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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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