## 2 Materials and Methods  
### System-Analytical Method FCAZ  
The system-analytical method FCAZ (formalized clustering and zoning) was created in 2012-2016 at the Geophysical Center of the Russian Academy of Sciences [31; 33; 34; 35; 36; 37; 38; 39; 40; 41] (and others). Some ideas of the mathematical construction of the method can be observed in earlier publications [42; 43; 44]. The basic idea of the FCAZ study is the topological filtrational clustering of the seismic catalog--a finite set \(W\) of epicenters of known earthquakes in the studied region. As already noted, FCAZ makes it possible to efficiently recognize areas prone to the strongest, strong, and significant earthquakes [29]. Figure 2: The integrated earthquake catalog of the Eastern Sector of the Arctic zone of the Russian Federation (1962–2020) [16]. The white frame shows the boundaries of the region (coincides with the region marked in Figure 1), for which the catalog was created and within which FCAZ recognition was performed. The FCAZ system represents a sequential application of 2 algorithms: DPS (discrete perfect sets) [31; 32; 33; 37; 45; 46] and E\({}^{2}\)XT [31; 34]. In a finite set \(W\) of the Euclidean space, DPS selects regions with a given density level \(\alpha\). The output is a set of points that is \(\alpha\)-dense in each of its elements. The task of the DPS algorithm is to construct such a set \(W(\alpha)\) that its density is not less than the level \(\alpha\) at all its points. The DPS algorithm, in particular, is effective in the current task because it \"attracts\" recognition objects (earthquake epicenters) into dense clusters, leaving no isolated points [35]. At the next, second stage of FCAZ recognition, the E\({}^{2}\)XT algorithm formalizes and implements the construction of a unique mapping of discrete DPS clusters into flat zones of nonzero measure, inside and at the boundaries of which earthquakes with a magnitude \(M\geq M_{0}\) can occur [31]. Here \(M_{0}\) is a given magnitude threshold, which depends on the seismic regime of the considered region [29] and determines which earthquakes we consider strong. The algorithms that form FCAZ have a number of input parameters: DPS-\(q<0\) to calculate the localization radius and the maximum density level \(\beta\in[-1,1]\) to determine the required density level of DPS clusters \(\alpha(\beta)\); E\({}^{2}\)XT-\(p<0\) and \(w<0\) to calculate the scannability of DPS clusters and the connectivity of calculated flat high seismicity zones [33]. Another parameter for DPS is the number of iterations of applying the algorithm in one task. In 2016, the DPS and E\({}^{2}\)XT algorithms were equipped with artificial intelligence blocks [31]. The latter allows it to automatically choose the optimal values of the free parameters. This makes the result of FCAZ recognition more objective and reproducible [34]. Previously, using the FCAZ method, earthquake-prone area recognition in the following seismically hazardous regions of the world was successfully performed:  
* The mountain belt of the Andes of South America (\(M_{0}=7.75\)) [31; 34];
* Pacific coast of the Kamchatka Peninsula (\(M_{0}=7.75\)) [34; 35; 36] and the Kuril Islands (\(M_{0}=7.75\));
* California (\(M_{0}=6.5\)) [34; 36; 37];
* Cisbaikalia-Transbaikalia (\(M_{0}=5.5;M_{0}=5.75\), \(M_{0}=6.0\)) [34; 39];
* Altai-Sayan (\(M_{0}=5.5\)) [34; 40];
* Caucasus (\(M_{0}=5.0\)) [31; 33; 34; 37; 38];
* Crimean Peninsula and northwestern Caucasus (\(M_{0}=4.5;M_{0}=5.0\)) [34; 41]. In these regions, the reliability of the FCAZ results was assessed using control experiments of the \"seismic history\" type [29]. Naturally, the recognized high seismicity zones were also compared with the location of the actual epicenters of the strongest, strong, and significant earthquakes that occurred after the end of the catalog used for recognition [31]. Thus, in each of the 8 regions noted above, a high degree of reliability of FCAZ recognition was substantiated [34].