## 4 Discussion  
An inspection of Figure 4 revealed that the epicenters of the impending EQs correlated favorably with the \(\langle\)EPS\(\rangle\) maps. Of course, \(M\geq 7.1\) EQs did not occur in areas where \(\langle\)EPS\(\rangle\) was highest, but rather in regions where \(\langle\)EPS\(\rangle\) was rather mediocre. Detailed results showed that the \(\langle\)EPS\(\rangle\) values at the grid points nearest to the epicenters laid in the range from 19% to 50%. Namely, this \(\langle\)EPS\(\rangle\) value equaled 22% for Lesvos EQ, 28% for Vrancea EQ, 21% for Aqaba EQ, 19% for Izmit EQ, 30% for Duzice EQ, and 50% for Van EQ. This result was probably related to the fact that, at the time of \(\beta_{W,min}\), long-range correlations started to develop in the magnitude time series [40; 95; 141]. Interestingly, the above results were consistent with respect to the two free parameters of the proposed method (i.e., the grid size and the radius \(R\)) were concerned. If we considered the five EQs with \(M\geq 7.1\) for which simultaneous minima were identified at the same time (i.e., see the first five rows of Table 1) and studied the statistics of \(\langle\)EPS\(\rangle\) of the closest to the epicenters grid points versus \(R\), we found that their mean exhibited a plateau centered at \(R\approx 250\) km, which was also accompanied by an inflection point for the corresponding standard deviation (STD); cf. Figure 3b. This result was obtained for a \(0.1^{\circ}\times 0.1^{\circ}\) grid and a similar behavior was found for the \(0.25^{\circ}\times 0.25^{\circ}\) grid used for drawing the maps of Figure 4. Indeed, the selection of \(R=250\) km in the latter figure was determined on this basis. Note that \(R=250\) km was also used in the NTA of seismicity of Japan [31] for estimating the epicenter of an impending \(M\geq 7.6\) EQ. At this point, it should be noted that when using the empirical CDF shown in Figure 3a instead of its Weibull approximation, the results did not change significantly and the maps remained almost the same. In view of the aforementioned ability of the \(\langle\)EPS\(\rangle\) maps calculated at the time of \(\beta_{W,min}\) to provide information on the impending EQ epicenter for \(M\geq 7.1\), we proceeded  
Figure 5: The value of EPS was considered unity inside the yellow-colored circular region of radius \(R\) with center at O—this disk was called region “Y” in the text—and zero outside. The \(\langle\)EPS\(\rangle\) was calculated for a point P lying at distance \(d\) from the center of the yellow-colored region and equals to the ratio of the (red) line-shaded region over the area \(\pi R^{2}\) of the circle having its center at P.  
to the calculation of such maps upon the occurrence of \(\beta_{W,min}\) that, although were not simultaneous in areas \(A_{5}\) and \(A_{6}\), were followed by an EQ of \(M\in[6.5,7.0]\) within six (or at the most seven) months. The dates of such minima are listed in the first column of Table 2, and were used for the construction of the \(\langle\)EPS\(\rangle\) maps shown in Figure 6. Figure 6 was drawn by using a \(0.25^{\circ}\times 0.25^{\circ}\) grid as in Figure 4. In the last column of Table 2, the \(\langle\)EPS\(\rangle\) estimated at the grid points nearest to the impending EQ epicenter are shown (cf. they had an average value 38% and an STD of 20%). A similar calculation revealed an average of 38% and an STD of 18% when a grid \(0.1^{\circ}\times 0.1^{\circ}\) was used, pointing to the stability of the calculation. Of course, the present method is a long way from becoming a really practical one, and we are still in the progress of improving it, since the cover of areas in Figures 4 and 6 was too large to find the final epicenter of an impending strong EQ. It provides, however, insight to the very difficult question of forecasting strong EQs.