Spectral-finite element approach to post-seismic relaxation in a spherical compressible Earth: Application to gravity changes due to the 2004 Sumatra-Andaman earthquake

Abstract

Global navigation satellite systems (GNSSs) have revealed that a mega-thrust earthquake that occurs in an island-arc trench system causes post-seismic crustal deformation. Such crustal deformation data have been interpreted by combining three mechanisms: afterslip, poroelastic rebound and viscoelastic relaxation. It is seismologically important to determine the contribution of each mechanism because it provides frictional properties between the plate boundaries and viscosity estimates in the asthenosphere which are necessary to evaluate the stress behaviour during earthquake cycles. However, the observation sites of GNSS are mostly deployed over land and can detect only a small part of the large-scale deformation, which precludes a clear separation of the mechanisms. To extend the spatial coverage of the deformation area, recent studies started to use satellite gravity data that can detect long-wavelength deformations over the ocean. To date, compared with theoretical models for calculating the post-seismic crustal deformation, a few models have been proposed to interpret the corresponding gravity variations. Previous approaches have adopted approximations for the effects of compressibility, sphericity and self-gravitation when computing gravity changes. In this study, a new spectral-finite element approach is presented to consider the effects ofmaterial compressibility for Burgers viscoelastic earth model with a laterally heterogeneous viscosity distribution. After the basic principles are explained, it is applied to the 2004 Sumatra-Andaman earthquake. For this event, post-seismic deformation mechanisms are still a controversial topic. Using the developed approach, it is shown that the spatial patterns of gravity change generated by the above three mechanisms clearly differ from one another. A comparison of the theoretical simulation results with the satellite gravity data obtained from the Gravity Recovery and Climate Experiment reveals that both afterslip and viscoelastic relaxation are occurring. Considering the spatial patterns in satellite gravity fields is an effective method for investigating post-seismic deformation mechanisms.