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Supporting Information
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Model and Numerical Method
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The equations, model setup and numerical solution method are basically the same as in
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Golabek et al. [2011] except in three dimensions (3D) rather than two dimensions (2D). We
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here give information that is specific to the present 3D experiments, and list all the parameters
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used. As a general overview, the I3ELVIS code is used to simulate the period between the
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impact and the end of core formation, then the thermal and compositional fields are
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transferred to the StagYY code, which is used to simulate Mars' long-term evolution to the
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present day.
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1. The I3ELVIS code
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The employed numerical code I3ELVIS [Gerya and Yuen, 2007; Gerya, 2010] combines
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conservative finite differences on a fully staggered grid and marker-in-cell techniques with
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multigrid solver. The Eulerian computational domain is equivalent to 8000x8000x8000 km
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and is resolved with a regular rectangular grid of 293x293x293 nodes and contains 100
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million randomly distributed Lagrangian markers to represent different materials. The
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"Spherical-Cartesian" approach, in which a spherical body is contained within a Cartesian
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mesh, is employed for modeling a 3D self-gravitating body with a free planetary surface
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[Gerya, 2010; Lin et al., 2009]. The momentum, mass and heat conservation equations and
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Poisson equation for gravitational potential are solved on a non-deforming Eulerian grid
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whereas the advection of transport properties including viscosity, temperature etc. is
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performed with moving Lagrangian markers. The free surface boundary condition at the
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planetary surface is implemented by using a “sticky” atmosphere [Schmeling et al., 2008]
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with low density (1 kg/m3) and viscosity (1018 Pa s).
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The initial post-impact 3D model setup is based on the simplified approach described in
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Golabek et al. [2011]. As an initial condition for the differentiation and core formation model
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after the giant impact, the planet is assumed to be fully accreted, yet not differentiated. This
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approach, in which the extended accretion history is compressed into an initial condition, has
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the advantage of conserving the potential energy released by core formation [Golabek et al.,
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2011]. The resulting mantle temperature profile has the benefit of being spatially variable,
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yielding an early onset of mantle convection. The impact is approximated by a thermal
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anomaly in the planetary interior containing a spherical iron diapir formed from the core of
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the impactor. The thermal anomaly is parameterized depending on the size of the impactor
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and its iron fraction as described by Golabek et al. [2011].
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The rheological model implies constant low viscosity (1018 Pa s) of iron and molten silicate
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and visco-plastic rheology of the solid silicate with temperature and strain rate dependent
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effective viscosity () computed according to experimentally determined flow laws [Ranalli,
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1995]: dry olivine flow law for the mantle and plagioclase (An75) flow law for the crust. At
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elevated stresses (typically superior to 0.1 GPa) dry Peierls creep (Katayama and Karato,
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2008) for the mantle and crust. In addition, visco-plastic rheology of the silicate assumes the
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viscosity limitation in form
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 ≤ (C+P)/ (2II)
(1)
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where II is second strain rate invariant (Pa), P is pressure (Pa),  is the internal friction
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coefficient (=0.3 is used for the mantle and =0.2 is used for the crust), C=100 MPa is the
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rock strength at P =0. The upper and lower viscosity cutoff limits for all materials are 10 24 Pa
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s and 1018 Pa s, respectively.
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Partial melting of the mantle, melt extraction and percolation toward the bottom of the
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forming basaltic crust is implemented in a simplified manner. According to our model, mafic
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magma added to the crust is balanced by melt production and extraction in the mantle.
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However, melt percolation is not modeled directly and considered to be nearly instantaneous
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(i.e. within one time step). The standard (i.e. without melt extraction) volumetric degree of
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mantle melting M0 changes with pressure and temperature according to the linear batch
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melting model [Golabek et al., 2011]. Lagrangian markers track the amount of melt extracted
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during the evolution of each experiment. The total amount of melt, M, for every marker takes
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into account the amount of previously extracted melt and is calculated as
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M = M0 − n Mext
(2)
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where n Mext is the total melt fraction extracted during the previous n extraction episodes.
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The rock is considered non-molten (refractory) when the extracted melt fraction is larger than
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the standard one (i.e. when n Mext > M0). If M >0 for a given marker, the melt fraction Mext =
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M is extracted and n Mext is updated. The extracted melt fraction Mext is assumed to
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propagate much faster than the rocks deform. Melts produced at depths are moved to the
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surface and added to the bottom of the forming crust. In order to ensure melt volume
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conservation and account for mantle compaction and subsidence in response to the melt
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extraction, melt addition to the bottom of the crust is performed at every time step by
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converting the shallowest markers of mantle into crustal markers. The local volume of these
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new crustal markers matches the local volume of extracted melt computed for the time step.
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Following Golabek et al. [2011], basaltic melts are assumed to be only extracted from
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relatively shallow (<300 km depth) mantle regions with low degree of melting (M0<0.2).
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The effective density of partially molten rocks depends on melt fraction
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temperature T, pressure P and changes linearly with the amount of melt fraction
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𝑀,
composition c,
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𝜌𝑒𝑓𝑓 (𝑐, 𝑃, 𝑇, 𝑀) = 𝜌𝑠𝑜𝑙 (𝑐, 𝑃, 𝑇) − 𝑀 [𝜌𝑠𝑜𝑙 (𝑐, 𝑃, 𝑇) − 𝜌𝑙𝑖𝑞 (𝑐, 𝑃, 𝑇)]
(3)
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where 𝜌𝑠𝑜𝑙 and 𝜌𝑙𝑖𝑞 are the densities of the solid and liquid silicates, respectively.
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Densities of solid mantle and crust are self-consistently calculated with the Perple_X package
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(Connolly, 2005), using the minimization of Gibbs free energy for the corresponding P–T
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conditions to determine stable minerals for a Mars-like mantle composition (Khan and
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Connolly, 2008) and basaltic crust. Latent heat associated with phase changes is also
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considered in the numerical model.
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2. Transferring composition and temperature from I3ELVIS to StagYY
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StagYY [Tackley, 2008] also uses a joint Eulerian-Lagrangian approach, with a fixed
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Eulerian fully staggered grid and moving Lagrangian markers. Thus, the markers from the
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I3ELVIS simulation are read into StagYY, transferring compositional information with no
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loss of accuracy. The initial CMB temperature is based on the mean temperature of the core
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from the I3ELVIS simulation. Two significant differences in the discretizations are
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straightforwardly addressed: (i) StagYY treats temperature advection and diffusion purely on
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the Eulerian grid (using a finite-volume scheme) rather than on markers; therefore the transfer
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step involves local averaging of marker temperatures to the appropriate locations on the grid.
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(ii) StagYY uses the yin-yang spherical mesh to model a spherical shell, the outer boundary of
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which corresponds to the surface of Mars and the inner boundary the core-mantle boundary,
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instead of embedding a sphere in a Cartesian mesh. This is handled using a straightforward
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coordinate transformation (from Cartesian to spherical polar coordinates) and discarding of
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markers that are outside the mantle (such tracers normally track 'air' or 'metal').
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3. The StagYY code
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The physical model and parameters used in the present 3-D experiments are identical to those
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in the 2-D experiments of Golabek et al. [2011], which is straightforward because StagYY
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can model both a full 3-D spherical shell used here and the 2-D spherical annulus [Hernlund
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et al. 2008] used in Golabek et al. [2011]. The physical parameters including the rheology,
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radioactive heating, solidus etc. in StagYY are adjusted to match as well as possible those
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used in the I3ELVIS part of the experiment. As in I3ELVIS, melt that is shallower than a
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certain depth is instantaneously moved to the crust. Golabek et al. [2011] detail the StagYY
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treatments of multiple composition-dependent phase transitions, heat-producing element
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fractionation, and increase in solidus with degree of depletion.
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4. Model parameters
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In all models, we include time-dependent radioactive heating by both short- and long-lived
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radiogenic isotopes, with concentrations based on chondritic abundances [Barr and Canup,
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2008]. We assume that 40K and 60Fe partition into the iron core, whereas
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The parameters of the model are defined in the following table:
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Al,
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U, 238U and
Th remain in the martian mantle.
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Parameter
Symbol
Value
Units
R
3.389 × 106
m
Density of uncompressed solid mantle
 sol
3500
kg m-3
Density of uncompressed molten mantle
 liq
2900
kg m-3
Density of uncompressed iron
 Fe
8000
kg m-3
Radius of Mars
Mantle basalt fraction after core formation
f
0.15
Cohesion

1.00 × 108
Friction coefficient

0.2-0.3
Peierls stress
P
9.1 × 109
Pa
Activation energy
Ea
532
kJ mol-1
Activation volume
Va
8.00 × 10-6
m3 mol-1
Dislocation creep onset stress
0
3.00 × 104
Pa
Power law exponent
n
3.5
Latent heat of melting
L
400
kJ kg-1
Heat capacity of silicate
cP
1000
J kg-1 K-1
cP-Fe
1000
J kg-1 K-1
Thermal expansivity of solid silicate
 Si-sol
3.0 × 10-5
K-1
Thermal expansivity of molten silicate
 Si-liq
6.0 × 10-5
K-1
Thermal expansivity of solid iron
 Fe-sol
1.0 × 10-5
K-1
Thermal expansivity of molten iron
 Fe-liq
1.0 × 10-5
K-1
Thermal conductivity of solid silicate
k Si-sol
3
W m-1 K-1
Thermal conductivity of molten silicate
k Si-liq
3.0 × 105
W m-1 K-1
Thermal conductivity of solid iron
k Fe-sol
1.0 × 102
W m-1 K-1
Thermal conductivity of molten iron
k Fe-liq
3.0 × 105
W m-1 K-1
Effective thermal conductivity of molten materials
Keff
3.0 × 105
W m-1 K-1
Crustal radiogenic heating enrichment factor

1
Heat capacity of iron
Pa
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The temperature and the viscosity of the sticky atmosphere have been considered constant all
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over the surface at values of 273 K and 1018 Pa s, respectively, and we used initial isothermal
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temperature profiles close to the surface solidus temperature of peridotite (T = 1200-1400 K).
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References
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Barr, A. C., and R. M. Canup (2008), Constraints on gas giant satellite formation from the interior states of
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136
137
138
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partially differentiated satellites, Icarus, 198(1), 163-177, doi:Doi 10.1016/J.Icarus.2008.07.004.
Connolly, J.A.D. (2005) Computation of phase equilibria by linear programming: A tool for geodynamic
modeling and its application to subduction zone decarbonation. Earth Planet. Sci. Lett., 236, 524–541.
Gerya, T. V. (2010), Introduction to Numerical Geodynamic Modelling, 345 pp., Cambridge University Press,
Cambridge.
Gerya, T. V., and D. A. Yuen (2007), Robust characteristics method for modelling multiphase visco-elasto-
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thermo-mechanical
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problems,
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Golabek, G. J., T. Keller, T. V. Gerya, G. Zhu, P. J. Tackley, and J. A. D. Connolly (2011), Origin of the martian
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dichotomy and Tharsis from a giant impact causing massive magmatism, Icarus (USA), 215(1), 346-357,
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doi:10.1016/j.icarus.2011.06.012.
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Hernlund, J. W., and P. Tackley (2008), Modeling mantle convection in the spherical annulus, Phys. Earth
Planet. Int., 171(1-4), 48-54, doi:10.1016/j.pepi.2008.07.037.
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Katayama, I., Karato, S.-I. (2008) Rheological structure and deformation of subducted slabs in the mantle
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transition zone: implications for mantle circulation and deep earthquakes. Phys. Earth Planet. Interiors,
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Khan, A., Connolly, J.A.D. (2008) Constraining the composition and thermal state of Mars from inversion of
geophysical data. J. Geophys. Res., 113, E07003.
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Lin, J.-R., T. V. Gerya, P. J. Tackley, D. A. Yuen, and G. J. Golabek (2009), Numerical modeling of protocore
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destabilization during planetary accretion: Methodology and results, Icarus (USA), 204(2), 732-748.
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Ranalli, G. (1995), Rheology of the Earth, 2nd ed., 413 pp., Chapman and Hall, London.
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Schmeling, H., et al. (2008), A benchmark comparison of spontaneous subduction models--Towards a free
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surface, Phys. Earth Planet. Inter. (Netherlands), 171(1-4), 198-223.
Tackley, P. J. (2008), Modelling compressible mantle convection with large viscosity contrasts in a three-
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dimensional
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doi:10.1016/j.pepi.2008.1008.1005
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spherical
shell
using
the
yin-yang
grid,
Phys.
Turcotte, D. L., Schubert, G., (2002), Geodynamics. Cambridge University Press.
Earth
Planet.
Int.,
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Fig. S1. Evolution of the Martian dichotomy, from 0.25 Ga to 3.5 Ga after CAI, formed by an
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impactor of 1600 km of radius and 80% of iron in radius. The first column shows the surface
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topography while the second column shows the crustal thickness. a) Surface topography 0.25
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Ga after CAI. The dichotomy has already formed. The highlands are indicated by red, the
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transition topography by yellow and green, and the lowlands by blue. b) Crustal thickness
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0.25 Ga after CAI. New crust has formed in the southern hemisphere. c) Surface topography
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0.5 Ga after CAI. The topography in the highlands has become heterogeneous while the
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transition topography (pale blue) decreases its extent. d) Crustal thickness 0.5 Ga after CAI.
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The growth of the new crust under the highlands occurs mainly at mid-high latitudes with
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pockets concentrated in the western hemisphere and an isolated ridge in the polar area of the
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eastern hemisphere. e) Surface topography 1.0 Ga after CAI. The highlands have stabilized at
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around 20 degrees of latitude south while the transition topography starts to expand towards
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the lowlands modified by volcanic processes occurring along the equatorial regions. f) Crustal
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thickness 1.0 Ga after CAI. The crust under the highlands grows following the pattern
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established in the previous 0.5 Ga. A few pockets of crust appear under the northern polar
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region. g) Surface topography 1.5 Ga after CAI. There is a vigorous expansion of the
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transition topography after the volcanic activity and the appearance of a topographic “island”
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of likely volcanic origin in the northern polar region. h) Crustal thickness 1.5 Ga after CAI.
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The growth of the crust under the highlands has become more homogeneous, decreasing the
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number of pockets, while the topographic island in the northern hemisphere is not followed by
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crustal growth underneath. The number of pockets of new crust increases in the northern
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hemisphere instead. i) Surface topography 2.0 Ga after CAI. The expansion of a Tharsis-like
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and an Elysium-like feature astride the Equator at the dichotomy boundary has begun (white
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arrows). The two features are at an angular distance of roughly 90 degrees to each other,
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similar to Tharsis and Elysium. j) Crustal thickness 2.0 Ga after CAI. The pockets of new
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crust increase both their extent and number under the southern and the northern hemispheres.
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k) Surface topography 2.5 Ga after CAI. The Tharsis-like and Elysium-like features start to
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take shape while sub-polar Scandia-like features start to appear (white arrows). l) Crustal
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thickness 2.5 GA after CAI. The crustal growth is now stabilized both under the southern and
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the northern hemispheres. m) Surface topography 3.5 Ga after CAI. The topographic island at
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the North Pole has disappeared while the Scandia-like features remain as well as the Tharsis-
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like and Elysium-like features (white arrows). The dichotomy has now acquired the final
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configuration that can be seen today. However, the Tharsis-like and Elysium-like features do
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not match the extent of the original ones at this resolution. n) Crustal thickness 3.5 Ga after
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CIA. The crustal thickness has also acquired the final configuration.
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Figure S2. Evolution of the Martian dichotomy, from 0.25 Ga to 3.5 Ga after CAI, formed by
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an impactor of 2000 km of radius and 50% of iron in radius. The first column shows the
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surface topography while the second column shows the crustal thickness. a) Surface
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topography 0.25 Ga after CAI. a) Surface topography 0.25 Ga after CAI. The dichotomy has
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already formed, the highlands are indicated by red, the transition topography by yellow and
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green, and the lowlands by blue. There is a striking similarity in latitude with the result
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obtained by the impactor of 1600 km and 80% of iron. b) Crustal thickness 0.25 Ga after CAI,
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new crust has formed in the southern hemisphere and it is almost comparable with the
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previous experiment. c) Surface topography 0.5 Ga after CAI. Although the latitude is also
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comparable to the corresponding one in the 1600 km impactor, the border of the dichotomy
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appears more frayed. d) Also the crustal thickness is comparable 0.5 Ga after CAI. e) Surface
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topography 1.0 Ga after CAI, the first “fjords” start to appear along the border. f) Crustal
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thickness 1.0 Ga after CAI, the frayed pattern that started to appear on the topography was
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already present in the crustal thickness since the beginning. g) Surface topography 1.5 Ga
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after CAI, the transition topography starts to protrude into the lowlands but is less developed
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than the one produced by the previous experiment. h) Crustal thickness 1.5 Ga after CAI, the
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crustal production under the transition topography starts to appear. i) Surface topography 2.0
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Ga after CAI, the transition topography is more extended in the northern polar area with
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respect to the previous experiment. j) Crustal thickness 2.0 Ga after CAI, patches of crust
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become more developed under the transition topography in the northern polar area and in the
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equatorial stripe. k-n) No significant variations are observed from 2.5 to 3.5 Ga after CAI.
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