Exploring seismic cycle dynamics via variations in probability models: Chile and Italy case studies

This study investigates the different phases of seismic cycles present in earthquake sequences recorded in Chile and Italy on the basis of variations in the probability model for the magnitude and for the spatial distribution of the epicenters. Chile and Italy are two countries that, despite having different tectonic characteristics, face significant challenges due to seismic activity.

The seismic records are analyzed on sliding time windows with a fixed number of events, which shift with each new earthquake. Two probabilistic models are proposed for earthquake magnitude: one is based on the q-exponential distribution, hereafter referred to as the “q-exponential” model for simplicity, and the other is the exponential distribution, which is well known to be consistent with the Gutenberg-Richter law (Rotondi et al., Geophys. J. Int., 2022). The q-exponential distribution is closely related to Tsallis entropy, a generalized form of entropy that accounts for non-extensive systems, and has been widely applied in statistical mechanics to study complex systems. It is characterized by the parameter q, and as q asymptotically approaches 1, it reduces to the exponential distribution. As for the spatial distribution of the earthquakes, we consider the cell areas of the Voronoi tessellation generated by epicenters and adopt four probability models: the q-exponential, exponential, generalized gamma, and tapered Pareto distributions (Rotondi & Varini, Front. Earth Sci., 2022).

By following the Bayesian approach, the posterior distribution of model parameters is estimated by a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm, and then the optimal distribution in each time window is selected by comparing the estimated values of the posterior marginal log-likelihood. Given the high computational cost, parallel programming has been chosen to drastically reduce the computational time from days to hours or even minutes.

The results obtained in the study areas agree in associating seismic phase changes to the variations of the estimated q-index in the magnitude case and of the best probability model as for the spatial distribution; this provides useful indications for the implementation of risk mitigation actions. In both study areas, despite their different tectonic behaviors, we obtain similar results for seismic sequences characterized by a strong earthquake preceded by foreshocks. During the foreshock activity (i.e., the preparatory phase leading to the strong event), we observe an increase in the q parameter of the magnitude distribution and a preference for the tapered Pareto model for the spatial distribution of the epicenters provided by the Voronoi cell areas.

This work is supported by: ICSC National Research Centre for High Performance Computing, Big Data and Quantum Computing (CN00000013, CUP B93C22000620006) within the European Union-NextGenerationEU program; Chilean National Agency for Research and Development (ANID), Fondecyt grant ID 1241881; Research Center for Integrated Disaster Risk Management (CIGIDEN), ANID/FONDAP/1523A0009.