High-order finite difference modeling of tsunami generation in a compressible ocean from offshore earthquakes

To study the full seismic, ocean acoustic, and tsunami wavefields generated by subduction zone earthquakes, we have developed a provably stable and accurate finite difference method that couples an elastic solid to a compressible fluid subject to gravitational restoring forces. We introduce a linearized dynamic traction-free boundary condition for the moving sea surface that is valid for small amplitude perturbations about an ocean initially in hydrostatic balance. We derive an energy balance for the continuous problem and then use high-order summation-by-parts finite difference operators and weak enforcement of boundary conditions to derive an equivalent discrete energy balance. The discrete energy balance is used to prove stability of the numerical scheme, and stability and accuracy are verified through convergence tests. The method is applied to study tsunami generation by time-dependent rupture on a thrust fault in an elastic solid beneath a compressible ocean. We compare the sea surface evolution in our model to that predicted by the standard tsunami modeling procedure, which assumes seafloor uplift occurs instantaneously and neglects compressibility of the ocean. We find that the leading shoreward-traveling tsunami wave in our model has a noticeably smaller amplitude than that predicted by the standard approach.