Modeling Tsunamis and Hydroacoustic Waves from Megathrust Earthquakes

The immense damage caused by the 11 March 2011 Tohoku, Japan earthquake demonstrated the importance of understanding tsunami excitation by megathrust ruptures. Of particular interest are any faster-propagating seismic or hydroacoustic signals that could be used to rapidly predict tsunami wave heights. To study the full seismic, acoustic, and tsunami wavefields, 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 new treatment of the dynamic (free surface) boundary condition on the moving sea surface in the presence of gravity that is valid for small-amplitude perturbations about an ocean initially in hydrostatic balance. This permits us to model surface gravity waves in the linearized limit, including dispersion from nonhydrostatic motions at short wavelengths. This is done using summation-by-parts (SBP) finite difference operators and weak enforcement of boundary conditions. Shallow coseismic slip during megathrust events causes seafloor uplift that excites both tsunamis and long-period (~10 s) hydroacoustic waves; the latter ocean sound waves travel at several km/s and reach the coast many minutes sooner than tsunami waves. These hydroacoustic waves might be used as part of local tsunami early warning systems. Our previous dynamic rupture simulations of the Tohoku event, which neglected surface gravity waves, revealed correlations between pressure perturbations recorded at the seafloor (associated with ~10 s hydroacoustic waves in the ocean) and near-trench seafloor uplift caused by shallow slip. Now that we can model tsunamis within the same code, we plan to quantify the correlation between these pressure perturbations and tsunami height. We are also investigating properties of these hydroacoustic modes, which involve significant motions of the solid Earth as well as the ocean. Phase and group velocity curves for a uniform ocean layer over an elastic half-space show that these waves become sound waves in an effectively rigid-bottomed ocean at short period and Rayleigh waves at long period. Transitional behavior occurs at periods comparable to 4H/c ~ 10 s, where H is ocean depth and c is the fluid sound speed. Our simulations show that these waves carry pressure changes ~1 MPa, two orders of magnitude larger than pressure changes associated with the direct passage of the tsunami. These waves can thus be easily recorded by ocean-bottom pressure gauge networks, such as those currently being installed in the Japan Trench, Nankai Trough, and Cascadia subduction zones.