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Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models

Author

Listed:
  • Irene Votsi

    (Aristotle University of Thessaloniki
    Université de Technologie de Compiègne)

  • Nikolaos Limnios

    (Université de Technologie de Compiègne)

  • George Tsaklidis

    (Aristotle University of Thessaloniki)

  • Eleftheria Papadimitriou

    (Aristotle University of Thessaloniki)

Abstract

The present paper aims at the introduction of the semi-Markov model in continuous time as a candidate model for the description of seismicity patterns in time domain in the Northern Aegean Sea (Greece). Estimators of the semi-Markov kernels, Markov renewal functions and transition functions are calculated through a nonparametric method. Moreover, the hitting times for spatial occurrence of the strongest earthquakes as well as the confidence intervals of certain important indicators are estimated. Firstly, the classification of model states is based on earthquakes magnitude. The instantaneous earthquake occurrence rate between the states of the model as well as the total earthquake occurrence rate are calculated. In order to increase the consistency between the model and the process of earthquake generation, seismotectonic features have been incorporated as an important component in the model. Therefore, a new classification of states is proposed which combines both magnitude and fault orientation states. This model which takes into account seismotectonic features contributes significantly to the seismic hazard assessment in the region under study. The model is applied to earthquake catalogues for the Northern Aegean Sea, an area that accommodates high seismicity, being a key structure from the seismotectonic point of view.

Suggested Citation

  • Irene Votsi & Nikolaos Limnios & George Tsaklidis & Eleftheria Papadimitriou, 2012. "Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 685-703, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9257-4
    DOI: 10.1007/s11009-011-9257-4
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    References listed on IDEAS

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    1. Enrique E. Alvarez, 2005. "Estimation in Stationary Markov Renewal Processes, with Application to Earthquake Forecasting in Turkey," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 119-130, March.
    2. Brahim Ouhbi & Nikolaos Limnios, 1999. "Nonparametric Estimation for Semi-Markov Processes Based on its Hazard Rate Functions," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 151-173, May.
    3. Ouhbi, Brahim & Limnios, Nikolaos, 2002. "The rate of occurrence of failures for semi-Markov processes and estimation," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 245-255, October.
    4. Ross S. Stein, 1999. "The role of stress transfer in earthquake occurrence," Nature, Nature, vol. 402(6762), pages 605-609, December.
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    Cited by:

    1. Votsi, I. & Limnios, N. & Tsaklidis, G. & Papadimitriou, E., 2013. "Hidden Markov models revealing the stress field underlying the earthquake generation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2868-2885.
    2. D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    3. He Yi & Lirong Cui & Narayanaswamy Balakrishnan, 2022. "On the Derivative Counting Processes of First- and Second-order Aggregated Semi-Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1849-1875, September.
    4. Danisman, Ozgur & Uzunoglu Kocer, Umay, 2021. "Hidden Markov models with binary dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    5. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.
    6. Md. Asaduzzaman & A. Latif, 2014. "A parametric Markov renewal model for predicting tropical cyclones in Bangladesh," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 73(2), pages 597-612, September.
    7. Somayajulu L. N. Dhulipala & Madeleine M. Flint, 2020. "Capabilities of multivariate Bayesian inference toward seismic hazard assessment," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 103(3), pages 3123-3144, September.

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