Steady-state convection in Mars’ mantle

The Martian geoid and topography of the Tharsis region can be understood as induced by a large underlying plume. Using a spherical harmonic representation, we compute the mantle flows induced by such a plume by solving numerically the equation of motion, the stress–strain relation, and Poissonʹs equation governing the potential readjustment due to mass redistribution. The uncertainties concerning the Martian interior structure are accounted for; the effects of the core size, of the core rheology, of a hypothetical phase transition spinel–perovskite at the bottom of the mantle, and of the mantle viscosity profile are investigated. The flow-induced boundary deformations are analyzed, and particular attention is paid to the core-mantle boundary topography and to its flattening because this parameter is important for the determination of the Free Core Nutation period of Mars in the case of a fluid core. Our results show that due to the large number of unknowns, it is impossible to constrain the internal parameters cited above from the observed geoid. Different combinations of these parameters allow the reconstruction of the geoid with reasonable density anomalies in the mantle. We have computed the non-hydrostatic core flattening corresponding to some of these models. The numerical results correspond to an increase of the difference between the equatorial and polar core radii in the range [0.7,2 km] for models with a perovskite layer above the core-mantle boundary, and in the range [1,5.3 km] for models without perovskite layer. The overlap between these ranges is mainly due to the uncertainty existing for the viscosity profile and the core radius.