Surface loading of a viscoelastic earth - I. General theory

We present a new normal-mode formalism for computing the response of an asp herical, self-gravitating, linear viscoelastic earth model to an arbitrary surface load. The formalism makes use of recent advances in the theory of t he Earth's free oscillations, and is based upon an eigenfunction expansion methodology, rather than the traditional Love-number approach to surface-lo ading problems. We introduce a surface-load representation theorem analogou s to Betti's reciprocity relation in seismology. Taking advantage of this t heorem and the biorthogonality of the viscoelastic modes, we determine the complete response to a surface load in the form of a Green's function. We a lso demonstrate that each viscoelastic mode has its own unique energy parti tioning, which can be used to characterize it. In subsequent papers, we app ly the theory to spherically symmetric and aspherical earth models.