A Unified Simulation Framework for Megathrust Rupture Dynamics and Tsunamis

Abstract:

Many earthquakes, including megathrust events in subduction zones, occur offshore. In addition to seismic waves, such earthquakes also generate tsunamis. We present a methodology for simultaneously investigating earthquake rupture dynamics and tsunamigenesis, based on solution of the elastic and acoustic wave equations, in the solid and fluid portions of the domain, respectively. Surface gravity waves or tsunamis emerge naturally in such a description when gravitational restoring forces are properly taken into account. In our approach, we adopt an Eulerian description of the ocean and within it solve for particle velocities and the perturbation in pressure, Δp, about an initial hydrostatic state. The key step is enforcing the traction-free boundary condition on the moving ocean surface. We linearize this boundary condition, in order to apply it on the initial surface, and express it as Δp−ρgη=0, where −ρg is the initial hydrostatic gradient in pressure and η is the sea surface uplift (obtained, to first order, by integrating vertical particle velocity on the initial ocean surface). We show that this is the only place one needs to account for gravity. Additional terms in the momentum balance and linearized equation of state describing advection of pressure and density gradients can be included to study internal gravity waves within the ocean, but these can be safely neglected for problems of interest to us. We present a range of simulations employing this new methodology. These include test problems used to verify the accuracy of the method for modeling seismic, ocean acoustic, and tsunami waves, as well as more detailed models of megathrust ruptures. Our present work is focused on tsunami generation in models with variable bathymetry, where previous studies have raised questions regarding how horizontal displacement of a sloping seafloor excites tsunamis. Our approach rigorously accounts for time-dependent seafloor motion, horizontal momentum transfer, and nonhydrostatic corrections to the commonly employed shallow water theory. We envision this approach being used to provide more accurate initial conditions for tsunami models.