Temporal variations of the probability distribution of voronoi cells generated by earthquake epicenters

Abstract

The area of the cells of Voronoi tessellations has been modelled through different probability distributions among which the most promising are the generalized gamma and tapered Pareto distributions. In particular the latter has been used to model times and distances between successive earthquakes besides area and perimeter of cells generated by earthquake epicenters. In the framework of nonextensive statistical mechanics applied in geophysics, variables like seismic moment, inter-event time or Euclidean distance between successive earthquakes or length of faults in a given region have been studied through the so-called q-exponential distributions obtained by maximizing the Tsallis entropy under suitable conditions. These distributions take also the name of generalized Pareto distributions in the context of the limit distributions of excesses. In this work we consider the spatial distribution of a set of earthquakes and its temporal variations by modelling the area of Voronoi cells generated by the epicenters through a generalized Pareto distribution. Following the Bayesian paradigm we analyze the recent seismicity of the central Italy and we compare the posterior marginal likelihood of the aforementioned distributions in shifting time windows. We point out that the best fitting distribution varies over time and the trend of all three distributions converges to that of the exponential distribution in the preparatory phase for the mainshock.

Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity

“…Similar results have also been found in other studies, in which the phases of a seismic cycle are related to changes in the probability distribution of the magnitude [26] and of the spatial location of the epicenters [9].…”

“…Properties such as fractal structures and long-range correlations present in the earthquake activity have led to adopt theoretical tools of non-extensive statistical physics in the analysis of the statistical properties of some quantities describing the seismic activity in the space-time-magnitude domain. This approach is based on a generalization of the classic Boltzmann-Gibbs entropy proposed by Tsallis in 1988 [6]; by maximizing the non-extensive Tsallis entropy, a probability distribution, denoted as q-exponential distribution, was obtained and then successfully applied to investigate the distribution of various seismic quantities, such as magnitude ( [7] and references therein), fault length [8], spatial distribution of epicenters [9], and interevent time [10]. To improve the fit of the gamma distribution by exploiting the results obtained through the q-exponential distribution, Michas et al [11] used the q-generalized gamma distribution, borrowed from Queirós [12], which behaves as a power-law function for both short and large interevent times so as to provide a best fit when the seismicity is correlated at all timescales.…”