Local Tsunamis and Earthquake Source Parameters

A persistent problem in estimating the severity of local tsunamis generated by earthquakes is explaining the great event-to-event variability of tsunami run-up heights relative to the magnitude of the earthquake. Undoubtedly, there is always variability in run-up that is dependent on local bathymetry. However, many earthquakes in recent years have produced unexpectedly high local run-up heights, given the magnitude of the earthquake, suggesting a complex relationship between local tsunami runup and the source processes of the earthquake. By contrast, the average tsunami amplitude run-up measured far from the earthquake seems to be more simply related to an accurate estimate of the size of the earthquake represented by its moment magnitude (Abe, 1979; Kajiura, 1981; Okal, 1988; Pelayo and Wiens, 1992; Okal, 1993). The purpose of this study is to establish the relationship between earthquake source parameters and the generation, propagation, and run-up of local tsunamis as summarized in Fig. 1. In general terms, displacement of the seafloor during earthquake rupture is modeled using elastic dislocation theory (left panel, Fig. 1) for which the displacement field is dependent on the slip distribution (D/x)), fault geometry 0:, Vj)' and elastic response and properties of the medium (u,:/ calculated from the elastic Green's tensor, Rybicki, 1986). The process of tsunami propagation generally is the result of an exchange between gravitational energy and horizontal kinetic energy in the water column (Okal, 1988). Specifically, nonlinear long-wave theory governs the propagation and run-up of tsunamis (middle and right panels, Fig. 1). Separation of tsunami wave propagation from dynamic seismic displacements away from the source (Comer, 1984; Okal, 1988) permits one to consider only long-wave propagation in the ocean, subject only to quasi-initial conditions given by the coseismic displacements at the source. Temporal dependence of coseismic displacement (u ,(x, I)) can be incorporated into the propagation calculations, using a spatially independent rise time ('0) and rupture front (n propagation defined by rupture velocity (v,), rupture length (L), and rupture direction