Real-time tsunami risk evaluation method by synthetic dynamics and Bayesian update

Abstract

This study presents a method of real-time tsunami risk evaluation by combined use of proper orthogonal decomposition (POD) and Bayesian update. The validity of the proposed method is demonstrated through the numerical example targeting plausible tsunamis induced by Nankai-Trough events. First, tsunami simulations are carried out for plausible tsunami scenarios determined by various patterns of fault rupture, and the time histories of wave heights are stored at selected synthetic gauge points. Then, POD is applied to the resulting data matrix of the synthetic dynamics (SD) composed of dynamics modes and coefficients, the latter of which represent scenario-specific information. In the real-time risk evaluation phase, the wave sequences of an actual tsunami event are sequentially measured at the synthetic gauge points and used to estimate the corresponding dynamics coefficients of the constructed SD. At the same time, by the application of Bayesian update, the likelihood of each of the dynamics coefficients pre-calculated for the selected tsunami scenarios is evaluated at each time and sequentially updated to detect the most probable scenario. Finally, the pre-calculated tsunami arrival time and inundation depth distribution corresponding to the detected scenario are determined as risk assessment indices seven minutes after the tsunami generation.