢- possible in the ¢rst 100 Ma. The time evolution of cantly in fully 3D models. degree-1 mantle convection and the core heat £ux in our models depend on choices of mantle vis- cosity, the heat production rate, and initial mantle 4. Discussion and conclusions temperature distribution [38,41]. A mantle with initially smaller temperature or smaller heat pro- Our Rayleigh^Taylor instability analyses and duction (i.e., possibly as a result of crustal forma- ¢nite amplitude thermal convection calculations tion that leads to more concentrated radioactive demonstrate that hemispherically asymmetric elements in the crust) would lead to larger core (i.e., degree-1) thermal and £ow structures may heat £ux over a longer time. Our models are develop in a dynamically self-consistent manner broadly consistent with early shutdown of the in the Martian mantle, if the early Martian mantle Martian magnetic ¢eld suggested by crustal rem- has a weak asthenosphere (i.e., V100 times weak- nant magnetic anomalies [12,13]. In addition, the er than the underlying mantle; the requirement is time scales are consistent with later formation of less strict for the thickness of asthenosphere). We the dichotomy boundary [2,10], although we rec- think that such a weak asthenosphere is very ognize that the boundary zone between the likely, based on our understanding of Earth's smooth northern lowlands and rough southern mantle viscosity structure [30,33,34] and the ef- highlands has also been in£uenced by other pro- fects of partial melting on mantle viscosity. The cesses such as erosion and perhaps impacts. degree-1 mantle convection may provide an ex- We suggest that degree-1 mantle convection planation to the dichotomy in crustal structure may lead to the dichotomy in crustal structure revealed by the MGS gravity and topography ob- in the following scenario. The hemisphere with servations [1]. Our models with a constant thick- the upwelling (e.g., Fig. 3c) would form the north-

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84 83 ern hemisphere. This scenario requires the lower ture may break up because the Earth's mantle part of the primordial crust to be deformable, convection is more vigorous. This leads to a pe- which is likely given the inferred 50-km average riodicity in the formation of supercontinents. Fu- crustal thickness [1] that would lead to relatively ture studies are needed to explore the model pa- high temperature in the crust to facilitate creep rameters for which degree-1 thermal convection deformation in the lower crust. Dynamic stresses can occur for the Earth's mantle. associated with convection should thin the crust in the hemisphere with the upwelling and thicken the crust in the other hemisphere. Accompanying Acknowledgements crustal thinning in the hemisphere above the up- welling should be surface subsidence and volcan- We thank E.M. Parmentier and S. Karato for ism, which would produce volcanic resurfacing. helpful discussions, L. Kellogg for permission to As the crust and lithosphere cool with time, this use the ¢nite element code, and O. Aharonson for would strengthen the lower crust to maintain the assistance with Fig. 1. We also thank H. Harder crustal structure throughout the Martian history. and F. Nimmo for constructive reviews. This re- A possible test for this model is to use the MGS search was supported by the NASA Planetary data to examine to what extent volcanic resurfac- and Program and the ing has a¡ected the northern hemisphere [42]. NASA Mars Global Surveyor Project.[SK] Alternatively, it is also conceivable that the southern hemisphere may form above the upwell- ing with excessive crustal materials that are pro- References duced by the upwelling and are retained in the southern hemisphere to produce the high eleva- [1] M.T. Zuber et al., Internal structure and early thermal tion there. However, this scenario requires that evolution of Mars from Mars Global Surveyor topogra- no signi¢cant volcanic resurfacing occur in the phy and gravity, Science 287 (2000) 1788^1793. [2] G.E. McGill, A.M. Dimitriou, Origin of the Martian southern hemisphere while the crustal materials global dichotomy by crustal thinning in the late Noachian are produced by the upwelling. Future studies or early Hesperian, J. Geophys. Res. 95 (1990) 12595^ are needed to investigate the dynamic interaction 12605. between degree-1 mantle convection and crustal [3] G. Schubert, D. Bercovici, G.A. Glatzmaier, Mantle dy- formation and deformation and to document geo- namics in Mars and : In£uences of an immobile lithosphere on three-dimensional mantle convection, logical and geophysical evidence to distinguish be- J. Geophys. Res. 95 (1990) 14105^14129. tween these competing scenarios. [4] W.K. Hartmann, Martian cratering, 4, Mariner 9 initial Our models for degree-1 thermal convection analysis of cratering chronology, J. Geophys. Res. 78 may also have implications for the formation of (1973) 4096^4116. supercontinents including the Pangea and Rodinia [5] D.U. Wise, M.P. Golombek, G.E. McGill, Tectonic evo- on the Earth. Because mantle £ow is signi¢cantly lution of Mars, J. Geophys. Res. 84 (1979) 7934^7939. [6] N.H. Sleep, Martian plate tectonics, J. Geophys. Res. 99 in£uenced by surface plates [43], supercontinents (1994) 5639^5655. and the distribution of subduction zones during [7] D.E. Wilhelms, S.W. Squyres, The Martian hemispheric the Pangea [44] imply a degree-1 structure of dichotomy may be due to a giant impact, 309 mantle £ow. While supercontinents may form as (1984) 138^140. [8] H. Frey, R.A. Schultz, Large impact basins and the mega- a result of continental collisions as suggested by impact origin for the crustal dichotomy on Mars, Geo- models of thermal convection in a 2D Cartesian phys. Res. Lett. 15 (1988) 229^232. geometry [45], supercontinents may also be attrib- [9] D.E. Smith et al., The global topography of Mars and uted to the degree-1 thermal convection in the implications for surface evolution, Science 284 (1999) mantle. Our models suggest that such degree-1 1495^1503. [10] K.L. Tanaka, D.H. Scott, R. Greeley, Global stratigra- thermal convection may be generated if the phy, in: H.H. Kie¡er, B.M. Jakosky, C.W. Snyder, M.S. Earth's asthenosphere is su¤ciently weak or/and Matthews (Eds.), Mars, Univ. Arizona Press, Tucson, AZ, thick. Supercontinents and degree-1 mantle struc- 1992, pp. 345^382.

EPSL 5855 5-6-01 Cyaan Magenta Geel Zwart 84 S. Zhong, M.T. Zuber / Earth and Planetary Science Letters 189 (2001) 75^84

[11] D.E. Smith et al., The gravity ¢eld of Mars: Results from [29] E.M. Parmentier, S. Zhong, M.T. Zuber, On the relation- Mars Global Surveyor, Science 286 (1999) 94^97. ship between chemical di¡erentiation and the origin of [12] M.H. Acuna et al., Global distribution of crustal magnet- lunar asymmetries, Proc. 31th LPSC, 2000. ization discovered by the Mars Global Surveyor MAG/ [30] B.H. Hager, M.A. Richards, Long-wavelength variations ER experiment, Science 284 (1999) 790^793. in Earth's geoid: Physical models and dynamical implica- [13] J.E.P. Connerney et al., Magnetic lineations in the ancient tions, Phil. Trans. R. Soc. Lond. Ser. A 328 (1989) 309^ crust of Mars, Science 284 (1999) 794^798. 327. [14] M. Purucker, D. Ravat, H.C. Frey, C. Voorhies, T. Sa- [31] S. Zhong, G.F. Davies, E¡ects of plate and slab viscos- baka, M. Acuna, An altitude-normalized magnetic map of ities on the geoid, Earth Planet. Sci. Lett. 170 (1999) 487^ Mars and its interpretation, Geophys. Res. Lett. 27, 2449^ 496. 2452. [32] G. Zheng, R. Dmowska, J.R. Rice, Modelling earthquake [15] J.T. Ratcli¡, G. Schubert, A. Zebib, Steady tetrahedral cycles in the Shumagin subduction segment, Alaska, with and cubic patterns of spherical-shell convection with tem- seismic and geodetic constraints, J. Geophys. Res. 101 perature-dependent viscosity, J. Geophys. Res. 101 (1996) (1996) 8383^8392. 25473^25484. [33] F.F. Pollitz, R. Burgmann, B. Romanowicz, Viscosity of [16] S. Zhong, M.T. Zuber, L. Moresi, M. Gurnis, The role of oceanic asthenosphere inferred from remote triggering of temperature-dependent viscosity and surface plates on earthquakes, Science 280 (1998) 1245^1249. spherical shell models of mantle convection, J. Geophys. [34] S. Karato, P. Wu, Rheology of the upper mantle: A syn- Res. 105 (2000) 11063^11082. thesis, Science 260 (1993) 771^778. [17] D.J. Stevenson, Lunar symmetry and paleomagnetism, [35] S. Karato, D.C. Rubie, H. Yan, Dislocation recovery in Nature 287 (1980) 520^521. under deep upper mantle conditions: Implications [18] J.H. Chen, G.J. Wasserburg, Formation ages and evolu- for creep and di¡usion, J. Geophys. Res. 98 (1993) 9761^ tion of Shergotty and its parent from U^Th^Pb system- 9768. atics, Geochim. Cosmochim. Acta 50 (1986) 955^968. [36] S. Zhang, D.A. Yuen, The in£uences of lower mantle [19] G.E. McGill, S.W. Squyres, Origin of the Martian crustal viscosity strati¢cation on 3-D spherical-shell mantle con- dichotomy: Evaluating hypotheses, Icarus 93 (1991) 386^ vection, Earth Planet. Sci. Lett. 132 (1995) 157^166. 393. [37] H.-P. Bunge, M.A. Richards, J.R. Baumgardner, E¡ect of [20] H. Harder, U. Christensen, A one-plume model of Mar- depth-dependent viscosity on the planform of mantle con- tian mantle convection, Nature 380 (1996) 507^509. vection, Nature 379 (1996) 436^438. [21] D. Breuer, D.A. Yuen, T. Spohn, S. Zhang, Three-dimen- [38] D.J. Stevenson, T. Spohn, G. Schubert, Magnetism and sional models of Martian mantle convection with phase thermal evolution of the terrestrial , Icarus 54 transitions, Geophys. Res. Lett. 25 (1998) 229^232. (1983) 466^489. [22] S. Zhong, E.M. Parmentier, M.T. Zuber, A dynamic ori- [39] A.B. Watts, S. Zhong, Observations of £exure and the gin for global asymmetry of lunar mare basalts, Earth viscoelastic properties of the lithosphere, Geophys. J. Planet. Sci. Lett. 177 (2000) 131^141. Int. 142 (2000) 855^875. [23] S. Zhong, M.T. Zuber, Long-wavelength topographic re- [40] Y. Iwase, S. Honda, E¡ects of geometry on the convec- laxation for self-gravitating planets and its implications tion with core-cooling, Earth Planets Space 50 (1998) for the time-dependent compensation of surface topogra- 387^395. phy, J. Geophys. Res. 105 (2000) 4153^4164. [41] G. Schubert, T. Spohn, Thermal history of Mars and the [24] D.L. Turcotte, G. Schubert, , John Wiley, sulphur content of its core, J. Geophys. Res. 95 (1990) New York, 1982. 14095^14104. [25] F. Selig, A theoretical prediction of salt dome patterns, [42] J.W. Head, III, M.A. Kreslavsky, Plains in eastern Elysi- Geophysics 30 (1965) 633^643. um Planitia, Mars: Topographic evidence for aqueous [26] J. Longhi, E. Knittle, J.R. Holloway, H. Wanke, The bulk channels and £ows, Proc. 32th LPSC, 2001. composition, mineralogy and internal structure of Mars, [43] B.H. Hager, R.J. O'Connell, Kinematic models of large- in: H.H. Kie¡er, B.M. Jakosky, C.W. Snyder, M.S. Mat- scale £ow in the Earth's mantle, J. Geophys. Res. 84 thews (Eds.), Mars, Univ. Arizona Press, Tucson, AZ, (1979) 1031^1048. 1992, pp. 184^208. [44] A.G. Smith, A.M. Hurley, J.C. Briden, Phanerozoic Pa- [27] L. Kellogg, S.D. King, E¡ect of mantle plumes on the laeocontinental World Maps, Cambridge University growth of DQ by reaction between the core and mantle, Press, Cambridge, 1981. Geophys. Res. Lett. 20 (1993) 379^382. [45] M. Gurnis, Large-scale mantle convection and the aggre- [28] W.M. Folkner, C.F. Yoder, D.N. Yuan, E.M. Standish, gation and dispersal of supercontinents, Nature 332 R.A. Preston, Interior structure and seasonal mass redis- (1988) 695^699. tribution of Mars from radio tracking of Mars Path¢nder, Science 278 (1997) 1749^1752.

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