Can weak crust explain the correlation of geoid and topography on Venus?

The effect on geoid and topography of low viscosity crust overlying a steady-state convecting mantle is estimated under the assumption that the shear between crust and mantle does not alter the mantle flow. The weak crustal layer can change the sign of the geoid to topography ratio (admittance). The positive long wavelength admittance for Venus is consistent with a weak crust overlying a mantle with a viscosity that increases strongly with depth. The accepted interpretation of the strong positive correlation of geoid and topography on Venus, is that the convecting mantle of Venus has a constant viscosity with depth. Topography results from vertical normal stresses caused by mantle convection and highlands occur where mantle upwells. For topography to be supported by normal stress, the time scale for crustal flow must be long compared to the time scale for changes in the pattern of mantle flow. Because the high surface temperature of Venus may cause the crust to have a low viscosity, this assumption may be false. Topography should then be dominated by shear coupling between the crust and mantle. In the absence of a crustal layer, convection in a constant viscosity layer gives rise to a geoid anomaly that correlates positively with surface topography. When the viscosity in the layer increases with depth by several orders of magnitude, the surface topography and geoid anomaly become anti-correlated.