A new method for the computation of global viscoelastic post-seismic deformation in a realistic earth model (I) - vertical displacement and gravity variation

We introduce a new method by which to compute global post-seismic deformation (PSD) in a spherically symmetric, self-gravitating viscoelastic earth model. Previous methods are based on simplified earth models that neglect compressibility and/or the continuous variation of the radial structure of Earth. This is because the previous mode summation technique cannot avoid intrinsic numerical difficulties caused by the innumerable poles that appear in a realistic earth model that considers such effects. In contrast, the proposed method enables both of these effects to be taken into account simultaneously. We carry out numerical inverse Laplace integration, which allows evaluation of the contribution from all of the innumerable modes of the realistic earth model. Using this method, a complete set of Green's functions is obtained, including functions of the time variation of the displacement, gravity change, and the geoid height change at the surface for strike-slip, dip-slip, horizontal and vertical tensile point dislocations. As an earth model, we employ the preliminary reference earth model (PREM) and a convex viscosity profile. Further, we investigate the effects of fine layering of the viscoelastic structure and compressibility on a time-series of PSD using the Green's function for a dip-slip fault. The result indicates that the effect of increasing number of layers is saturated at several tens of layers even when compressibility is taken into account and that the effect of compressibility is detectable with modern observational techniques for a shallower large earthquake (Mw similar to 8). As an application, the PSD due to the Sumatra-Andaman Islands earthquake (Mw = 9.3) is estimated. We show that the rate of post-seismic vertical displacement and gravity change is possibly detected in the far field where the epicentral distance exceeds 400 km.