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Statistical models for earthquakes: A Bayesian analysis

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  • Costa, M.O.
  • da Silva, S.L.E.F.
  • Silva, R.
  • França, G.S.
  • Vilar, C.S.
  • Alcaniz, J.S.

Abstract

The Gutenberg–Richter (GR) relation is an exponential law widely used for describing earthquakes’ statistical magnitude distributions. Using statistical physics approaches, we present robust models based on the Tsallis q- and Kaniadakis κ-entropies, aiming to capture the influence of irregular fragments occupying space between two tectonic plates with irregular surfaces. The proposed models are called q-GR and κ-GR laws, respectively. Using Bayesian statistical analysis, we examined a large dataset of over 450,000 seismic events recorded along the San Andreas Fault between 2000 and 2023. Our findings reveal that the q-GR and κ-GR models outperform the classical GR law. The results show the κ-GR model exhibits particularly strong empirical support, with optimal performance occurring when κ≈1.

Suggested Citation

  • Costa, M.O. & da Silva, S.L.E.F. & Silva, R. & França, G.S. & Vilar, C.S. & Alcaniz, J.S., 2025. "Statistical models for earthquakes: A Bayesian analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
    • Handle: RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125003309
    DOI: 10.1016/j.physa.2025.130678
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    References listed on IDEAS

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    1. Gergely, Attila & Biró, Tamás Sándor & Járai-Szabó, Ferenc & Néda, Zoltán, 2024. "Statistics of earthquakes based on the extended LGGR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
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    3. Vega-Jorquera, Pedro & de la Barra, Erick & da Silva, Sérgio Luiz E.F., 2023. "Antropogenic seismicity and the breakdown of the self-similarity described by nonextensive models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    4. Vilar, C.S. & França, G.S. & Silva, R. & Alcaniz, J.S., 2007. "Nonextensivity in geological faults?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 285-290.
    5. Darooneh, Amir H. & Mehri, Ali, 2010. "A nonextensive modification of the Gutenberg–Richter law: q-stretched exponential form," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 509-514.
    6. 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.
    7. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    8. Gustavo Z dos Santos Lima & João V T de Lima & João M de Araújo & Gilberto Corso & Sérgio Luiz E F da Silva, 2023. "Generalized statistics: Applications to data inverse problems with outlier-resistance," PLOS ONE, Public Library of Science, vol. 18(3), pages 1-22, March.
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    10. Sérgio Luiz E. F. Silva & Gilberto Corso, 2021. "Nonextensive Gutenberg–Richter law and the connection between earthquakes and marsquakes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-5, January.
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