Surface loading of a viscoelastic planet-III. Aspherical models

In Paper I of this series we developed a generalized normal-mode formalism for computing the response of an aspherical, self-gravitating, linear viscoelastic earth model to a surface load. In the present article we introduce an expansion for the normal modes of an aspherical earth model, using as basis functions the normal modes of a spherically symmetric reference model. This expansion leads to a non-linear eigenvalue problem for the expansion coefficients and decay rates. We develop a linearization of this problem using perturbation theory, which incorporates arbitrary levels of coupling between normal-mode multiplets. As an illustration, we consider the special case of radial perturbations to a spherically symmetric model, and compare predictions based upon perturbation theory with those based upon the usual non-perturbative forward theory. We demonstrate that including overtone coupling is necessary for the accurate prediction of perturbations to the normal-mode decay times and eigenfunctions. These calculations suggest that our theory can accurately accommodate order of magnitude lateral variations in mantle viscosity and significant changes in lithospheric thickness.