We analyse seismicity during the 6-year period 2012–2017 in the new time domain termed natural time in the Chiapas region where the M8.2 earthquake occurred, Mexico’s largest earthquake in more than a century, in order to study the complexity measures associated with fluctuations of entropy as well as with entropy change under time reversal. We find that almost three months before the M8.2 earthquake, i.e., on 14 June 2017, the complexity measure associated with the fluctuations of entropy change under time reversal shows an abrupt increase, which, however, does not hold for the complexity measure associated with the fluctuations of entropy in forward time. On the same date, the entropy change under time reversal has been previously found to exhibit a minimum [Physica A 506, 625–634 (2018)]; we thus find here that this minimum is also accompanied by increased fluctuations of the entropy change under time reversal. In addition, we find a simultaneous increase of the Tsallis entropic index q.

Seismic electric signals (SES) have been considered precursors of strong earthquakes, and, recently, their dynamics have been investigated within the Natural Time Domain (NTD) (Varotsos et al., 2004). In this paper we apply the NTD approach and the chaotic map signal analysis to two geoelectric time series recorded in a seismically very active area of Mexico, where two strong earthquakes, M=6.6 and M=7.4, occurred on 24 October 1993 and 14 September 1995, respectively. The low frequency geoelectric signals measured display periods with dichotomic behavior. Our findings point out to an increase of the correlation degree of the geoelectric signals before the occurrence of strong earthquakes; furthermore, the power spectrum and entropy in NTD are in good agreement with the results published in literature. Our results were validated by the analysis of a chaotic map simulated time series, which revealed the typical characteristics of artificial noise.

Non-extensive statistical mechanics (or q-statistics) is based on the so-called non-additive Tsallis entropy. Since its introduction by Tsallis, in 1988, as a generalization of the Boltzmann–Gibbs equilibrium statistical mechanics, it has steadily gained ground as a suitable theory for the description of the statistical properties of non-equilibrium complex systems. Therefore, it has been applied to numerous phenomena, including real seismicity. In particular, Tsallis entropy is expected to provide a guiding principle to reveal novel aspects of complex dynamical systems with catastrophes, such as seismic events. The exploration of the existing connections between Tsallis formalism and real seismicity has been the focus of extensive research activity in the last two decades. In particular, Tsallis q-statistics has provided a unified framework for the description of the collective properties of earthquakes and faults. Despite this progress, our present knowledge of the physical processes leading to the initiation of a rupture, and its subsequent growth through a fault system, remains quite limited. The aim of this paper was to provide an overview of the non-extensive interpretation of seismicity, along with the contributions of the Tsallis formalism to the statistical description of seismic events.

In this work we present a spectral and multifractal study of the electric self-potential fluctuations registered in an electroseismic station located at 100km from the epicenter of an earthquake (EQ) with M_w=6.5 in the Pacific coast of Mexico. Our study suggests that in general the time series analyzed displays a persistent behavior. Our results show an anticorrelation between the spectral exponent β and the width of the multifractal spectrum Δα, when they are calculated during a time interval of five months (four months before the EQ and one month after the EQ). In addition, we also calculate the time evolution of the correlation coefficient finding that it has a very similar behavior that the time evolution of Δα.

This article is focused on a new procedure concerning a more accurate identification of the occurrence time of an impending major earthquake (EQ). Specifically, we first recapitulate that, as was recently shown [P. Varotsos et al., Communications in Nonlinear Science and Numerical Simulation 125 (2023) 107370], natural time analysis of seismicity supplemented with the non-additive Tsallis entropy $S_q$ leads to a shortening of the time window of an impending major EQ. This has been shown for the Tohoku mega-EQ of magnitude M9 that occurred in Japan on 11 March 2011, which is the largest event ever recorded in Japan. Here, we also show that such a shortening of the time window of an impending mainshock can be achieved for major, but smaller EQs, of the order of M8 and M7. In particular, the following EQs are treated: the Chiapas M8.2 EQ, which is Mexico’s largest EQ for more than a century that took place on 7 September 2017 near the coast of Chiapas state in Mexico, the 19 September 2017 M7.1 EQ that occurred within the Mexican flat slab, and the M7.1 Ridgecrest EQ on 6 July 2019 in California.