Application of Bayesian Markov Chain Monte Carlo method with mixed gumbel distribution to estimate extreme magnitude of tsunamigenic earthquake

Earthquake or tsunami is a disaster that could bring massive life damages and economic loss. Although various studies on forecasting the earthquake have been conducted, the Gutenberg-Richter equation is generally used in practice. In this study, a practical method using statistical frequency analysis was suggested to estimate extreme magnitude of tsunamigenic earthquake. The study employed Bayesian approach to take into account uncertainty of earthquake occurrence corresponding to specific return periods, and mixed distribution functions to incorporate the effect of intermittent occurrence of earthquake into frequency analysis. This study utilized tsunamigenic earthquake data acquired from NOAA (National Oceanic and Atmospheric Administration), for Kamchatka and Kuril Island, Japan within Kamchatka-Kuril-Japan Trench. Using the Metropolis Hasting Markov Chain Monte Carlo (MH-MCMC) sampling, the parameters were estimated for the tsunamigenic earthquake data. Considering the uncertainty of parameters, 95% credible intervals were constructed for various return periods. This study quantified the uncertainty of possibility of earthquake occurrence so that it could be utilized as basic reference for earthquake risk analysis.