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.