The geoid signal of 2-D convection with temperature and pressure-dependent rheology

Abstract

Upper and lower boundary deformation and the geoid signal of 2-D steady state convection of an infinite Prandtl number fluid with variable viscosity and Rayleigh numbers appropriate to the earth's mantle are studied numerically. The boundary deformations are estimated from the normal stress at the upper and lower free slip boundaries. Several laws resulting in variable viscosity are considered. The dependence of the observables topography and geoid on the control parameters of the system is analysed. At a sufficiently high Rayleigh number, power law dependencies coinciding with the prediction of a boundary layer theory are found. The sign of the geoid is controlled mainly by the pressure dependence: a strong dependence leads to a negative signal above the upflow. This may be prevented by the thick conducting lid typical of Arrhenius type rheologies with low surface temperatures.