Nonextensive triplet in a geological faults system

Abstract

-The San Andreas fault (SAF) in the USA is one of the most investigated selforganizing systems in nature. In this paper, we studied some geophysical properties of the SAF system in order to analyze the behavior of earthquakes in the context of Tsallis's q-Triplet. To that end, we considered 134,573 earthquake events in magnitude interval 2 ≤ m < 8, taken from the Southern Earthquake Data Center (SCEDC, 1932(SCEDC, -2012. The values obtained ("qTriplet"≡{qstat,qsen,q rel }) reveal that the qstat-Gaussian behavior of the aforementioned data exhibit long-range temporal correlations. Moreover, qsen exhibits quasi-monofractal behavior with a Hurst exponent of 0.87.

Nonextensivity at the Circum-Pacific subduction zones—Preliminary studies

“…Since those works, many used Tsallis statistics to develop models in Seismology, e.g. : SotolongoCosta and Posadas [19], Silva et al [20] and Darooneh and Mehri [21] proposed earthquake energy distributions using Tsallis nonextensive approach, considering the energy released by each earthquake is proportional to the distribution of the size of fragments (assumed differently in each model) between tectonic plates; Kalimeri et al [22] evaluate pre-seismic emissions; Darooneh and Dadashinia [23] applied it in spatial-temporal distribution between successive earthquakes; Vallianatos [24] use it to estimate a risk function of natural hazards; Vallianatos and Sammonds [25] developed and tested a model for the fault length distribution in the Valles Marineris extensional province, Mars; in 2013 they also suggest the existence of a coherent global scale intermediate-term nonextensive tectonic premonitory of impending mega-earthquake processes in the lithosphere; de Freitas et al [26] identified the Tsallis q-Triplet (q stat = 1.36 + / − 0.04, q sen = −6.65 + / − 0.35, q rel = 2.69 + / − 0.13) revealing a strong evidence that the seismic activity has a hierarchical structure on small scales.…”

Investigating the signatures of long-range persistence in seismic sequences along Circum-Pacific subduction zones

“…Their typical values are: 0.5 < H < 1 which indicates a persistence or long memory process, H = 0.5 which indicates an uncorrelated process, and 0 < H < 0.5 denotes anticorrelation. In a geophysical scenario, earthquakes bear dual features of randomicity and regularity, and therefore a H value of between 0.5 and 1 is expected [18].…”

“…Many studies in different subject areas (e.g., economy, neuroscience, and astrophysics) have shown that the so-called Hurst exponent extracted from the R/S analysis provides a robust and powerful statistical method to characterize nonstationary fluctuations at different timescales [16], [17] and [2]. More recently, [18] found a Hurst exponent of 0.87 for the San Andreas fault, which indicated a strong long-term persistence. Other studies (e.g., [2]) also point out that the Hurst exponent is greater than 0.5, indicating a persistent behavior.…”

Market Efficiency, Roughness and Long Memory in PSI20 Index Returns: Wavelet and Entropy Analysis

“…The nearness of the curves indicates that PSI20 returns have a high degree of unpredictability. For the q-triplet, the reference value is one (see, for instance, [6,9]). In our data, the q-triplet assumes the following results: q rel = 1 for the PSI20 returns (the fact that there are negative correlations in the returns indicates that there is no long memory) and q rel = 1.5 in the squared returns, indicating long memory in volatility; q stat = 1.44 (either using a maximum likelihood method or using the scaling based method), which indicates rougher paths than in the Gaussian reference case; q sens = 0.541 (obtained using the multifractal spectrum estimated for the PSI20 returns and a third order polynomial approximation, presented in Figure 3); we have q sens < 1, which means that the return series is sensitive to initial conditions (as opposed to insensitivity if q sens > 1).…”

“…It consists of a threefold determination of an entropic coefficient, q, in the context of: (1) the sensitivity to initial conditions in a dynamical system, which may be seen as reflecting unpredictability; (2) relaxation of macroscopic variable towards a stationary state, which in a time series, may be taken to detect the existence of long memory; (3) the stationary distribution obtained after the constrained optimization of an entropy function, where the departure of this distribution from the Gaussian distribution is the result of self-organization in the market leading to a rougher path. For several empirical approaches, see Pavlos et al [7], Ferri et al [8], de Freitas et al [9], De Sousa and Rostirolla [10] and, in the finance area, Queirós et al [11].…”