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Hidden Markov models revealing the stress field underlying the earthquake generation

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  • Votsi, I.
  • Limnios, N.
  • Tsaklidis, G.
  • Papadimitriou, E.

Abstract

The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:13:p:2868-2885
    DOI: 10.1016/j.physa.2012.12.043
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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. Giovanni Masala, 2012. "Earthquakes occurrences estimation through a parametric semi-Markov approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 81-96, March.
    3. 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.
    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:

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    2. Chorozoglou, D. & Kugiumtzis, D. & Papadimitriou, E., 2018. "Testing the structure of earthquake networks from multivariate time series of successive main shocks in Greece," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 28-39.
    3. Gámiz, María Luz & Limnios, Nikolaos & Segovia-García, María del Carmen, 2023. "Hidden markov models in reliability and maintenance," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1242-1255.
    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. C. E. Pertsinidou & G. Tsaklidis & E. Papadimitriou & N. Limnios, 2017. "Application of hidden semi-Markov models for the seismic hazard assessment of the North and South Aegean Sea, Greece," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(6), pages 1064-1085, April.
    6. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Jian & Wang, Zhen, 2019. "Passive state estimation for fuzzy jumping neural networks with fading channels based on the hidden Markov model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).

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