Statistical models for earthquakes: A Bayesian analysis

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 $\kappa$-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 $\kappa$-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 $\kappa$-GR models outperform the classical GR law. The results show the $\kappa$-GR model exhibits particularly strong empirical support, with optimal performance occurring when $\kappa \approx 1$.