Numerical studies on the structure of Venusian mantle convection constrained by the geoid and topography

Venus is a planet very similar to the Earth in terms of size, density and composition. However, different from the Earth which has active plate tectonics, Venus is a one-plate planet covered by a thick immobile lithosphere. Observations show that there may be nine hotspots on Venus and they may be still active. The topography and geoid of Venus have relatively long wavelength character with the degree 3 terms are the highest. Analysis about the geoid and topography of Venus shows that their correlation is high and the admittance ratio at lower degrees is large, suggesting a mainly dynamic origin for the topography and geoid at lower degrees. Using these results above as the main constraints, we systematically investigated the influence of phase transitions on the structure of Venusian mantle convection in 3D spherical shell. Both mantle phase transitions from olivine to spinel and from spinel to perovskite are included in our model. We employed an extended Boussinesq approximation, an infinite Prandtl number assumption and strongly temperature- and pressure-dependent viscosity in our model. Calculations are performed with the finite element code CitcomS. Numerical simulations show that convective structure is affected significantly by phase changes. The amplitude of the Clapeyron slops of phase changes and Rayleigh number control the dominant convective wavelength. When no phase changes are included in the model, a representative convective structure shows dominant short-wavelengths with numerous of plumes, typical of stagnant-lid convection. The geoid and the surface topography are highly correlated with large admittance at lower degrees and the powers of the topography and geoid spectra are significantly reduced at long-wavelengths compared with the observed. Phase changes could promote long-wavelength convective structures as previous findings. When other parameters are kept the same, increasing the Clapeyron slops of the phase changes will increase the powers of the topography and geoid spectra at the lower degrees and decrease the number of plumes. The increase of Rayleigh number will also increase the powers of the topography and geoid spectra at the lower degrees, but it will decrease the powers of the topography and geoid spectra at the relatively higher degrees. All these cases have Venus like large admittance ratio at lower degrees and high correlation for the topography and geoid. The model parameters that most satisfy Venus' observations are with a Rayleigh number of 2×10^8 and Clapeyron slops of +-3.5 MPa/K, which generally satisfy the number of plumes, the geoid amplitude spectra, and the admittance and correlation of Venus. The lithosphere is about 256 Km and the lower mantle viscosity is about 2×10^21 Pa.s.