The estimation of the hazard function of earthquakes in aceh province with likelihood approach

Ikhsan Maulidi , Fanny Novika , Mahmudi Mahmudi , Vina Apriliani , Muhamad Syazali

Abstract


In this article, we propose a novel application of the single decrement method with a likelihood approach to estimate the hazard function of earthquake events in Aceh province. While this method has traditionally been used in actuarial sciences for mortality table estimation, its application in seismic hazard estimation represents a new perspective in the field of earthquake risk analysis. To enhance the accuracy of the model, we applied the Box-Cox transformation to normalize the data and used simple regression to formulate the hazard function. Our results demonstrate that a cubic equation provides a more accurate model compared to linear and quadratic equations, as evidenced by the lower Mean Square Error (MSE). This study offers a new approach to hazard rate estimation that surpasses conventional methods by providing more informative and interpretable results for earthquake risk assessment.


Keywords


hazard rate, single decrement method, maximum likelihood estimation.

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References


Anagnos, T., & Kiremidjian, A. S. (1988). A review of earthquake occurrence models for seismic hazard analysis. Probabilistic Engineering Mechanics, 3(1), 3–11. https://doi.org/10.1016/0266-8920(88)90002-1

Banyunegoro, V. H., Alatas, Z. A., Jihad, A., Eridawati, & Muksin, U. (2019). Probabilistic seismic hazard analysis for aceh region. IOP Conference Series: Earth and Environmental Science, 273(1). https://doi.org/10.1088/1755-1315/273/1/012015

Cipta, A., Rudyanto, A., Afif, H., Robiana, R., Solikhin, A., Omang, A., … Hidayati, S. (2021). Unearthing the buried palu–koro fault and the pattern of damage caused by the 2018 sulawesi earthquake using hvsr inversion. In Geological Society Special Publication (Vol. 501). https://doi.org/10.1144/SP501-2019-70

Corral, Á. (2005). Time-decreasing hazard and increasing time until the next earthquake. Physical Review E, 71(1), 017101. https://doi.org/10.1103/PhysRevE.71.017101

Daley, D. J. (2006). Introduction to the theory of point processes: Elementary theory and methods. An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods.

Danciu, L., Kale, Ö., & Akkar, S. (2018). The 2014 earthquake model of the middle east: Ground motion model and uncertainties. Bulletin of Earthquake Engineering, 16(8). https://doi.org/10.1007/s10518-016-9989-1

Jena, R., Pradhan, B., & Beydoun, G. (2020). Earthquake vulnerability assessment in northern sumatra province by using a multi-criteria decision-making model. International Journal of Disaster Risk Reduction, 46. https://doi.org/10.1016/j.ijdrr.2020.101518

Jena, R., Pradhan, B., Beydoun, G., Al-Amri, A., & Sofyan, H. (2020). Seismic hazard and risk assessment: a review of state-of-the-art traditional and gis models. Arabian Journal of Geosciences, Vol. 13. https://doi.org/10.1007/s12517-019-5012-x

Jena, R., Pradhan, B., Beydoun, G., Nizamuddin, Ardiansyah, Sofyan, H., & Affan, M. (2020). Integrated model for earthquake risk assessment using neural network and analytic hierarchy process: Aceh province, indonesia. Geoscience Frontiers, 11(2). https://doi.org/10.1016/j.gsf.2019.07.006

Kameshwar, S., & Padgett, J. E. (2014). Multi-hazard risk assessment of highway bridges subjected to earthquake and hurricane hazards. Engineering Structures, 78, 154–166. https://doi.org/10.1016/j.engstruct.2014.05.016

Kijko, A., & Sellevoll, M. A. (1989). Estimation of earthquake hazard parameters from incomplete data files. Part I. Utilization of extreme and complete catalogs with different threshold magnitudes. Bulletin of the Seismological Society of America, 79(3), 645–654. https://doi.org/10.1785/BSSA0790030645

Koshimura, S., Oie, T., Yanagisawa, H., & Imamura, F. (2009). Developing fragility functions for tsunami damage estimation using numerical model and post-tsunami data from banda aceh, Indonesia. Coastal Engineering Journal, 51(3). https://doi.org/10.1142/S0578563409002004

Lee, H., Ha, H., & Lee, T. (2021). Decrement rates and a numerical method under competing risks. Computational Statistics and Data Analysis, 156. https://doi.org/10.1016/j.csda.2020.107125

Liu, L., Chen, Z., Li, Y., Liu, Z., Hu, L., Wang, X., … Zhou, X. (2023). Emission of rn and co2 from soil at fault zones caused by seismic waves. Earth and Space Science, 10(6). https://doi.org/10.1029/2023EA003012

Lu, Y., Wang, W., Huang, Y., & Chen, H. (2023). How big is a big hazard ratio in clinical trials? International Journal of Clinical Trials, 10(3). https://doi.org/10.18203/2349-3259.ijct20232191

Novika, F., Maulidi, I., Marsanto, B., & Amalina, A. N. (2022). Comparative model analysis time of earthquake occurrence in indonesia based on hazard rate with decrement method. JTAM: Jurnal Teori Dan Aplikasi Matematika, 6(1).

Nurtiti, S., Kresna, A. J. , Islamiyati, A., & Raupong. (2013). Hazard rate estimation of temporal point process, case study: Earthquake hazard rate in nusatenggara region. International Journal of Physical and Mathematical Sciences, 7(6), 1059–1062.

Price, L. F., Drovandi, C. C., Lee, A., & Nott, D. J. (2018). Bayesian synthetic likelihood. Journal of Computational and Graphical Statistics, 27(1). https://doi.org/10.1080/10618600.2017.1302882

Putra, R. R., Kiyono, J., Ono, Y., & Parajuli, H. R. (2012). Seismic hazard analysis for indonesia. Journal of Natural Disaster Science, 33(2), 59–70. https://doi.org/10.2328/jnds.33.59

Socquet, A., Hollingsworth, J., Pathier, E., & Bouchon, M. (2019). Evidence of supershear during the 2018 magnitude 7.5 Palu earthquake from space geodesy. Nature Geoscience, 12(3). https://doi.org/10.1038/s41561-018-0296-0

Tokuda, T., & Nagao, H. (2023). Seismic-phase detection using multiple deep learning models for global and local representations of waveforms. Geophysical Journal International, 235(2). https://doi.org/10.1093/gji/ggad270

Triyoso, W. (2023). Probabilistic seismic hazard function based on spatiotemporal earthquake likelihood simulation and akaike information criterion: The pshf study around off the west coast of Sumatra Island before large earthquake events. Frontiers in Earth Science, 11. https://doi.org/10.3389/feart.2023.1104717

Youngs, R. R., & Coppersmith, K. J. (1986). Implications of fault slip rates and earthquake recurrence models to probabilistic seismic hazard estimates. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 23(4), 125. https://doi.org/10.1016/0148-9062(86)90651-0

Zhao, W., Khosa, S. K., Ahmad, Z., Aslam, M., & Afify, A. Z. (2020). Type-I heavy tailed family with applications in medicine, engineering and insurance. PLoS ONE, 15(8 August). https://doi.org/10.1371/journal.pone.0237462




DOI: http://dx.doi.org/10.24042/djm.v7i3.21489

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