Analyzing the Annual Maximum Magnitude of Earthquakes in Japan by Extreme Value Theory

Fumio Maruyama

doi:10.4236/ojapps.2020.1012057

Abstract

One of the most important and interesting issues associated with the earthquakes is the long-term trend of the extreme events. Extreme value theory provides methods for analysis of the most extreme parts of data. We estimated the annual maximum magnitude of earthquakes in Japan by extreme value theory using earthquake data between 1900 and 2019. Generalized extreme value (GEV) distribution was applied to fit the extreme indices. The distribution was used to estimate the probability of extreme values in specified time periods. The various diagnostic plots for assessing the accuracy of the GEV model fitted to the magnitude of maximum earthquakes data in Japan gave the validity of the GEV model. The extreme value index, ξ was evaluated as −0.163, with a 95% confidence interval of [−0.260, −0.0174] by the use of profile likelihood. Hence, the annual maximum magnitude of earthquakes has a finite upper limit. We obtained the maximum return level for the return periods of 10, 20, 50, 100 and 500 years along with their respective 95% confidence interval. Further, to get a more accurate confidence interval, we estimated the profile log-likelihood. The return level estimate was obtained as 7.83, 8.60 and 8.99, with a 95% confidence interval of [7.67, 8.06], [8.32, 9.21] and [8.61, 10.0] for the 10-, 100- and 500-year return periods, respectively. Hence, the 2011 off the Pacific coast of Tohoku Earthquake, which was the largest in the observation history of Japan, had a magnitude of 9.0, and it was a phenomenon that occurs once every 500 year.

Highlights

Extreme value theory has emerged as one of the most important statistical disciplines for the applied science
The various diagnostic plots for assessing the accuracy of the Generalized extreme value (GEV) model fitted to the magnitude of maximum earthquakes data in Japan gave the validity of the GEV model
The extreme value index, ξ was evaluated as −0.163, with a 95% confidence interval of [−0.260, −0.0174] by the use of profile likelihood

Summary

Introduction

Extreme value theory has emerged as one of the most important statistical disciplines for the applied science. Using the extreme value theory, the theoretical. Statistical approaches focused on extreme values have shown promising results in forecasting unusual events in earth sciences, genetics and finance. Extreme Value Theory (EVT) was developed in the 1920s [1] and has been used to predict the occurrence of events as varied as droughts and flooding [2] or financial crashes [3]. Application of extreme value modeling has been published in the fields of ocean wave modeling [4]; wind engineering [5]; biomedical data processing [6]; thermodynamics of earthquakes [7]; food science [8]; and public health [9]

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