A Comparison of Generalized Pareto and Weibull Distributions for Modeling Megathrust Seismic Hazard in Indonesia

Aimmatul Ummah Alfajriyah, Moch Taufik Hakiki, Muhammad Haekhal Aqila

Abstract


Mapping extreme earthquake risks in Indonesia's megathrust zones is critical for disaster mitigation. This study compares the Generalized Pareto (GPD) and Weibull distributions in modeling extreme earthquake magnitude probabilities. We analyzed 74,514 events (Mw>5.5) across 16 megathrust segments from 1973 to 2024. This data representing a comprehensive large-scale analysis at the national level. To ensure statistical independence of observations, a declustering algorithm was applied to isolate mainshocks. Parameters were estimated using Maximum Likelihood Estimation (MLE) via Nelder-Mead optimization, and evaluated using PDF/CDF plots, AIC, and Cramer-von Mises statistics. Results indicate a significant disparity: the Weibull distribution failed to fit any of the segments, whereas the GPD proved suitable for all 16. Consistently lower AIC and test statistics confirm the GPD's superior accuracy in representing extreme magnitude patterns. Furthermore, return periods and corresponding return levels were calculated to explicitly quantify future extreme seismic hazards.

Keywords


Extreme Earthquakes; Generalized Pareto Distribution (GPD); Parameter Estimation; Seismic Risk Mapping; Weibull Distribution.

Full Text:

PDF

References


S. Pasari, A. V. H. Simanjuntak, A. Mehta, Neha, and Y. Sharma, “The Current State of Earthquake Potential on Java Island, Indonesia,” Pure Appl. Geophys., vol. 178, no. 8, pp. 2789–2806, Aug. 2021, doi: 10.1007/s00024-021-02781-4.

M. Foote, J. Hillier, K. Mitchell‐Wallace, and M. Jones, Natural catastrophe risk management and modelling. Wiley, 2017. doi: 10.1002/9781118906057.

C. A. Isnard and E. C. Zeeman, “Some models from catastrophe theory in the social sciences,” in The Use of Models in the Social Sciences, vol. 1, L. Collins, Ed., Routledge, 1976, pp. 38–75. doi: 10.4324/9781315014227.

D. R. Tampubolon, R. Pratama, and A. Y. Gunawan, “Modeling the risk of financial losses due to tectonic earthquakes: Case study on damages to school buildings in a region in Indonesia,” 2024, p. 060001. doi: 10.1063/5.0171170.

P. Taylor, “Calculating Financial Loss from Catastrophes,” in Earthquake Risk and Engineering towards a Resilient World, Cambridge: SECED, Jul. 2015, pp. 1–15.

M. I. Gomes and A. Guillou, “Extreme Value Theory and Statistics of Univariate Extremes: A Review,” International Statistical Review, vol. 83, no. 2, pp. 263–292, Aug. 2015, doi: 10.1111/insr.12058.

W. Anggraeni, S. Supian, Sukono, and N. B. A. Halim, “Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach,” Mathematics, vol. 10, no. 22, p. 4196, Nov. 2022, doi: 10.3390/math10224196.

J. Beirlant, A. Kijko, T. Reynkens, and J. H. J. Einmahl, “Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case,” Natural Hazards, vol. 98, no. 3, pp. 1091–1113, Sep. 2019, doi: 10.1007/s11069-017-3162-2.

R. Shcherbakov, J. Zhuang, G. Zöller, and Y. Ogata, “Forecasting the magnitude of the largest expected earthquake,” Nat. Commun., vol. 10, no. 1, p. 4051, Sep. 2019, doi: 10.1038/s41467-019-11958-4.

C. T. Guloksuz and N. Celik, “An Extension of Generalized Extreme Value Distribution: Uniform-GEV Distribution and Its Application to Earthquake Data,” 2020. [Online]. Available: http//:statassoc.or.th

M.-H. Wu, J. P. Wang, and K.-W. Ku, “Earthquake, Poisson and Weibull distributions,” Physica A: Statistical Mechanics and its Applications, vol. 526, p. 121001, Jul. 2019, doi: 10.1016/j.physa.2019.04.237.

A. Arshad, A. H. Hasan, and S. M. Ahmed, “Optimizing Weibull Distribution Parameters for Improved Earthquake Modeling in Japan: A Comparative Approach,” International Journal of Neutrosophic Science, vol. 24, no. 1, pp. 65–73, 2024, doi: 10.54216/IJNS.240106.

K. H. Coban and N. Sayil, “Evaluation of earthquake recurrences with different distribution models in western Anatolia,” J. Seismol., vol. 23, no. 6, pp. 1405–1422, Nov. 2019, doi: 10.1007/s10950-019-09876-5.

S. Pasari and O. Dikshit, “Stochastic earthquake interevent time modeling from exponentiated Weibull distributions,” Natural Hazards, vol. 90, no. 2, pp. 823–842, Jan. 2018, doi: 10.1007/s11069-017-3074-1.

V. F. Pisarenko, A. Sornette, D. Sornette, and M. V. Rodkin, “Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory,” Pure Appl. Geophys., vol. 171, no. 8, pp. 1599–1624, Aug. 2014, doi: 10.1007/s00024-014-0882-z.

A. Dutfoy, “Earthquake Recurrence Model Based on the Generalized Pareto Distribution for Unequal Observation Periods and Imprecise Magnitudes,” Pure Appl. Geophys., vol. 178, no. 5, pp. 1549–1561, May 2021, doi: 10.1007/s00024-021-02712-3.

M. Zhang and H. Pan, “Application of generalized Pareto distribution for modeling aleatory variability of ground motion,” Natural Hazards, vol. 108, no. 3, pp. 2971–2989, Sep. 2021, doi: 10.1007/s11069-021-04809-3.

M. Ren, “Uncertainty analysis of strong earthquake hazard estimation based on the generalized Pareto distribution model: a case study of the northeastern Tibetan Plateau,” Annals of Geophysics, vol. 64, no. 6, p. SE656, May 2022, doi: 10.4401/ag-8610.

R. Chattamvelli and R. Shanmugam, Continuous Distributions in Engineering and the Applied Sciences - Part I. Cham: Springer International Publishing, 2021. doi: 10.1007/978-3-031-02430-6.

C. Chaudhary and M. L. Sharma, “Probabilistic Models For Earthquakes With Large Return Periods In Himalaya Region,” Pure Appl. Geophys., vol. 174, no. 12, pp. 4313–4327, Dec. 2017, doi: 10.1007/s00024-017-1667-y.

Y. D. W. Sari and Sutikno, “Estimasi Parameter Generalized Pareto Distribution Pada Kasus Identifikasi Perubahan Iklim di Sentra Produksi Padi Jawa Timur,” Jurnal Sains dan Seni ITS, vol. 2, no. 2, pp. 2337–3520, 2013.

A. A. Balkema and L. de Haan, “Residual Life Time at Great Age,” The Annals of Probability, vol. 2, no. 5, Oct. 1974, doi: 10.1214/aop/1176996548.

J. Pickands, “Statistical Inference Using Extreme Order Statistics,” The Annals of Statistics, vol. 3, no. 1, Jan. 1975, doi: 10.1214/aos/1176343003.

S. Kotz and S. Nadarajah, Extreme Value Distributions. Imperial College Press, 2000. doi: 10.1142/p191.

S. Ghosh and S. Resnick, “A discussion on mean excess plots,” Stoch. Process. Their Appl., vol. 120, no. 8, pp. 1492–1517, Aug. 2010, doi: 10.1016/j.spa.2010.04.002.

S. Coles, An Introduction to Statistical Modeling of Extreme Values. London: Springer London, 2001. doi: 10.1007/978-1-4471-3675-0.

C. Scarrott and A. Macdonald, “A Review of Extreme Value Threshold Estimation and Uncertainty Quantification,” 2012.

J. I. McCool, Using the Weibull Distribution. Wiley, 2012. doi: 10.1002/9781118351994.

J. R. M. Hosking and J. R. Wallis, “Parameter and Quantile Estimation for the Generalized Pareto Distribution,” Technometrics, vol. 29, no. 3, p. 339, Aug. 1987, doi: 10.2307/1269343.




DOI: http://dx.doi.org/10.30829/zero.v10i2.28556

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 
 
✉  Contact & Indexing
Get in touch with ZERO: Jurnal Sains, Matematika dan Terapan
Email
zero_journal@uinsu.ac.id
WhatsApp · Admin Official
085270009767