THE RESPONSE OF A COMPRESSIBLE, NONHOMOGENEOUS EARTH TO INTERNAL LOADING - THEORY

Convective flow inside the mantle will cause topography at the Core Mantle Boundary (CMB). The amplitude and shape of the topography depend on details of the flow pattern, and on the Earth's rheology. The topography can be modeled by using seismic tomography results. When lateral variations density are inferred, they are used as internal loads in a viscous Earth. So far, all models have assumed the Earth is incompressible and composed of homogeneous layers. 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. These functions can be convolved with tomography results inside the mantle to get the geoid or the CMB topography, for example.