## 2 Methods  
### Natural Time Analysis  
For the NTA of a time-series comprising \(N\) EQs, the natural time is defined by \(\chi_{k}=k/N\) and serves as an index for the occurrence of the \(k\)-th EQ. The quantity \(\chi_{k}\) together with the energy \(E_{k}\) released during the \(k\)-th EQ of magnitude \(M_{k}\), i.e., the pair \((\chi_{k},E_{k})\), is studied in NTA. Alternatively, we study the pair \((\chi_{k},p_{k})\), where  
\[p_{k}=\frac{E_{k}}{\sum_{n=1}^{N}E_{n}} \tag{1}\]  
denotes the normalized energy released during the \(k\)-th EQ. The variance of \(\chi\) weighted for \(p_{k}\), labeled \(\kappa_{1}\), is given by [9; 11; 26; 63]:  
\[\kappa_{1}=\sum_{k=1}^{N}p_{k}(\chi_{k})^{2}-\left(\sum_{k=1}^{N}p_{k}\chi_{k} \right)^{2}, \tag{2}\]  
where \(E_{k}\), and therefore \(p_{k}\), for EQs is estimated through the usual relation suggested by [PERSON] [64]:  
\[E_{k}\propto 10^{1.5M_{k}} \tag{3}\]  
and \(M_{k}\) corresponds to the moment magnitude \(M_{w}\)[65]. The magnitude reported in each EQ catalog should be converted to \(M_{w}\); for example, in the case of Japan the magnitudes reported from the Japan Meteorological Agency (JMA) \(M_{JMA}\) were converted to \(M_{w}\) using the formulae suggested by [PERSON] et al. [25].  
As already mentioned, the quantity \(\kappa_{1}\), i.e., the variance of natural time \(\chi_{k}\), plays an important role in seismicity. [PERSON] et al. [26] proposed that \(\kappa_{1}\) given by Equation (2) can be considered as an order parameter for seismicity since its value changes abruptly when a strong EQ occurs and its fluctuations have statistical properties similar to other nonequilibrium and equilibrium critical systems [16; 26]. When considering an excerpt of an EQ catalog comprising \(W\) consecutive events, we can estimate various \(\kappa_{1}\) values that correspond to subexcerpts of consecutive EQs, e.g., by using the first 6 EQs, the second 6 EQ, the first seven EQs, etc. This multitude of \(\kappa_{1}\) values enable the calculation of their average value \(\mu(\kappa_{1})\) and their standard deviation \(\sigma(\kappa_{1})\). We then determine the variability \(\beta\) of \(\kappa_{1}\)[56]:  
\[\beta_{W}=\frac{\sigma(\kappa_{1})}{\mu(\kappa_{1})}. \tag{4}\]  
that corresponds to this natural time window of length \(W\) and quantifies the intensity of the fluctuations of the order parameter of seismicity. Note that \(\beta_{W}\) of Equation (4) could be identified [62] as effectively the square root of the Ginzburg criterion, e.g., see Equation (6.25) on p. 175 of [PERSON] [66], the importance of which in EQ processes has been discussed by [PERSON] et al. [53]. The time evolution of \(\beta_{W}\) is followed by sliding the window of \(W\) consecutive EQs, event by event, through the EQ catalog and assigning to its value the occurrence time of the EQ which follows the last EQof the window studied in the EQ catalog. The fluctuations of the order parameter of seismicity as quantified by \(\beta_{W}\) have been studied in various seismically active regions, like Japan [30; 31; 59] or Eastern Mediterranean [62], and in the global seismicity as well [60; 61]. These studies have revealed that before strong EQs \(\beta_{W}\)s exhibit characteristic minima labeled \(\beta_{min}\) and were focused, so far, on a small number of the stronger EQs in each geographic region (see Tables 1-5) for which their preceding minima exhibited a clear characteristic behavior. Moreover, in the \(\beta_{W}\) computations in each region only EQs with magnitude exceeding a certain value have been considered to ensure data completeness [30; 31; 59; 60; 61; 62].