Long-range correlations in the electric signals that precede rupture

Abstract

The Smoluchowski-Chapman-Kolmogorov functional equation is applied to the electric signals that precede rupture. The results suggest a non-Markovian character of the analyzed data. The rescaled range Hurst and detrended fluctuation analyses, as well as that related with the "mean distance a walker spanned," lead to power-law exponents, which are consistent with the existence of long-range correlations. A "universality" in the power spectrum characteristics of these signals emerges, if an analysis is made (not in the conventional time frame, but) in the "natural" time domain. Within this frame, it seems that certain power spectrum characteristics of ion current fluctuations in membrane channels distinguish them from the electric signals preceding rupture. The latter exhibit a behavior compatible with that expected from a model based on the random field Ising Hamiltonian at the critical point.

Identifying the occurrence time of an impending major earthquake: a review

“…It has been found that the aforementioned quantity j 1 , the variance of natural time v k , is a key parameter that enables recognition of the complex dynamic system under study entering the critical stage (Varotsos et al 2001(Varotsos et al , 2002a(Varotsos et al , b, 2011c. This occurs when the variance j 1 converges to 0.070, as it will be discussed in detail in ''Appendix''.…”

“…It has been found that unique dynamic features hidden behind the time series of complex systems can be unveiled, if we analyze them in terms of natural time v (Varotsos et al 2001(Varotsos et al , 2002a. For a time series comprising N events, we define an index for the occurrence of the k-th event by v k = k/N, which we term natural time.…”

Tsallis-Based Nonextensive Analysis of the Southern California Seismicity

“…In terms of energy, this empirical relationship represented one of the features characterizing the self-organizing criticality due to the power-law dependence of the cumulative number of earthquakes with energy [2]. Although this relationship is very important, because it explains from a statistical viewpoint the seismicity occurring in seismic regions, it was not related with general physical principles apart from a recent attempt [3] in which the GR law seems to result from the Maximum Entropy Principle when considering the natural time concept [4], which, among others, allows the determination of an impending mainshock [3] when OPEN ACCESS analyzing in natural time the seismicity that occurs after the recording of a Seismic Electric Signals activity [5,6].…”

M W9 Tohoku earthquake in 2011 in Japan: precursors uncovered by natural time analysis

“…Natural time analysis, introduced in the beginning of 2000s (Varotsos et al 2001b(Varotsos et al , 2002a(Varotsos et al , b, 2003a, uncovers unique dynamic features hidden behind the time series of complex systems. It has found applications in a large variety of diverse fields, and the relevant results have been compiled in a monograph (Varotsos et al 2011c).…”

“…249-253 of Varotsos et al 2011c) that the quantity j 1 given by Eq. (2)-or the normalized power spectrum in natural time P(x) as defined by Varotsos et al (2001bVarotsos et al ( , 2002a for natural angular frequency x ? 0-can be considered as an order parameter for seismicity since its value changes abruptly when a mainshock (the new phase) occurs, and in addition, the statistical properties of its fluctuations resemble those in other non-equilibrium and equilibrium critical systems.…”