Multidimensional earthquake frequency distributions consistent with Non-Extensive statistical physics: The interdependence of magnitude, interevent time and interevent distance in North California

Abstract

It is now accepted that the active tectonic grain comprises a self-organized complex system, therefore its expression (seismicity) should be manifested in the temporal and spatial statistics of energy release rates, and exhibit memory due to long-range interactions in a fractal

Tsallis q-Statistics in Seismology

“…The fragment–asperity model has been applied to different earthquake catalogs to examine the frequency–magnitude distribution of seismicity [ 37 , 38 , 39 , 40 , 41 , 68 , 69 ]. In particular, similar -values to those calculated by Sotolongo-Costa and Posadas [ 36 ] for different earthquake catalogs were also estimated for seismicity in different regions, including the Samambaia fault in Brazil ( for 100 events), the New Madrid fault in the USA ( for 173 events) and the Anatolian fault in Turkey ( for 8980 events) [ 61 ].…”

“…Tzanis et al [ 40 ] proposed that the problem could be addressed by constructing multivariate frequency distributions based on the formulation of joint distribution laws, where it is assumed that the distributions of the magnitude, M , and inter-event time, T , are statistically independent, in the sense that the joint probability factorizes into the product . Then, the empirical probability can be written as where is the entropic index for the inter-event times, is the q -relaxation time and is the total number of earthquakes at .…”

“…Starting from the fragment–asperity interaction model, proposed by Sotolongo-Costa and Posadas, in 2004 [ 36 ], there has been a growing number of publications on seismicity, faulting, plate tectonics and precursory electromagnetic anomalies demonstrating the consistency between NESM and observations and providing further insight into the physics of earthquakes and the processes involved in the rupture initiation and growth through a fault system. In particular, good progress has been made in understanding the frequency–magnitude and energy distribution of seismicity, as well as the connection existing between the preparatory process of an earthquake and the temporal variation of the q -index [ 37 , 38 , 39 , 40 , 41 ]. On the other hand, the combination of non-extensivity with natural time and detrended fluctuation analysis has proved to be a powerful tool for the analysis of seismic data [ 42 ], while Tsallis entropy has also been employed in the analysis of precursory electromagnetic emissions [ 43 ].…”

On the Nature and Dynamics of the Seismogenetic System of South California, Usa: An Analysis Based on Non-Extensive Statistical Physics

“…5 yields excellent approximations of the observed F-M-T distributions (for details see Tzanis et al, 2013 andEfstathiou et al, 2015). For the sake of experimental rigour, this presentation will only consider models associated with a goodness of fit (R 2 ) better than 0.97.…”

“…Moré and Sorensen, 1983;Steihaug, 1983) was chosen, together with Least Absolute Residual minimization so as to down-weight possible outliers. Typical examples/results of the performance of this procedure can be found in Tzanis et al (2013) and Efstathiou et al (2015) and will not be included herein for the sake of brevity.…”