Highorder finite difference modeling of tsunami g

Authors: Gabriel C Lotto Eric M Dunham

Publish Date: 2015/03/12

Volume: 19, Issue: 2, Pages: 327-340

PDF Link

Abstract

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 tractionfree 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 highorder summationbyparts 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 timedependent 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 shorewardtraveling tsunami wave in our model has a noticeably smaller amplitude than that predicted by the standard approach

Keywords: