Modeling the Influence of Coseismic Horizontal Seafloor Displacement on Tsunami Generation and Propagation

Conventional tsunami generation theory assumes that vertical uplift at the seafloor is entirely responsible for sea surface uplift after an earthquake. This vertical uplift, which includes direct vertical displacement as well as contributions from horizontal displacement of the sloped seabed, is low-pass filtered to account for nonhydrostatic ocean response at short wavelengths and used as an initial condition in tsunami models. However, Song et al. [2008] suggest that for geometries and horizontal displacements associated with realistic tsunamis, horizontal momentum transfer plays a key role in determining tsunami height. To gain insight into this problem, we use a provably stable and accurate finite difference method that can model the full seismic, ocean acoustic, and tsunami wavefield generated by megathrust earthquakes in two dimensions. This is done using summation-by-parts (SBP) finite difference operators and weak enforcement of boundary conditions via the simultaneous approximation term (SAT) method. Our numerical method rigorously couples the elastodynamic response of the solid Earth with that of a compressible ocean, in the presence of gravity. We model surface gravity waves using a linearized traction-free boundary condition on the perturbed free surface of an ocean initially in hydrostatic balance. We have applied our method to study the seismic, ocean acoustic, and tsunami waves generated by rupture on a thrust fault extending to the bottom of an ocean of constant depth. The results of our model disagree somewhat with the tsunami predicted by the standard approach; the amplitude of the landward traveling tsunami is smaller than predicted, while the amplitude of the seaward traveling tsunami is larger than predicted. We are presently studying if this difference is a directivity effect associated with up-dip rupture propagation or is related to horizontal momentum transfer to the ocean. Using our method, we have the potential to investigate tsunamis generated by vertical and horizontal displacements in oceans with realistically complex seafloor geometries.