The Probability Model of Earthquake Frequency in the Enggano Segment using Poisson Mixture Models

Siska Yosmar; Ramya Rachmawati; Septri Damayanti; Jose Rizal

doi:10.31764/jtam.v10i1.33446

The Probability Model of Earthquake Frequency in the Enggano Segment using Poisson Mixture Models

Siska Yosmar, Ramya Rachmawati, Septri Damayanti, Jose Rizal

Abstract

An earthquake is a natural disaster that occurs suddenly resulting in numerous casualties, such as loss of life and property. Bengkulu Province is among the provinces affected by severe earthquakes. Studies on probability models for the frequency of earthquake events in Bengkulu Province are still scarce, as outlined in the 2017 book “Map of Sources and Hazards of Indonesian Earthquakes.” This research uses Poisson mixture models to build a probability model for the frequency of earthquake events in the Enggano segment, located in the coastal area of Bengkulu Province. .. The phases of model building are the model diagnosis phase, testing the dispersion state relative to the Poisson distribution, testing the dependence of research data on time variables using the Ljung-Box test, and testing the criteria for selecting the best model using the Bayesian Tests Measures of Information Criterion (BIC) and Akaike Information Criterion (AIC). Annual earthquake frequency data from January 1, 1971, to December 31, 2022, were retrieved from the USGS catalog of data on the frequency of major earthquakes with a magnitude of Mw ≥ 4.40, which occurred a total of 633 times. After completing the model building phase, the AIC and BIC values for each model were determined by determining the number of unobserved groups. Both Poisson mixture models and Poisson hidden Markov models produced the same number of unobserved groups of 3 groups with AIC=302.91 and BIC=324.38.

Keywords

AIC; BIC; Earthquake; Poisson Mixture Models; Poisson Hidden Markov Models.

Full Text:

DOWNLOAD [PDF]

References

Boden, D. R. (2016). Geologic fundamentals of geothermal energy. CRC Press.

Daniell, J. E., Schaefer, A. M., & Wenzel, F. (2017). Losses associated with secondary effects in earthquakes. Frontiers in Built Environment, 3, 30. https://doi.org/10.3389/fbuil.2017.00030

Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x

Ding, J., Tarokh, V., & Yang, Y. (2017). Bridging AIC and BIC: A new criterion for autoregression. IEEE Transactions on Information Theory, 64(6), 4024–4043. https://doi.org/10.1109/TIT.2017.2785860

George, S., & Jose, A. (2020). Generalized Poisson hidden Markov model for overdispersed or underdispersed count data. Revista Colombiana de Estadística, 43(1), 71–82.

Greff, K., Van Steenkiste, S., & Schmidhuber, J. (2017). Neural expectation maximization. In Advances in neural information processing systems (Vol. 30).

Hafiez, H. A. (2015). Estimating the magnitude of completeness for assessing the quality of earthquake catalogue of the ENSN, Egypt. Arabian Journal of Geosciences, 8, 9315–9323. https://doi.org/10.1007/s12517-015-1887-5

Hassani, H., & Yeganegi, M. R. (2020). Selecting optimal lag order in Ljung–Box test. Physica A: Statistical Mechanics and Its Applications, 541, 123700. https://doi.org/10.1016/j.physa.2019.123700

Irsyam, M., Cummins, P. R., Asrurifak, M., Faizal, L., Natawidjaja, D. H., Widiyantoro, S., Meilano, I., Triyoso, W., Rudiyanto, A., Hidayati, S., Ridwan, M., Hanifa, N. R., & Syahbana, A. J. (2020). Development of the 2017 national seismic hazard maps of Indonesia. Earthquake Spectra, 36(1), 112–136. https://doi.org/10.1177/8755293020951206

Kuha, J. (2004). AIC and BIC: Comparisons of assumptions and performance. Sociological Methods & Research, 33(2), 188–229. https://doi.org/10.1177/0049124103262065

Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303. https://doi.org/10.1093/biomet/65.2.297

Mannering, F. L., Shankar, V., & Bhat, C. R. (2016). Unobserved heterogeneity and the statistical analysis of highway accident data. Analytic Methods in Accident Research, 11, 1–16. https://doi.org/10.1016/j.amar.2016.04.001

McLachlan, G. J., Lee, S. X., & Rathnayake, S. I. (2019). Finite mixture models. Annual Review of Statistics and Its Application, 6, 355–378. https://doi.org/10.1146/annurev-statistics-031017-100325

Orfanogiannaki, K., Karlis, D., & Papadopoulos, G. A. (2014). Identification of temporal patterns in the seismicity of Sumatra using Poisson hidden Markov models. Research in Geophysics, 4(1), 1–6. https://doi.org/10.4081/rg.2014.4969

Radziminovich, N. A., Miroshnichenko, A. I., & Zuev, F. L. (2019). Magnitude of completeness, b-value, and spatial correlation dimension of earthquakes in the South Baikal Basin, Baikal Rift System. Tectonophysics, 759, 44–57. https://doi.org/10.1016/j.tecto.2019.03.011

Reid, A. (2015). History and seismology in the Ring of Fire: Punctuating the Indonesian past. In Environment, trade and society in Southeast Asia (pp. 1–16). Brill. https://doi.org/10.1163/9789004288058_006

Rizal, J., Gunawan, A. Y., Indratno, S. W., & Meilano, I. (2018). Identifying dynamic changes in megathrust segmentation via Poisson mixture model. In Journal of Physics: Conference Series (Vol. 1097, No. 1, Article 012083). IOP Publishing. https://doi.org/10.1088/1742-6596/1097/1/012083

Rizal, J., Gunawan, A. Y., Indratno, S. W., & Meilano, I. (2021). The application of copula continuous extension technique for bivariate discrete data: A case study on dependence modeling of seismicity data. Mathematical Modelling of Engineering Problems, 8(5), 793–804. https://doi.org/10.18280/mmep.080516

Rizal, J., Gunawan, A. Y., Indratno, S. W., & Meilano, I. (2023). Seismic activity analysis of five major earthquake source segments in the Sumatra megathrust zone: Each segment and two adjacent segments points of view. Bulletin of the New Zealand Society for Earthquake Engineering, 56(2), 55–70. https://doi.org/10.5459/bnzsee.1555

Sebastian, T., Jeyaseelan, V., Jeyaseelan, L., Anandan, S., George, S., & Bangdiwala, S. I. (2019). Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models. Statistical Methods in Medical Research, 28(5), 1552–1563. https://doi.org/10.1177/0962280218761154

Wang, J., Zhao, J., Lei, X., & Wang, H. (2018). New approach for point pollution source identification in rivers based on the backward probability method. Environmental Pollution, 241, 759–774. https://doi.org/10.1016/j.envpol.2018.06.017

Williams, Q. (2018). The thermal conductivity of Earth’s core: A key geophysical parameter’s constraints and uncertainties. Annual Review of Earth and Planetary Sciences, 46, 47–66. https://doi.org/10.1146/annurev-earth-082517-010208

Yip, C. F., Ng, W. L., & Yau, C. Y. (2017). A hidden Markov model for earthquake prediction. Stochastic Environmental Research and Risk Assessment, 1–20. https://doi.org/10.1007/s00477-017-1443-1

Zucchini, W., MacDonald, I. L., & Langrock, R. (2017). Hidden Markov models for time series: An introduction using R. Chapman and Hall/CRC. https://doi.org/10.1201/b20790

DOI: https://doi.org/10.31764/jtam.v10i1.33446