## 4 Discussion  
It has been shown by [PERSON] et al. [89] that, for regional studies, the precursory \(\beta_{min}\) occur upon the initiation of a series of precursory low frequency (\(\leq\)0.1 Hz) electric signals, termed SES activity [90; 91], as for example the one recorded by [PERSON] et al. [27; 92]. Briefly, once an SES activity has been recorded, a major EQ takes place a few weeks to \(5\frac{1}{2}\) months later within a candidate epicentral area that can be determined on the basis of the so-called \"selectivity\" map of the recording station as well as by considering the ratio of the two horizontal electric field SES components (see, e.g., [90; 91; 93]). Considering the case of the strongest EQ in Japan which is tabulated in the last row of Table 1, the minimum \(\beta_{min}\) of the fluctuations of the order parameter of seismicity before the M9 Tohoku EQ that occurred on 11 March 2011 was observed on 5 January 2011 being the deepest (\(\beta_{min}\) ever observed in Japan, [30; 59]) and is almost simultaneous with the initiation of anomalous magnetic field variations mainly in the z component. The latter were measured [94; 95; 96] at two geomagnetic stations (at Esashi and Mizusawa) lying approximately 130 km from the epicenter of the Tohoku EQ (cf. detectable magnetic field variations in the vertical component are expected to accompany SES activities before strong EQs, see, e.g., [97]). In view of this interrelation between SES activities and \(\beta_{min}\), we employed a range (170d) of around \(5\frac{1}{2}\) months in the ECA of the regional studies depicted in Figures 2 and 3. The result that the lowest \(p\)-values, i.e., p\({}_{I}\) and p\({}_{EM}\), were found for \(\tau=22\)d, \(\Delta T=52\)d (\(\tau+\Delta T<6\) months) and \(\tau=\)19d, \(\Delta T=164\)d (\(\tau+\Delta T\approx\)6 months), respectively, strengthens the aforementioned simultaneity of the initiation of SES activities and \(\beta_{min}\). Additionally, the \(\tau\) values found in both cases lie in the range 18 to 24d, which was revealed by ECA as the shortest period between the observation of an SES activity and the impending EQ occurrence in Greece [7] (as the cases studied in the latter work involve EQs of considerably lower target magnitudes, it is worthwhile in a future work to compare by means of ECA the resulting lead times for both precursors, i.e., \(\beta_{min}\) and SES activities, and discuss the results against their simultaneity found in [89]). Finally, the fact that both p\({}_{I}(=1.88\times 10^{-7})\) and p\({}_{EM}(=5.80\times 10^{-7})\) are almost two orders of magnitude smaller than the \(p\)-values estimated [98] for the original variability study of Japan [30], shows that the use of appropriate EQ networks (i.e., the ENBOSAP suggested by [74]) may significantly optimize the predictive power of the minima of the fluctuations of the order parameter of seismicity in natural time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline M & Latitude (\({}^{\circ}\)) & Longitude (\({}^{\circ}\)) & EQ Date & \(\beta_{min}\) Date \\ \hline
8.4 & \(-16.26\) & \(-73.64\) & 2001-06-23 & 2001-05-05 \\
9.0 & 3.30 & 95.78 & 2004-12-26 & 2004-09-04 \\
8.6 & 2.09 & 97.11 & 2005-03-28 & 2005-01-11 \\
8.5 & \(-4.44\) & 101.37 & 2007-09-12 & 2007-03-14 \\
8.8 & \(-35.85\) & \(-72.71\) & 2010-02-27 & 2009-11-09 \\
9.1 & 38.32 & 142.37 & 2011-03-11 & 2010-12-03 \\
8.6 & 2.33 & 93.06 & 2012-04-11 & 2011-08-20 \\  & & & & 1986-04-25 \\  & & & & 1989-02-09 \\  & & & & 1991-04-04 \\  & & & & 2002-04-18 \\  & & & & 2003-11-24 \\  & & & & 2006-03-31 \\  & & & & 2008-10-22 \\  & & & & 2012-05-30 \\  & & & & 2013-03-09 \\  & & & & 2013-04-06 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The epicenters and dates of occurrence of all EQs with M \(\geq\) 8.4 during the study period 1 January 1976 to 1 October 2014 as reported by the Global Centroid Moment Tensor Catalog together with the dates of their precursory variability minima.