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 Tsal...
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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 .
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