Topography and geoid induced by a convecting mantle beneath an elastic lithosphere

SUMMARY In the absence of seismological measurements, observations of the topography and gravity fields of solid planets are the primary constraints on their internal structure. To compute the synthetic geoid and topography induced by the dynamics of planetary interiors, we introduce a 3-D numerical tool describing mantle convection beneath an elastic lithosphere. Although the energy conservation is treated in the whole spherical domain, the deformation aspect is solved using a hybrid technique (finite volume method for the viscous flow, spectral method for elastic deformation). The mechanical coupling is achieved via the imposition of the traction at the surface of the viscous flow as a basal boundary condition for the elastic deformation. We present both response functions and full thermal convection cases computed with our new method for planetary bodies of varying dimensions: the filtering effect of the lithosphere on the dynamic topography and geoid is specific for each planetary body, justifying the importance of such a tool. Furthermore, since our approach specifically focuses on the mechanical coupling at the base of the lithosphere, it will permit future, more elaborate, rheological treatments. It also enables to discriminate between the radial and tangential components of the viscous traction. The latter is found to have a significant influence on the elastic deformation. The effect on geoid is prominent. More specifically, while a thin elastic lithosphere is usually considered to play little role on the dynamic topography and geoid of Venus, a ∼35 per cent reduction is obtained for geoid height in the numerical example we propose. On a planet with thicker elastic lithosphere such as Mars, the consequence of this filtering effect is to rule out the possibility of a dynamical support for the Tharsis Rise, even for the lowest admissible values of elastic thickness in this region.