Analysis of temporal and spatial distributions between earthquakes in the region of California through Non-Extensive Statistical Mechanics and its limits of validity

In this work we study the influence of considering partial sets of earthquakes data has on the temporal and spatial probability distributions of earthquakes, using data from the California region between 2003 and 2016, with different thresholds for magnitude and depth of hypocenters. For this we have considered sequences of earthquakes where we have “jump”, or pulled, a given fixed number of actually sequential earthquakes. Through the concepts of Non-Extensive Statistical Mechanics for the time interval between earthquakes, we have found that the increase of the jump between earthquakes forming the sequence, affects the non-extensive characteristic of the system in the temporal probability distribution, denoted by a change in the value of the entropic index q, for relatively small jump sizes. However, for the distance between earthquakes, we observe that the increase of jumps lets untouched the non-extensive characteristic of the system, keeping the entropic index values q approximately constant. This analysis allows not just to show the robustness of the Non-Extensive Statistical Mechanics treatments for the study of earthquakes, but also their limits of applicability with respect to jumps or data loss. At the same time, it is a very useful test for memory effects and long-range interactions.