Coseismic and post-seismic gravity disturbance induced by seismic sources using a 2.5-D spectral element method

I present a prescription for computing free-air coseismic and post-seismic gravity changes induced by seismic sources in a viscoelastic earth model. I assume a spherical earth geometry and a 2.5-D calculation, that is, 3-D motions that satisfy the equations of quasi-static equilibrium on a 2-D viscoelastic structure. The prescription permits application to regional gravity computations where a 2-D structure adequately represents the structural heterogeneity. I use a hybrid approach where deformation is computed on a discretized domain and the resulting density perturbations are expanded with spherical harmonics to produce the free-air gravity field. Starting with a solution to the equations of quasi-static displacements in the Laplace transform domain for a given dislocation source, I solve Poisson’s equation using Lagrangian interpolation on spectral element nodes to compute the required deformation quantities that contribute to free-air gravity. A numerical inverse Laplace transform then yields time domain results. This methodology is tested with analytic solutions on a spherically stratified viscoelastic structure, then applied to evaluate the effect of a descending slab of relatively high viscosity on post-seismic gravity in a megathrust faulting setting.