Analysis of temporal variations of seismicity through non-extensive statistical physics

In recent years, there has been increasing interest in theoretical descriptions of seismicity in terms of statistical physics. Most aspects of these studies are encompassed by the concept of 'intermittent criticality', in which a region alternately approaches and retreats from a critical point. In this study, we analyse a descriptor of seismic activity that acts as a measure of the criticality of a system, such that its variations can be associated with changes in the state of the system. As some classical methods of analysis are not suitable for dealing with some of the features of complex systems such as the Earth's crust, we derive the probability distribution of the magnitude by maximizing a non-extensive generalization of the Boltzmann-Gibbs entropy given by the Tsallis entropy. In particular, the shape parameter q of this distribution, called the entropic index, characterizes the subadditive q > 1 and superadditive q < 1 regimes. Following the Bayesian approach for parameter esti...