Convection‐driven tectonics on Venus

Abstract

An analysis is presented for convective stress coupling to an elastic lithosphere as it applies to tectonic deformation on Venus. Theoretical solutions are introduced for the response of a mathematically thick elastic plate overlying a Newtonian viscous medium with an exponential depth dependence of viscosity. A Green's function solution is obtained for the viscous flow driven by a harmonic density distribution at a specified depth. It is shown that during the transient phase of the solution, the field quantities (stress, velocity, displacement) in both media depend upon the rheology of both media, whereas in steady state the solutions become uncoupled. Due to this uncoupling, stresses obtained from a purely viscous solution can be applied as boundary conditions at the base of an isolated elastic plate. I show for such a plate that (1) shear stress imparted at the base of the lower boundary can induce large in‐plane stretching mode forces and (2) these forces can be estimated directly from free‐air gravity anomalies without detailed knowledge of the density distribution in the underlying flow. Free‐air gravity anomalies for Venus imply in‐plane forces of about 2–3×1012 N/m. In‐plane forces of this magnitude are capable of extensive disruption of the Venusian lithosphere. To demonstrate this, an elastic‐plastic analysis is carried out for the deformation of a model Venus lithosphere; the calculation is based on a lithospheric strength envelope and uses gravity and topography as a guide to the magnitude of stresses imparted by convective flow. The results predict that dynamic uplift of Venusian topography must be accompanied by extensive brittle failure and viscous flow in the lithosphere. Geoid anomalies and geoid‐to‐topography ratios for Venusian topographic features are large compared to values for thermal swells in Earth's ocean basins; this suggests that dynamic support of topography must be an important process on Venus. Further, a low‐viscosity zone is probably not present beneath the Venusian lithosphere. A comparative analysis suggests that tectonic deformation of the lithosphere associated with dynamically supported topography on Earth is unimportant.