On the modelling of self-gravitation for full 3-D global seismic wave propagation

Abstract

SUMMARY We present a new approach to the solution of the Poisson equation present in the coupled gravito-elastic equations of motion for global seismic wave propagation in time domain aiming at the inclusion of the full gravitational response into spectral element solvers. We leverage the Salvus meshing software to include the external domain using adaptive mesh refinement and high order shape mapping. Together with Neumann boundary conditions based on a multipole expansion of the right-hand side this minimizes the number of additional elements needed. Initial conditions for the iterative solution of the Poisson equation based on temporal extrapolation from previous time steps together with a polynomial multigrid method reduce the number of iterations needed for convergence. In summary, this approach reduces the extra cost for simulating full gravity to a similar order as the elastic forces. We demonstrate the efficacy of the proposed method using the displacement from an elastic global wave propagation simulation (decoupled from the Poisson equation) at $200\, \mbox{s}$ dominant period to compute a realistic right-hand side for the Poisson equation.