Generalized Extreme Value Distribution for Modeling Earthquake Risk in Makran Subduction Zone Using Extreme Value Theory

Adil Rehman; Huai  Zhang

doi:10.52562/injoes.2023.819

Authors

Adil Rehman Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Beijing 100049, China
Huai Zhang Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Beijing 100049, China

DOI:

https://doi.org/10.52562/injoes.2023.819

Keywords:

Makran subduction zone, Earthquake, Generalized extreme distribution, Extreme value theory, Return Period

Abstract

The long-term pattern of severe incidents is one of the most crucial and fascinating topics of seismic events. This work aims to analyze the maximum annual earthquake magnitude in the Makran subduction zone using extreme value theory by implementing the block maxima method. The seismic data utilized for the current study was collected from the International Seismological Center (ISC) ranging from 1934 to 2022. The extreme parameters have fitted utilizing the generalized extreme value distribution. Numerous plots of the generalized extreme value distribution approach gave the accuracy of the used model when fitted to seismic data of the Makran subduction zone. Using the profile likelihood approach, the shape parameters (?) calculated is 0.29. According to the model fit, the Fréchet distribution is the best model for predicting the annual maximum earthquake magnitude in the Makran subduction zone. The estimated return levels for different return periods 10, 20, 50, and 100 are 6.35, 6.81, 7.58, and 8.31, respectively, indicating that an earthquake's maximum magnitude is increasing across the future 100 years. We also computed the profile likelihood to achieve a precise confidence interval. Thus, the 1945 earthquake of the Makran region with magnitude 8.1(Mw) was one of the most significant events in this area and occurred once every 100 years. The significance of this research is to inform decision-makers to implement suitable risk-mitigation methods.

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References

Al Abbasi, J. N., Risan, H. K., & 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(11), 8971-8980.

Arreyndip, N. A., & Joseph, E. (2015). Extreme temperature forecast in mbonge, cameroon through return level analysis of the Generalized Extreme Value (GEV) distribution. International Journal of Physical and Mathematical Sciences, 9(6), 347-352. https://doi.org/10.5281/zenodo.1338456

Beirlant, J., Goegebeur, Y., Segers, J., & Teugels, J. L. (2006). Statistics of extremes: theory and applications. John Wiley & Sons.

Buishand, T. A., de Haan, L., & Zhou, C. (2008). On spatial extremes: with application to a rainfall problem.

Bustos, S. L. G., Navarrete, S., Chancay, A., Mendoza, M., Pincay, M., & Teran, M. (2021). Zoning of Ecuador According to Maximum Magnitudes of Earthquakes and their Frequency of Occurrence using Statistical Models Estimated by Maximum Likelihood. Gazi University Journal of Science, 34(3), 916-935. https://doi.org/10.35378/gujs.780279

Byrne, D. E., Sykes, L. R., & Davis, D. M. (1992). Great thrust earthquakes and aseismic slip along the plate boundary of the Makran subduction zone. Journal of Geophysical Research: Solid Earth, 97(B1), 449-478. https://doi.org/10.1029/91JB02165

Carreau, J., Neppel, L., Arnaud, P., & Cantet, P. (2013). Extreme rainfall analysis at ungauged sites in the South of France: comparison of three approaches. Journal de la Société Française de Statistique, 154(2), 119-138.

Chikobvu, D., & Sigauke, C. (2013). Modelling influence of temperature on daily peak electricity demand in South Africa. Journal of Energy in Southern Africa, 24(4), 63-70.

Chu, L. F., McAleer, M., & Wang, S. H. (2012). Statistical Modeling of Recent Changes in Extreme Rainfall in Taiwan.

Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer Verlag, Berlin.

Embrechts, P., Klüppelberg, C., & Mikosch, T. (2013). Modelling extremal events: for insurance and finance (Vol. 33). Springer Science & Business Media.

Ender, M., & Ma, T. (2014). Extreme value modeling of precipitation in case studies for China. International Journal of Scientific and Innovative Mathematical Research (IJSIMR), 2(1), 23-36.

Epstein, B., & Lomnitz, C. (1966). A model for the occurrence of large earthquakes. Nature, 211(5052), 954-956. https://doi.org/10.1038/211954b0

Ferreira, A., & De Haan, L. (2015). On the block maxima method in extreme value theory: PWM estimators. The Annals of statistics, 276-298. https://doi.org/10.1214/14-AOS1280

Fisher, R. A., & Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. In Mathematical proceedings of the Cambridge philosophical society (Vol. 24, No. 2, pp. 180-190). Cambridge University Press. https://doi.org/10.1017/S0305004100015681

García-Bustos, S., Landín, J., Moreno, R., Chong, A. S. E., Mulas, M., Mite, M., & Cárdenas, N. (2020). Statistical analysis of the largest possible earthquake magnitudes on the Ecuadorian coast for selected return periods. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 14(1), 56-68. https://doi.org/10.1080/17499518.2018.1542500

Gilleland, E., Ribatet, M., & Stephenson, A. G. (2013). A software review for extreme value analysis. Extremes, 16, 103-119. https://doi.org/10.1007/s10687-012-0155-0

Gnedenko, B. (1943). Sur la distribution limite du terme maximum d'une serie aleatoire. Annals of mathematics, 423-453. https://doi.org/10.2307/1968974

Haan, L., & Ferreira, A. (2006). Extreme value theory: an introduction (Vol. 3). New York: Springer. https://doi.org/10.1007/0-387-34471-3

Hasan, H., Radi, N. A., & Kassim, S. (2012). Modeling of extreme temperature using generalized extreme value (GEV) distribution: A case study of Penang. In Proceedings of the world congress on engineering (Vol. 1, pp. 181-186).

Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quarterly Journal of the Royal Meteorological Society, 81(348), 158-171. https://doi.org/10.1002/qj.49708134804

Jenkinson, A. F. (1969). Statistics of extremes of maximum floods. WMO Technical Note, 98. World Meteorological Organization, Geneva, 183-228.

Katz, R. W., Parlange, M. B., & Naveau, P. (2002). Statistics of extremes in hydrology. Advances in water resources, 25(8-12), 1287-1304. https://doi.org/10.1016/S0309-1708(02)00056-8

Kijko, A., & Sellevoll, M. A. (1981). Triple exponential distribution, a modified model for the occurrence of large earthquakes. Bulletin of the Seismological Society of America, 71(6), 2097-2101.

Kopp, C., Fruehn, J., Flueh, E. R., Reichert, C., Kukowski, N., Bialas, J., & Klaeschen, D. (2000). Structure of the Makran subduction zone from wide angle and reflection seismic data. Tectonophysics, 329(1-4), 171–191. https://doi.org/10.1016/S0040-1951(00)00195-5

Lavenda, B. H., & Cipollone, E. (2000). Extreme value statistics and thermodynamics of earthquakes: aftershock sequences.

Li, Y., Cai, W., & Campbell, E. P. (2005). Statistical modeling of extreme rainfall in southwest Western Australia. Journal of climate, 18(6), 852-863. https://doi.org/10.1175/JCLI-3296.1

Li-Ge, C., Jun, Z., Bu-Da, S., Jian-Qing, Z., & Gemmer, M. (2013). Probability distribution and projected trends of daily precipitation in China. Advances in climate change research, 4(3), 153-159. https://doi.org/10.3724/SP.J.1248.2013.153

Macleod, A. J. (1989). Comment on maximum-likelihood estimation of the parameters of the generalized extreme-value distribution. Applied Statistics, 38, 198-199.

Maposa, D., Cochran, J. J., Lesaoana, M., & Sigauke, C. (2014). Estimating high quantiles of extreme flood heights in the lower Limpopo River basin of Mozambique using model based Bayesian approach. Natural Hazards and Earth System Sciences Discussions, 2(8), 5401-5425. https://doi.org/10.5194/nhessd-2-5401-2014

Maruyama, F. (2020): Analyzing the Annual Maximum Magnitude of Earthquakes in Japan by Extreme Value Theory. Open Journal of Applied Sciences, 10(12), 817. https://doi.org/10.4236/ojapps.2020.1012057

Mokhtari, M., Abdollahie Fard, I., & Hessami, K. (2008). Structural elements of the Makran region, Oman sea and their potential relevance to tsunamigenisis. Natural hazards, 47, 185-199. https://doi.org/10.1007/s11069-007-9208-0

Mokhtari, M., Ala Amjadi, A., Mahshadnia, L., & Rafizadeh, M. (2019). A review of the seismotectonics of the Makran Subduction Zone as a baseline for Tsunami Hazard Assessments. Geoscience Letters, 6(1), 1-9. https://doi.org/10.1186/s40562-019-0143-1

Mothupi, T., Thupeng, W. M., Mashabe, B., & Mokoto, B. (2016). Estimating extreme quantiles of the maximum surface air temperatures for the Sir Seretse Khama International Airport using the Generalized Extreme Value Distribution. American Journal of Theoretical and Applied Statistics, 5(6), 365-375. https://doi.org/10.11648/j.ajtas.20160506.16

Parey, S., Hoang, T. T. H., & Dacunha?Castelle, D. (2013). The importance of mean and variance in predicting changes in temperature extremes. Journal of Geophysical Research: Atmospheres, 118(15), 8285-8296. https://doi.org/10.1002/jgrd.50629

Pavlenko, V. A. (2017). Estimation of the upper bound of seismic hazard curve by using the generalised extreme value distribution. Natural Hazards, 89(1), 19-33. https://doi.org/10.1007/s11069-017-2950-z

Pickands, J. (1975). Statistical inference using extreme order statistics. The Annals of Statistics, 3(1), 119-131.

Pisarenko, V. F., Sornette, D., & Rodkin, M. V. (2010). Distribution of maximum earthquake magnitudes in future time intervals: application to the seismicity of Japan (1923–2007). Earth, planets and space, 62, 567-578. https://doi.org/10.5047/eps.2010.06.003

Prescott, P., & Walden, A. T. (1980). Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika, 67(3), 723-724. https://doi.org/10.1093/biomet/67.3.723

Prescott, P., & Walden, A. T. (1983). Maximum likelihood estimation of the parameters of the three-parameter generalized extreme-value distribution from censored samples. Journal of Statistical Computation and Simulation, 16(3-4), 241-250. https://doi.org/10.1080/00949658308810625

Rajendran, C. P., Rajendran, K., Shah-Hosseini, M., Beni, A. N., Nautiyal, C. M., & Andrews, R. (2013). The hazard potential of the western segment of the Makran subduction zone, northern Arabian Sea. Natural hazards, 65, 219–239. https://doi.org/10.1007/s11069-012-0355-6

Scordilis, E. M. (2005). Globally valid relations converting Ms, mb and MJMA to Mw. In Meeting on earthquake monitoring and seismic hazard mitigation in Balkan Countries, NATO ARW, Borovetz, Bulgaria (pp. 11-17).

Shahid, S. (2011). Trends in extreme rainfall events of Bangladesh. Theoretical and applied climatology, 104, 489-499. https://doi.org/10.1007/s00704-010-0363-y

Siliverstovs, B., Ötsch, R., Kemfert, C., Jaeger, C. C., Haas, A., & Kremers, H. (2010). Climate change and modelling of extreme temperatures in Switzerland. Stochastic environmental research and risk assessment, 24, 311-326. https://doi.org/10.1007/s00477-009-0321-3

Varathan, N., Perera, K., & Wikramanayake, N. (2010). Statistical modeling of daily extreme rainfall in Colombo.

Vernant, P. H., Nilforoushan, F., Hatzfeld, D., Abbasi, M. R., Vigny, C., Masson, F., Nankali, H., Martinod, J., Ashtiani, A., Bayer, R., Tavakoli, F., & Chery, J. (2004). Present-day crustal deformation and plate kinematics in the middle east constrained by GPS measurements in Iran and Northern Oman. Geophysical Journal International, 157(1), 381–398. https://doi.org/10.1111/j.1365-246X.2004.02222.x

Wals, J. E., Kelleher, G. (1971). lnstitute of Mathematical statistics is collaborating with JSTOR to digitize, preserve,

and extend access the annals of mathematical statistics. sil. The Annals of Mathematical Statistics, 42(3), 1142-53 (1971).

Wen, X., Fang, G., Qi, H., Zhou, L., & Gao, Y. (2016). Changes of temperature and precipitation extremes in China: past and future. Theoretical and Applied Climatology, 126, 369-383. https://doi.org/10.1007/s00704-015-1584-x

Wiedicke, M., Neben, S., & Spiess, V. (2001). Mud volcanoes at the front of the Makran accretionary complex, Pakistan. Marine Geology, 172(1-2), 57-73. https://doi.org/10.1016/S0025-3227(00)00127-4

Zimbidis, A. A., Frangos, N. E., & Pantelous, A. A. (2007). Modeling earthquake risk via extreme value theory and pricing the respective catastrophe bonds. ASTIN Bulletin: The Journal of the IAA, 37(1), 163-183. https://doi.org/10.2143/AST.37.1.2020804