Natural Time Analysis: The New View of Time

Varotsos, P.; Sarlis, N. V.; Skordas, E. S.

doi:10.1007/978-3-642-16449-1

Cited by 197 publications

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“…The emission of SES was attributed to a phase transition of second order. It was also shown empirically that the same condition κ 1 ¼ 0.070 holds for other time series, including turbulence (8) and seismicity preceding main shocks (3,(7)(8)(9)(10)(11). Moreover, it has been found empirically that main shocks occur, in terms of the conventional time, a few days up to one week after the condition κ 1 ¼ 0.070 was attained for the seismicity subsequent to SES activity (1, 3, 7-10) supporting the concept that seismicity is a critical phenomenon (e.g., refs.…”

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confidence: 67%

“…Note that χ k is "rescaled" as natural time changes to χ k ¼ k∕ðN þ 1Þ together with rescaling p k ¼ Q k ∕ ∑ Nþ1 n¼1 Q n upon the occurrence of any additional event. It has been demonstrated that this analysis enables recognition of the complex dynamic system under study entering the critical stage (1)(2)(3). This occurs when the variance κ 1 converges to 0.070.…”

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confidence: 99%

“…This occurs when the variance κ 1 converges to 0.070. Originally the condition κ 1 ¼ 0.070 for the approach to criticality was theoretically derived for the seismic electric signals (SES) (1, 2), which are transient low frequency (≤1 Hz) electric signals that have been repeatedly observed before earthquakes (3,5,6). The experimental data showed that κ 1 obtained from SES activities in Greece and Japan attain the value 0.070 (1-3, 7-10).…”

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confidence: 99%

“…Despite these numerous successes (e.g., see refs. 3,14), however, the condition κ 1 ¼ 0.070 for criticality has remained a major stumbling block for wider acceptance, because the validity of this condition has not been theoretically demonstrated for the cases other than the SES activities and the Burridge-Knopoff "train" model for earthquakes (15). In order to remedy this situation, in this paper, we will try to identify the origin of the validity of the κ 1 ¼ 0.070 condition for a wider range of critical systems.…”

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Natural time analysis of critical phenomena

Varotsos

Sarlis

Skordas

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance κ 1 ð≡hχ 2 i − hχ i 2 Þ of natural time χ , where hfðχ Þi ¼ ∑ p k f ðχ k Þ and p k is the normalized energy released during the kth event of which the natural time is defined as χ k ¼ k∕N and N stands for the total number of events. Then we show that κ 1 becomes equal to 0.070 at the critical state for a variety of dynamical systems. This holds for criticality models such as 2D Ising and the Bak-Tang-Wiesenfeld sandpile, which is the standard example of self-organized criticality. This condition of κ 1 ¼ 0.070 holds for experimental results of critical phenomena such as growth of rice piles, seismic electric signals, and the subsequent seismicity before the associated main shock.short-term earthquake prediction | dynamic exponent | fractional Gaussian noise | fractional Brownian motion | Burridge-Knopoff "train" model I t has been shown that some unique dynamic features hidden behind can be derived from the time series of complex systems, if we analyze them in terms of natural time χ (1-3). For a time series comprising N events, we define an index for the occurrence of the kth event by χ k ¼ k∕N, which we term natural time. In doing so, we ignore the time intervals between consecutive events, but preserve their order and energy Q k . We, then, study the evolution of the pair (χ k , Q k ) by using the normalized power spectrumdefined by ΦðωÞ ¼ ∑ N k¼1 p k expðiωχ k Þ, where ω stands for the angular natural frequency andis the normalized energy for the kth event. In the time-series analysis using natural time, the behavior of ΠðωÞ at ω close to zero is studied for capturing the dynamic evolution, because all the moments of the distribution of the p k can be estimated from ΦðωÞ at ω → 0 (see ref. 4, p. 499). For this purpose, a quantity κ 1 is defined from the Taylor expansionWe found that this quantity, the variance of natural time χ k , is a key parameter for the distribution of energy within the natural time interval (0,1]. Note that χ k is "rescaled" as natural time changes to χ k ¼ k∕ðN þ 1Þ together with rescaling p k ¼ Q k ∕ ∑ Nþ1 n¼1 Q n upon the occurrence of any additional event. It has been demonstrated that this analysis enables recognition of the complex dynamic system under study entering the critical stage (1-3). This occurs when the variance κ 1 converges to 0.070. Originally the condition κ 1 ¼ 0.070 for the approach to criticality was theoretically derived for the seismic electric signals (SES) (1, 2), which are transient low frequency (≤1 Hz) electric signals that have been repeatedly observed before earthquakes (3,5,6). The experimental data showed that κ 1 obtained from SES activities in Greece and Japan attain the value 0.070 (1-3, 7-10). The emission of SES was attributed to a phase transition of second order. It was also shown empirically that the same condition κ 1 ¼ 0.070 holds for other time series, including turbule...

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confidence: 67%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Natural time analysis of critical phenomena

Varotsos

Sarlis

Skordas

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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“…precursor | VAN method T he VAN method, named after the initials of Varotsos, Alexopoulos, and Nomicos, for short-term earthquake (EQ) prediction by means of the monitoring of preseismic telluric current signals, called seismic electric signals (SES), has been in successful practice since the 1980s (1). The VAN method, however, has been a contentious subject with regard to the causal relationship between SES and EQs (e.g., refs.…”

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Preseismic anomalous telluric current signals observed in Kozu-shima Island, Japan

Orihara

Kamogawa

Nagao

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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Monitoring of telluric current, which is practically a synonym for geoelectric potential difference, was conducted on Kozu-shima Island about 170 km south of Tokyo from May 14, 1997 to June 25, 2000. During the monitoring period, 19 anomalous telluric current changes (ATCs) were observed. Their possible correlation with nearby earthquakes was statistically examined by assuming various lead times for different ranges of magnitude and focal distance. The best correlation may be obtained for earthquakes with a magnitude greater than 3.0 occurring within 20 km of focal distance. There were 23 such earthquakes, of which 11 were preceded by ATCs within 30 d. Of these 11 earthquakes, preceding ATCs of 5 and 6 were positive and negative polarities of telluric current, respectively. Their epicenters were spatially well clustered in the east and west of the island. These facts were clearly beyond those expected by chance and led to a simple speculative model.T he VAN method, named after the initials of Varotsos, Alexopoulos, and Nomicos, for short-term earthquake (EQ) prediction by means of the monitoring of preseismic telluric current signals, called seismic electric signals (SES), has been in successful practice since the 1980s (1). The VAN method, however, has been a contentious subject with regard to the causal relationship between SES and EQs (e.g., refs. 2, 3). One way to get around this would be to accumulate as many case studies as possible on one hand and to build plausible physical models on the other (1, 4, 5, 6).The VAN method is characterized by the notion of "selectivity," which has two aspects (3, 7): (i) there are only selected sites which are sensitive to SES, and (ii) a sensitive site is sensitive only to the SES from some specific focal area(s). A map identifying those focal area(s) is called the "selectivity map" of that site. The selectivity is thought to originate from inhomogeneity of the subterranean electrical structures, implying that SES is transmitted only through subterranean conductive channels (1, 4). Another remarkable property of SES, called the "VAN relation," is expressed by Eq. 1 in terms of the focal distance r, the magnitude M, and the amplitude E of SES.where a is a constant ∼0.34-0.37 and b is a site-dependent constant. The selectivity and VAN relation are the backbone of the VAN method. In Japan, VAN-type telluric current monitoring was conducted and significant preseismic signals were observed in the late 1990s and early 2000s (6,8,9). The site in Kozu-shima Island was unique in showing SES-like telluric current changes before many EQs (9), whereas other stations showed such signals only for one EQ (6,8). In addition, the EQs occurred in the east and west of Kozu-shima Island after the positive and negative polarities of the SES-like telluric current changes, respectively (9). So, in this paper we have tried to statistically examine the correlation between the SES-like telluric current changes and the EQs for Kozu-shima Island. In the following, the term "geoelectric potential dif...

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Study of the temporal correlations in the magnitude time series before major earthquakes in Japan

2014

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A characteristic change of seismicity has been recently uncovered when the precursory Seismic Electric Signals activities initiate before an earthquake occurrence. In particular, the fluctuations of the order parameter of seismicity exhibit a simultaneous distinct minimum upon analyzing the seismic catalog in a new time domain termed natural time and employing a sliding natural time window comprising a number of events that would occur in a few months. Here we focus on the minima preceding all earthquakes of magnitude 8 (and 9) class that occurred in Japanese area from 1 January 1984 to 11 March 2011 (the day of the M9 Tohoku earthquake). By applying Detrended Fluctuation Analysis to the earthquake magnitude time series, we find that each of these minima is preceded as well as followed by characteristic changes of temporal correlations between earthquake magnitudes. In particular, we identify the following three main features. The minima are observed during periods when long-range correlations have been developed, but they are preceded by a stage in which an evident anticorrelated behavior appears. After the minima, the long-range correlations breakdown to an almost random behavior possibly turning to anticorrelation. The minima that precede M ≥ 7.8 earthquakes are distinguished from other minima which are either nonprecursory or followed by smaller earthquakes. Furthermore, it is discussed whether Tsallis statistical mechanics, in the frame of which it has been suggested that kappa distributions arise, can capture the effects of temporal correlations between earthquake magnitudes.

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Natural Time Analysis: The New View of Time

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a speci®c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 197 publications

References 0 publications

Natural time analysis of critical phenomena

Natural time analysis of critical phenomena

Preseismic anomalous telluric current signals observed in Kozu-shima Island, Japan

Study of the temporal correlations in the magnitude time series before major earthquakes in Japan

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