Probabilistic calculation of near-field tsunami edge waves

Probabilistic tsunami hazard analysis (PTHA) has recently become an important tool to assess tsunami hazards for a given mean return time. The basic elements of PTHA are (1) specification of the source, including uncertainties, (2) calculation of wave heights and other hazard variables at the site, and (3) aggregation over all possible sources and parameters. A stochastic model for earthquake slip generates a suite of initial conditions for tsunami wave calculations and estimates an important source of aleatoric uncertainty. The ensemble of stochastic sources, in combination with a range of source parameters (earthquake probability, magnitude, location, dimensions) derived from historic catalogs, is input to hydrodynamic calculations. The aggregation of these calculations results in a single tsunami hazard curve. One of the more difficult aspects of implementing PTHA is dealing with nonlinear aspects of the tsunami wavefield. In this study, the probabilistic calculation of edge waves associated with tsunamis is addressed, with particular focus on nonlinear interactions among discrete edge-wave modes in the near field. Subduction-zone earthquakes, which generate most of the world’s devastating tsunamis, are particularly efficient at exciting edge waves if the source zone is near or straddles the coastline. In addition, edge waves are an important component of the tsunami hazard along oblique raypaths to the source zone: for example, in calculating the tsunami hazard at San Francisco from a Cascadia subduction zone earthquake. I demonstrate that nonlinear resonant coupling of edge waves develops slowly in time and directly depends on the parameterization of the stochastic source model. The effect of nonlinear resonant coupling on PTHA calculations is examined for an ensemble of magnitude 9 Cascadia subduction-zone earthquakes.