Viscoelastic relaxation of a ductile asthenosphere underlying a purely elastic plate is a strong candidate process for explaining anomalous rates of crustal deformation observed following large earthquakes. The nongravitational treatment of Pollitz , which is valid on a global scale and includes the effects of compressibility, is here extended to permit the calculation of gravitational viscoelastic relaxation for a specified spherically layered viscoelastic rheology following an earthquake in an elastic layer. The simple approximations we adopt make the resulting treatment particularly suitable for near-field calculations. For an asthenosphere with a Maxwell rheology, the effect of gravitational coupling is manifested only many relaxation times after the earthquake, as obtained by previous investigators. Its effect is generally to speed up the long-wavelength component of the relaxation process and attenuate the overall vertical displacement pattern. Several subtle features common to the relaxation behavior from several different fault types (thrust, rift, and strike-slip) are identified. The effect of gravitational coupling on horizontal displacements is consistent with flexure of the upper elastic plate driven by the corresponding effects on the vertical displacement. Stress diffusion away from the source region generally exhibits pulse-like behavior which is dispersive in both space and time. If the asthenosphere is confined to a relatively narrow channel, then the dispersion branches governing relaxation are radically altered, and stress diffusion effects far from the coseismic rupture zone exhibit a complicated time dependence reflecting the competing tendencies of toroidal and spheroidal mode relaxation.
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