The topography and geoid anomalies produced from an upwelling plume are sensitive to the depth of plume buoyancy, Dp, and elastic lithospheric thickness, Te, both of which control the degree of compensation. We formulated spherically axisymmetric convection models of mantle plumes with temperature- and pressure-dependent viscosity to dynamically determine Dp and Te and the resulting topography and geoid anomalies from the plume. From 10 cases with different Rayleigh number, activation energy, and activation volume, we determined Te ranging from 100 km to 180 km and Dp that is approximately twice Te. The ratio of geoid to topography, RG/T, from these plume models is either negative or slightly positive (<0.03) at wavelengths that are most relevant to the Tharsis rise (low harmonics from degrees 2 to 4). The modeled RG/T is significantly smaller than that observed for the Tharsis rise, suggesting that Tharsis is unlikely to be dynamically supported.