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.
References
[1]
Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag. https://doi.org/10.1007/978-1-4471-3675-0
[2]
Katz, R.W., Parlange, M.B. and Naveau, P. (2002) Statistics of Extremes in Hydrology. Advances in Water Resources, 25, 1287-1304. https://doi.org/10.1016/S0309-1708(02)00056-8
[3]
Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance. Springer-Verlag. https://doi.org/10.1007/978-3-642-33483-2
[4]
Dawson, T.H. (2000) Maximum Wave Crests in Heavy Seas. Journal of Offshore Mechanics and arctic Engineering-Transactions of the AMSE, 122, 222-224. https://doi.org/10.1115/1.1287039
[5]
Harris, R.I. (2001) The Accuracy of Design Values Predicted from Extreme Value Analysis. Journal of Wind Engineering and Industrial Aerodynamics, 89, 153-164. https://doi.org/10.1016/S0167-6105(00)00060-X
[6]
Roberts, S.J. (2000) Extreme Value Statistics for Novelty Detection in Biomedical Data Processing. IEE Proceedings-Science Measurement and Technology, 147, 363-367. https://doi.org/10.1049/ip-smt:20000841
[7]
Lavenda, B.H. and Cipollone, E. (2000) Extreme Value Statistics and Thermodynamics of Earthquakes: Aftershock Sequences. Annali di geofisica, 43, 967-982.
[8]
Kawas, M.L. and Moreira, R.G. (2001) Characterization of Product Quality Attributes of Tortilla Chips during the Frying Process. Journal of Food Engineering, 47, 97-107. https://doi.org/10.1016/S0260-8774(00)00104-7
[9]
Thomas, M., Lemaitre, M., Wilson, M.L., Vibound, C., Yordanov, Y., Wackernagel, H. and Carrat, F. (2016) Applications of Extreme Value Theory in Public Health. PLoS ONE, 11, e0159312. https://doi.org/10.1371/journal.pone.0159312
[10]
Alexandros, A.Z., Nickolaos, E.F. and Athanasios, A.P. (2007) Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds. Astin Bulletin, 37, 163-183. https://doi.org/10.1017/S0515036100014793
[11]
Pisarenko, V.F., Sornette, D. and Rodkin, M.V. (2010) Distribution of Maximum Earthquake Magnitudes in Future Time Intervals: Application to the Seismicity of Japan (1923-2007). Earth Planets Space, 62, 567-578. https://doi.org/10.5047/eps.2010.06.003
[12]
Abbasi, J.N.A., Risan, H.K. and Resen, I.A. (2018) Application of Kumaraswamy Extreme Values Distributions to Earthquake Magnitudes in Iraq and Conterminous Regions. International Journal of Applied Engineering Research, 13, 8971-8980.
