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The Weibull–log Weibull distribution for interoccurrence times of earthquakes

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  • Hasumi, Tomohiro
  • Akimoto, Takuma
  • Aizawa, Yoji

Abstract

By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes–interoccurrence times–can be described by the superposition of the Weibull distribution and the log-Weibull distribution. In particular, the distribution of large earthquakes obeys the Weibull distribution with the exponent α1<1, indicating the fact that the sequence of large earthquakes is not a Poisson process. It is found that the ratio of the Weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude. Our results infer that Weibull statistics and log-Weibull statistics coexist in the interoccurrence time statistics, and that the change of the distribution is considered as the change of the dominant distribution. In this case, the dominant distribution changes from the log-Weibull distribution to the Weibull distribution, allowing us to reinforce the view that the interoccurrence time exhibits the transition from the Weibull regime to the log-Weibull regime.

Suggested Citation

  • Hasumi, Tomohiro & Akimoto, Takuma & Aizawa, Yoji, 2009. "The Weibull–log Weibull distribution for interoccurrence times of earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 491-498.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:4:p:491-498
    DOI: 10.1016/j.physa.2008.10.023
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    References listed on IDEAS

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    1. T. Huillet & H.-F. Raynaud, 1999. "Rare events in a log-Weibull scenario - Application to earthquake magnitude data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 12(3), pages 457-469, December.
    2. Abe, Sumiyoshi & Suzuki, Norikazu, 2005. "Scale-free statistics of time interval between successive earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 588-596.
    3. Hasumi, Tomohiro & Akimoto, Takuma & Aizawa, Yoji, 2009. "The Weibull–log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge–Knopoff Earthquake model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 483-490.
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    Cited by:

    1. Hasumi, Tomohiro & Akimoto, Takuma & Aizawa, Yoji, 2009. "The Weibull–log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge–Knopoff Earthquake model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 483-490.
    2. Ahmed Zohair Djeddi & Ahmed Hafaifa & Abdellah Kouzou & Salam Abudura, 2017. "Exploration of reliability algorithms using modified Weibull distribution: application on gas turbine," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1885-1894, November.
    3. Sumair, Muhammad & Aized, Tauseef & Aslam Bhutta, Muhammad Mahmood & Siddiqui, Farrukh Arsalan & Tehreem, Layba & Chaudhry, Abduallah, 2022. "Method of Four Moments Mixture-A new approach for parametric estimation of Weibull Probability Distribution for wind potential estimation applications," Renewable Energy, Elsevier, vol. 191(C), pages 291-304.
    4. Hristopulos, Dionissios T. & Mouslopoulou, Vasiliki, 2013. "Strength statistics and the distribution of earthquake interevent times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(3), pages 485-496.
    5. J. P. Wang, 2016. "Reviews of seismicity around Taiwan: Weibull distribution," 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. 80(3), pages 1651-1668, February.
    6. J. Wang, 2016. "Reviews of seismicity around Taiwan: Weibull distribution," 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. 80(3), pages 1651-1668, February.

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