Viscoelastic crustal deformation by finite quasi‐static sources

Abstract

A method is formulated for the exact calculation of Green functions for finite quasi‐static sources in an elastic layer over a linear viscoelastic half space. The displacements due to the same sources in an elastic layer over an elastic half space are first computed, and then the well‐known correspondence principle of linear viscoelasticity is applied. The most difficult part of the problem, the inversion into the time domain, is accomplished by means of a novel technique. As a first example of the method, the growth of the error in an approximate Green function for a strike slip source is evaluated. Second, the viscoelastic uplifts due to an expanding sphere are calculated for two half‐space rheologies. Third, the time dependent uplifts due to point dip slip sources are computed. Finally, the dip slip Green functions are integrated over a finite rectangular fault surface, and the coseismic and postseismic uplifts are compared.