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

• 作者: Fumio Maruyama
• 来源期刊: 应用科学(英文)
• 学科: 地球科学
• 关键词: Extreme Value Theory Generalized Extreme Value Distribution EARTHQUAKES
• 年，卷（期）: 2020,（12）
• 页码范围: 817-824
• 页数: 8页
• 分类号: P31

摘要

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, <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em>&#958;</em></span></span> was evaluated as <span style="white-space:nowrap;"><span style="white-space:nowrap;">&#8722;</span></span>0.163, with a 95% confidence interval of [<span style="white-space:nowrap;"><span style="white-space:nowrap;">&#8722;</span></span>0.260, <span style="white-space:nowrap;"><span style="white-space:nowrap;">&#8722;</span></span>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.