Admittance for a convection in a layered spherical shell

A formalism based on an analytical approximation for convection in a layered spherical shell leads to the computation of the Green kernels for topography and gravity, and to the admittance of gravity over topography for the harmonics of the Earth. We study the role of increasing viscosity with depth, of two layers of convection, and of the coupling with lithospheric plates. It is found that a planet with constant viscosity will have positive values for the admittance for all wavenumbers. However, when a step of viscosity between the lower and upper mantle is assumed, negative values for the first harmonics are achieved. This result explains some long-wave observations and provides evidence for an increase of viscosity in the lower mantle.