## 3 Results  
Following Reference [13], we calculated \(\beta_{\text{W}}\) for \(W=100\) and \(W=160\) (see Figure 4) in order to identify the precursory--within 9 months (for example compare the second with the fourth column of Table 1)--fluctuation minima that precede all \(M\geq 8.5\) EQs in global seismicity. A fluctuation minimum can be considered as 'precursory' when the following conditions [13] are satisfied: A local minimum of either \(\beta_{100}\) or \(\beta_{160}\) is considered as such if it is smaller than its 15 previous and 15 future values. Since we assume [11] that there exists a single critical process (one fluctuation minimum), 90% of the EQs that lead to the minimum \(\beta_{100,min}\) should appear in the minimum \(\beta_{160,min}\). Moreover, since this processis characteristic, the ratio \(r=\beta_{160,min}/\beta_{100,min}\) should lie within the limits defined by the minima preceding the \(M\geq 8.5\) EQs [13], i.e., \(r\in(r_{1}=1.05,r_{2}=1.15)\) or:  
\[1.05<\frac{\beta_{160,min}}{\beta_{100,min}}<1.15. \tag{10}\]  
Finally, \(\beta_{100,min}\) should be smaller than the shallowest \(\beta_{100,min}\) precursory to \(M\geq 8.5\) EQ, denoted by \(\beta_{0}\), i.e.,  
\[\beta_{100,min}<\beta_{0}, \tag{11}\]  
and \(\beta_{0}=0.285\), as found in Reference [13]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Label**} & \multicolumn{2}{c}{**Predicted**} & \multirow{2}{*}{\(\beta_{100,min}\)} & \multirow{2}{*}{\(\beta_{160,min}\)} & \multirow{2}{*}{\(\beta_{160,min}\)} & \multirow{2}{*}{\(\beta_{160,min}\)} & \multirow{2}{*}{\(\alpha_{160}\)} & \multirow{2}{*}{\(\alpha_{300}\)} & \multirow{2}{*}{\(\langle\mathbf{\alpha}\rangle\)} \\  & & & & & & & \\ \hline H1 & 9.0 & 0.227 & 0.243 & & & & \\  & (20041226) & (20040405) & (20040405) & 1.071 & 0.560 & 0.621 & 0.591 \\ H2 & 8.6 & 0.160 & 0.170 & 1.060 & 0.546 & 0.486 & 0.516 \\  & (20050328) & (20050128) & (20050202) & & & & \\ H3 & 8.5 & 0.277 & 0.297 & 1.073 & 0.581 & 0.632 & 0.607 \\  & (20070912) & (20061202) & (20061220) & & & & \\ FA1 & - & 0.280 & 0.305 & & & & \\  & (20080825) & (20080825) & 1.088 & 0.532 & 0.550 & 0.541 \\ H4 & 8.8 & 0.232 & 0.246 & & & & \\  & (20100227) & (20100201) & (20100216) & 1.063 & 0.527 & 0.545 & 0.536 \\ H5 & 9.1 & 0.237 & 0.264 & & & & \\  & (20110311) & (20101129) & (20101130)1 & 1.114 & 0.511 & 0.531 & 0.521 \\  & 8.6 & 0.285 1 & 0.323 & & & & \\ H6 & (20120411) & (20110727) & (20110804) & 1.134 & 0.584 & 0.508 & 0.546 \\ FA2 & - & 0.279 & 0.305 & & & & \\  & (20120520) & (20120603) & 1.095 & 0.544 & **0.732** & **0.638** \\ FA3 & - & 0.261 & 0.277 & & & & \\  & (20131228) & (20140113) & 1.059 & **0.630** & 0.606 & **0.618** \\ FA4 & - & 0.276 & 0.302 & & & & \\  & (20150913) & (20150913) & 1.096 & **0.622** & **0.727** & **0.674** \\ FA5 & - & 0.234 & 0.251 & & & & \\  & (20200314) & (20200323) & 1.072 & **0.510** & **0.478** & **0.494** \\ FA6 & - & 0.272 & 0.303 & & & & \\  & (20210616) & (20210702) & 1.115 & 0.555 & 0.615 & 0.585 \\ \hline \hline \end{tabular}  
* \({}^{1}\) In this case, \(\beta_{100,min}=0.2849\) and hence \(\beta_{100,min}<\beta_{0}\).  
\end{table} 
Table 1: The ‘precursory’ fluctuation minima, i.e., the variability minima that satisfy Conditions (10) and (11), together with DFA exponents \(\alpha_{160}\), \(\alpha_{300}\), and their mean value \(\langle\mathbf{\alpha}\rangle\). The exponents typed boldface lie outside the range defined by the corresponding exponents estimated for the precursory variablility minima that preceded all EQs with \(M\geq 8.5\). For each row, a label is also inserted to express whether it is a hit (H1 to H6) or a false alarm (FA1 to FA6). For the hits, a brief reference to the predicted \(M\geq 8.5\) EQ is inserted in the corresponding column, for more details, see Table 2.  
Figure 4: The order parameter fluctuations for global seismicity as depicted by the variabilities \(\beta_{\rm W}\) for \(W=100\) (red) and \(W=160\) (blue) during the period from 1 January 1976 to 31 January 2022.