Deformation of the core‐mantle boundary induced by spherical‐shell, compressible convection

We derive the single‐mode, mean‐field equations for spherical‐shell convection with variable viscosity and compressibility included. Core‐mantle boundary (CMB) topography produced by whole mantle convection is computed for various rheologies and different thermal boundary conditions at CMB. Results for long‐wavelength undulations show the extreme sensitivity of these signatures to rheological and equation of state parameters. In order to obtain excess ellipticity of about 1 km, the activation energy and volume in the lower mantle should be low and the temperatures at CMB around 4,500 K, in accord with recent experimental findings.