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 estimation, we examine the seismic activity that has affected two seismogenic areas in central Italy that were hit recently by destructive earthquakes: L'Aquila in 2009, and Amatrice-Norcia in 2016. To analyse in detail the variations of the q index and the entropy, we estimate these for time windows of a fixed number of events that shift at each new event. Both the q index and the Tsallis entropy show significant and lasting decreases before the first strong earthquake in the sequences, and sudden increases after them. This indicates that these quantities can be considered as indicators of the level of concentration of energy, and hence of the activation state of the systems. More reliable results need to come from further studies of different cases in different seismotectonic settings.