The Complexity Measures Associated with the Fluctuations of the Entropy in Natural Time before the Deadly México M8.2 Earthquake on 7 September 2017

Abstract

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.

On the Statistical Significance of the Variability Minima of the Order Parameter of Seismicity by Means of Event Coincidence Analysis

“…Furthermore, we plan to study β min as precursors to strong avalanches observed in EQ models which can produce a large amount of data such as the Carlson-Langer model [109] or the Olami-Feder-Christensen model [110] to see if they show a similar drop in the variability. Concerning the latter model, it has been studied by means of the entropy in natural time [17] revealing minima of the entropy change ∆S under time reversal which have been also observed before strong EQs [36,37].…”

“…NTA has found applications in a wide variety of fields ranging from cardiology (see, e.g., [12][13][14][15]) to statistical physics (see, e.g., [16][17][18][19][20][21]), and atmospheric science (see, e.g., [22][23][24]). One of the main applications of NTA, however, is the study of the physics of EQs (see, e.g., [25][26][27][28][29][30][31][32][33][34][35][36][37]). In addition, natural time is considered as the basis of the "nowcasting earthquakes" methodology that has been introduced recently [38][39][40][41][42][43][44][45][46].…”

Phenomena preceding major earthquakes interconnected through a physical model

“…For example, S has been applied for the identification of the time of an impending sudden cardiac death risk (Varotsos et al, 2007). Furthermore, it has been used for the study of the predictability of the Olami-Feder-Christensen (OFC) model for earthquakes (Olami et al, 1992), which is probably (Ramos et al, 2006) the most studied nonconservative self-organized criticality (SOC) model. The OFC model originated by a simplification of the Burridge and Knopoff spring-block model (Burridge and Knopoff, 1967) by mapping it into a non-conservative cellular automaton simulating the earthquake's behavior and introducing dissipation in the family of SOC systems.…”

Tsallis Entropy Index q and the Complexity Measure of Seismicity in Natural Time under Time Reversal before the M9 Tohoku Earthquake in 2011

“…In particular, it was found that exhibits a clear minimum [ 11 ] (or maximum if we define [ 15 ] instead of used here, see Section 2 ) before a large avalanche in the OFC model, which corresponds to a large earthquake. Furthermore, in a more recent study [ 18 ], by analyzing the seismicity during the six-year period 2012–2017 in natural time in the Chiapas region where the M8.2 earthquake occurred, we found that, on the same date as above, i.e., 14 June 2017, the complexity measure (see Section 2 ) associated with the fluctuations of the entropy change under time reversal exhibits an abrupt increase along with a simultaneous increase of the Tsallis entropic index q [ 19 , 20 , 21 , 22 , 23 , 24 ].The temporal variations of the latter entropic index before strong earthquakes arouse an intense international interest and has been studied by several workers [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ].…”