From interpreting data to scenario modeling of subduction events, numerical modeling has been crucial for studying tsunami generation by earthquakes. Seafloor instruments in the source region feature complex signals containing a superposition of seismic, ocean acoustic, and tsunami waves. Rigorous modeling is required to interpret these data and use them for tsunami early warning. However, previous studies utilize separate earthquake and tsunami models, with one-way coupling between them and approximations that might limit the applicability of the modeling technique. In this study, we compare four earthquake-tsunami modeling techniques, highlighting assumptions that affect the results, and discuss which techniques are appropriate for various applications. Most techniques couple a 3D Earth model with a 2D depth-averaged shallow water tsunami model. Assuming the ocean is incompressible and that tsunami propagation is negligible over the earthquake duration leads to technique (1), which equates earthquake seafloor uplift to initial tsunami sea surface height. For longer duration earthquakes, it is appropriate to follow technique (2), which uses time-dependent earthquake seafloor velocity as a time-dependent forcing in the tsunami mass balance. Neither technique captures ocean acoustic waves, motivating newer techniques that capture the seismic and ocean acoustic response as well as tsunamis. Saito et al. (2019) propose technique (3), which solves the 3D elastic and acoustic equations to model the earthquake rupture, seismic wavefield, and response of a compressible ocean without gravity. Then, sea surface height is used as a forcing term in a tsunami simulation. A superposition of the earthquake and tsunami solutions provides the complete wavefield, with one-way coupling. The complete wavefield is also captured in technique (4), which utilizes a fully-coupled solid Earth and ocean model with gravity (Lotto & Dunham, 2015). This technique, recently incorporated into the 3D code SeisSol, simultaneously solves earthquake rupture, seismic waves, and ocean response (including gravity). Furthermore, we show how technique (3) follows from (4) subject to well-justified approximations.
