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

Abstract

The observed earthquake scaling laws indicate the existence of phenomena closely associated with the proximity of the system to a critical point. Taking this view that earthquakes are critical phenomena (dynamic phase transitions), here we investigate whether in this case the Lifshitz–Slyozov–Wagner (LSW) theory for phase transitions showing that the characteristic size of the minority phase droplets grows with time as t 1 / 3 is applicable. To achieve this goal, we analyzed the Japanese seismic data in a new time domain termed natural time and find that an LSW behavior is actually obeyed by a precursory change of seismicity and in particular by the fluctuations of the entropy change of seismicity under time reversal before the Tohoku earthquake of magnitude 9.0 that occurred on 11 March 2011 in Japan. Furthermore, the Tsallis entropic index q is found to exhibit a precursory increase.

Phenomena preceding major earthquakes interconnected through a physical model

“…Recently we have shown that almost three months before the M9 Tohoku earthquake, i.e., on 22 December 2010, the following additional facts have been observed: First, the complexity measure Λ i associated with the fluctuations of the entropy change of seismicity under time reversal exhibited abrupt increase which conforms to the seminal work by Lifshitz and Slyozov (Lifshitz and Slyozov, 1961) and independently by Wagner (Wagner, 1961) for phase transitions showing that the characteristic size of the minority phase droplets exhibits a scaling behavior in which time growth has the form A(t − t 0 ) 1/3 (Varotsos et al, 2018). It was also found that the increase ∆Λ i of Λ i follows the latter form and that the prefactors A are proportional to the scale i, while the exponent (1/3) is independent of i (Varotsos et al, 2018). Second, the Tsallis entropic index q (Tsallis, 1988), shows a simultaneous increase which interestingly exhibits the same exponent (1/3) but the prefactors A are not proportional to the scale i (Varotsos et al, 2018).…”

Phenomena preceding major earthquakes interconnected through a physical model

“…Fourth, studying the fluctuations β of κ 1 of seismicity in the entire Japanese region N 46 25 E 148 125 versus the conventional time from 1 January 1984 until the Tōhoku EQ occurrence on 11 March 2011, we find (Varotsos et al, 2019) a large fluctuation of β upon the occurrence of the M 7.8 earthquake near Chichijima on 22 December 2010. This finding has also been checked for several lengths from i = 150 to 500 events, which also revealed the following (Varotsos et al, 2019): upon increasing i it is observed (see Figs. 2b and 4e of Sarlis et al, 2013) that the increase β i of the β i fluctuation on 22 December 2010 becomes distinctly larger -obeying the interrelation β i = 0.5 ln(i/114.3) -which does not happen (see Fig.…”

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

“…Thus, it is highly likely that a preparation stage has already started even before the observation of the local β min at 5 January 2011. Interestingly, recent findings [8,37,99,100] based on the analysis of seismicity in natural time and non-extensive statistical mechanics [101][102][103] have revealed signs of critical behavior related with the preparation of a strong EQ around 22 December 2010 which lies between the date of the global and the regional β min . Fourth, p G 3 , that corresponds to the β min observed when analyzing the mid-scale global seismicity in natural time, is one order of magnitude smaller than p G 2 strengthening the importance of the mid-scale for EQ prediction (cf.…”