Estimating earthquake-induced tsunami height probabilities without sampling

TL;DR

This paper introduces a novel optimization-based method to estimate the probability of earthquake-induced tsunamis reaching certain sizes without relying on sampling, using fault slip models and shallow water equations.

Contribution

It presents a new approach combining optimization and probabilistic modeling to efficiently estimate tsunami height probabilities from earthquake fault slip distributions.

Findings

The method accurately estimates annual probabilities of different tsunami sizes.

It identifies the most effective fault slip mechanisms for tsunami generation.

The approach reduces computational effort compared to sampling-based methods.

Abstract

Given a distribution of earthquake-induced seafloor elevations, we present a method to compute the probability of the resulting tsunamis reaching a certain size on shore. Instead of sampling, the proposed method relies on optimization to compute the most likely fault slips that result in a seafloor deformation inducing a large tsunami wave. We model tsunamis induced by bathymetry change using the shallow water equations on an idealized slice through the sea. The earthquake slip model is based on a sum of multivariate log-normal distributions, and follows the Gutenberg-Richter law for moment magnitudes 7--9. For a model problem inspired by the Tohoku-Oki 2011 earthquake and tsunami, we quantify annual probabilities of differently sized tsunami waves. Our method also identifies the most effective tsunami mechanisms. These mechanisms have smoothly varying fault slip patches that lead to an expansive but moderately large bathymetry change. The resulting tsunami waves are compressed as they approach shore and reach close-to-vertical leading wave edge close to shore.