Surface loading of a viscoelastic earth-II. Spherical models

We apply the general theory described in Paper I to the special case of a spherically symmetric, self-gravitating, linear viscoelastic earth model. We begin by deriving equations governing the biorthogonality relations, normalization conditions and energy partitioning of the associated normal modes. Our numerical tests indicate that radially dependent profiles of gravitational- and bulk-energy density provide a characterization of the normal modes that is distinct from the shear-energy density profile considered in previous studies. We formulate expressions governing the response of the earth model to an arbitrary surface-mass load. To facilitate comparison with previous work, we recast these expressions into an impulse-response, Love-number formalism. Our new expressions are mathematically compact, and involve only the inverse decay times and eigenfunctions associated with the homogeneous problem. Numerical tests verify the validity of our new expressions, and confirm the general theory outlined in Paper I.