Fluctuations, under time reversal, of the natural time and the entropy distinguish similar looking electric signals of different dynamics

Abstract

We show that the scale dependence of the fluctuations of the natural time itself under time reversal provides a useful tool for the discrimination of seismic electric signals (critical dynamics) from noises emitted from manmade sources as well as for the determination of the scaling exponent. We present recent data of electric signals detected at the Earth's surface, which confirm that the value of the entropy in natural time as well as its value under time reversal are smaller than that of the entropy of a "uniform" distribution.PACS numbers: 91.25. Qi, 91.30.Px, 05.45.Tp

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

“…It is dynamic entropy, and its value upon considering the time reversal T, i.e., Tp k = p N-k?1 , is labeled by S -. The value of S -is, in general, different from S (e.g., see Varotsos et al 2007Varotsos et al , 2008b, and references therein), and thus S does satisfy the conditions to be ''causal.'' The entropy S u of a ''uniform'' (u) distribution is S u = 0.0966.…”

Entropy in Natural Time and the Associated Complexity Measures

“…In all the cases mentioned above the validity of the inequalities (14) characterizes (together with other conditions, e.g., see Refs. [118,129]) the approach to criticality. Apart from this application, the study of the time series of the difference ∆S of the entropy in natural time under time reversal may reveal useful information concerning the evolution of the system towards an extreme event.…”

“…Both the entropy S and the entropy under time-reversal S − have been used for the determination of the occurrence time of an impending mainshock. This has been done [59,[116][117][118] in a variety of cases in Greece where SES have been identified. The procedure followed is that upon the recording of the SES a candidate area for suffering the strong earthquake can be selected and hence the seismicity due to the small earthquakes occurring there can be studied in natural time as described in Section 5.…”

Detecting breakpoints in artificially modified- and real-life time series using three state-of-the-art methods

“…In the former case, the identi cation of transient electric signals preceding earthquakestermed Seismic Electric Signals activity [19] -characterized by critical dynamics [20,21] can be distinguished from similar-looking signals emitted from nearby noise sources [22] by analyzing them in a new time domain, termed 'natural time' [23]. It can also be an interesting issue in geodesy regarding o sets of Global Positioning System time series [24,25].…”