## 4 Discussion
In the last ten rows, we also include the dates of ten more variability minima that could not be separated from the precursory ones when using the mid-scale time series of the global seismicity (compiled from Table 2 in [61]). We now turn to ECA for the \(\beta_{min}\) of the global seismicity depicted in Figures 4-6. First, we have to mention that in these cases, where we do not employ ENBOSAP, we inevitably have \(\beta_{min}\) that are followed by EQs of a magnitude smaller than the target M\({}_{thres}\), which as mentioned correspond to FA. This fact explains why p\({}_{G_{1}}\), p\({}_{G_{2}}\), and p\({}_{G_{3}}\) are almost two orders magnitude larger than p\({}_{J}\) and p\({}_{EM}\) of the regional cases (i.e., they are comparable to those found for the Japanese case by [98]). Second, in all three cases presented, p\({}_{G_{1}}\), p\({}_{G_{2}}\), and p\({}_{G_{3}}\) are almost one order of magnitude smaller than the corresponding trigger \(p\)-values, thus ECA reveals the precursory character (risk enhancement factor, [4]) of \(\beta_{min}\) for the strongest EQs. Third, the values of \(\tau=11\)d, \(\Delta T=255\)d and \(\tau=49\)d, \(\Delta T=186\)d sum up to a maximum lead time of nine or eight months, respectively, pointing to a different mechanism behind these minima compared to the regional ones. For example, the study of the situation before the aforementioned 2011 Tohoku EQ, as described in Tables 3-5, shows that the global \(\beta_{min}\) was observed around 30 November to 3 December 2010, i.e., at dates markedly different than those of the regional \(\beta_{min}\) and the simultaneous initiation of the anomalous variations in the vertical component of the geomagnetic field at Esashi and Mizusawa. Thus, it is highly likely that a preparation stage has already started even before the observation of the local \(\beta_{min}\) 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 \(\beta_{min}\). Fourth, p\({}_{G_{3}}\), that corresponds to the \(\beta_{min}\) 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. mid-scale focuses, see Figure 7 of [61] to scales that comprise a number of seismic events that on average occur within a period of around a few months or so thus it compares favorably with the SES activities time lag and lead time). Finally, the fact that the three \(p\)-values (p\({}_{G_{1}}\), p\({}_{G_{2}}\), and p\({}_{G_{3}}\)) are by two orders of magnitude smaller than 5% indicates the statistical significance of the appearance of \(\beta_{min}\) as precursors to strong EQs in a global scale. It would be fruitful to investigate, in a future work, whether such minima appear in other systems of rich complexity (see, e.g., [104; 105; 106]) that exhibit avalanches or large sudden events, such as stock market crashes or turbulence (cf. the similarity between the latter two systems has been discussed in [107] while stock markets are known to exhibit EQ like phenomena [108]). Furthermore, we plan to study \(\beta_{min}\) 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 \(\Delta S\) under time reversal which have been also observed before strong EQs [36; 37].