The response of a compressible, non-homogeneous Earth to internal loading: Theory.

In this paper, we describe a formalism for computing mantle flow, geoid perturbations, and boundary deformation (at the surface or at the CMB) due to internal loading by lateral density heterogeneities for a spherically-symmetric Earth that is compressible and that has radially dependent viscosity and density. We assume the Earth is neutrally stable below the lithosphere. The solution vector, as well as the density anomalies, are expanded as sums of spherical harmonics with coefficients that depend on radius. Green's functions, responses to a unit mass load, are computed for each order of the spherical harmonics

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