A comparison of methods for modeling the complete seismic, ocean acoustic, and tsunami wavefield from offshore earthquakes

Seafloor instruments in the earthquake-tsunami source region feature complex signals containing a superposition of seismic, ocean acoustic, and tsunami waves. Most studies utilize a two-step modeling method with one-way coupling between separate earthquake and tsunami models. The earthquake model provides the seismic wavefield or at least the static elastic displacements, which are used as forcing or to set initial conditions in a tsunami model. The tsunami model assumes the ocean is incompressible, thereby neglecting ocean acoustic waves. This motivates the development of alternative methods that capture the seismic and ocean acoustic response as well as tsunamis. The fully-coupled method, which utilizes a coupled solid Earth and ocean model with gravity (Lotto & Dunham, 2015), was recently incorporated into the 3D code SeisSol (Krenz et al., 2021). This method captures the complete wavefield which simultaneously solves earthquake rupture, seismic waves, and ocean response (including gravity). The complete wavefield is also captured in the Saito et al. (2019) superposition method, but through a two-step modeling procedure. The superposition method first solves the 3D elastic and acoustic equations to model the seismic wavefield and response of a compressible ocean without gravity. Then, in a separate tsunami simulation based on the shallow water equations, changes in sea surface height from the zero-gravity solution are used as a forcing term. A superposition of the earthquake and tsunami solutions provides the complete wavefield. We show through mathematical derivation that the superposition method emerges as an approximation to the fully-coupled method, subject to often well-justified assumptions. In addition, we show a 3D comparison of the solution from the different methods in response to both imposed seafloor uplift and to a dynamic rupture source. We highlight similarities and differences in the methods and identify conditions that permit use of one of the approximate methods.