Worldwide seismicity in view of non extensive statistical physics
Statement of the problem
Earthquakes have always been one the most intriguing natural phenomena for the mankind. However, the complexity of the earth’s interior makes the investigation of this system more and more complicated. Among the years many models have been proposed for the description of the seismic behavior and the last years has been made significant progress, since now we are in position to understand many aspects of the seismic behavior and how this extremely complex system works. The most promising and adequate model for describing systems such as the Earth seems to be the Non Extensive Statistical Physics model, introduced by Tsallis in 1988. This model is strongly supported by the fact that this type of statistical mechanics is the appropriate methodological tool to describe entities with (multi) fractal distributions of their elements and where long-range interactions or intermittency are important, as in earthquakes. The NESP approach starting from the classic Boltzman-Gibbs statistics develops an entire model, based on the maximization of the Tsallis entropy, that gives us the opportunity to study the collective properties of even very large earthquakes (mega earthquakes ), such as the earthquake occurred occurred in Sumatra ( 2004 ) with magnitude Mw=9.0 and the recent Japan mega earthquake with magnitude Mw=9.1 (2011) .
In the present work we study the distribution of worldwide shallow strong seismic events occurred from 1981 to 2011 extracted from the CMT catalog, with magnitude equal or greater than Mw5.0. Our analysis based on the subdivision of the Earth surface into seismic zones that are homogeneous with regards to seismic activity and orientation of the predominant stress field. We analyze the magnitude-frequency distribution along with the interevent time distribution between successive earthquakes using the Tsallis entropy approach in each of the seismic zones.
Our aim is to understand how this model works, under which conditions is valid and how non extensive parameters, such as the entropic index qM and qT, extracted from the frequency magnitude and interevent time distributions respectively, are affected by factors such as the magnitude threshold and the earthquake depth and finally what information can we extract by applying the NESP model in global seismicity catalogs.