Entropy of seismic electric signals: Analysis in natural time under time reversal

Abstract

Electric signals have been recently recorded at the Earth's surface with amplitudes appreciably larger than those hitherto reported. Their entropy in natural time is smaller than that, S u , of a "uniform" distribution. The same holds for their entropy upon time-reversal. This behavior, as supported by numerical simulations in fBm time series and in an on-off intermittency model, stems from infinitely ranged long range temporal correlations and hence these signals are probably Seismic Electric Signals (critical dynamics). The entropy fluctuations are found to increase upon approaching bursting, which reminds the behavior identifying sudden cardiac death individuals when analysing their electrocardiograms.

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

“…In other words, the use of high magnitude thresholds leading to a number of earthquakes smaller than six is not recommended for obtaining reliable j 1 value and hence for a description of the real situation approaching criticality. It has been observed (Varotsos et al 2001(Varotsos et al , 2006c(Varotsos et al , b, 2008b) that the aforementioned true coincidence appears usually a few days (up to around one week) before the occurrence of the mainshock.…”

“…We also calculate the evolution of the quantities S and S -to ascertain that the condition S,S -\ S u (see p. 292 of Varotsos et al 2011c) is also satisfied. The actual criteria for recognizing a true coincidence of the observed time series with that of critical state were as follows (Varotsos et al 2001(Varotsos et al , 2002b(Varotsos et al , 2006c(Varotsos et al , b, 2008b(Varotsos et al , 2011cUyeda et al 2009): First, the ''average'' D h i distance between the curves of P(x) of the evolving seismicity and Eq. (5) should be smaller than 10 -2 (cf.…”

Natural time analysis of critical phenomena

“…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.…”

Entropy in Natural Time and the Associated Complexity Measures

“…[9,13,16]) together with S and S − . In particular, both entropies S and S − have been experimentally found [13,58,59] to be smaller than S u for the electric signals that precede rupture…”

“…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.…”