Surface loading of a viscoelastic earth - II. Spherical models

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