## 3 Results
### FCAZ Recognition of the Strongest Earthquake-Prone Areas  
Three regions of the Pacific Seismic Belt are considered. Within their limits by the FCAZ method the areas prone to the strongest earthquakes with \(M\geq 7.75\) are recognized. The epicenters of earthquakes with the focal depth of up to 70 km from the ANSS catalog (1963-2013, the mountain belt of the South American Andes), the earthquakes catalog of Kamchatka and the Commander Islands (1962-2015, the coast of the Kamchatka Peninsula), and the catalog of the Kuril-Okhotsk region (1962-2009, the coast of the Kuril Islands) are  
Figure 6: Presentation of a joint result of earthquake-prone areas recognition with \(M\geq 6.0\) by the Barrier-3 and Cora-3 algorithms as a fuzzy set of vicinities of the intersections of lineaments: (**a**) the Altai–Sayan–Baikal region (white circles—epicenters of earthquakes with \(M\geq 6.0\) (1900–2012); blue star—epicenter of the earthquake, which occurred on 11 January 2021); (**b**) the Caucasus (white circles—epicenters of earthquakes with \(M\geq 6.0\); minor ones—before 1900; medium ones—1900–1992; major ones—after 1992). Highlighted in red are the vicinities of intersections of lineaments with membership function to the high seismicity set \(\mu=1\); in blue, \(\mu=0.5\); in green, \(\mu=0\). The function \(\mu\) is determined by the formula (17). used as recognition objects. To select the magnitude threshold \(M_{\text{R}}\), starting from which the epicenters were used as recognition objects, completeness magnitude \(M_{\text{c}}\) was assessed in the catalogs [46; 47; 48]. Taking into account \(M_{\text{c}}\) assessment, it was decided to use as FCAZ recognition objects in the Andes the earthquake epicenters with \(M\geq M_{\text{R}}=4.5\) (16,556 epicenters) [21]; in Kamchatka, \(M\geq M_{\text{R}}=3.5\) (44,113 epicenters) [49; 50; 51]; in the Kuril Islands, \(M\geq M_{\text{R}}=4.2\) (11,725 epicenters). In Figure 7a, the totality of blue and green colors shows recognition objects in the mountain belt of the South American Andes. The lists of the strongest crustal earthquakes, beginning in 1900, have been formed based on the above-listed instrumental catalogs, EPA recognition works, and the catalog of strong earthquakes in the USSR from ancient times to 1975 [52]. As a result, the catalog of the strongest earthquakes of the mountain belt of the Andes contains 24 events for the period of 1900-2013; the catalog of Kamchatka, 8 (1900-2015); and that of the Kuril Islands, 11 (1900-2009). The epicenters of earthquakes with \(M\geq 7.75\) are shown in Figures 7b and 8. Figure 7: Mountain belt of the Andes: (**a**) FCAZ recognition objects—the epicenters of earthquakes with \(M\geq 4.5\) and recognized DPS clusters; (**b**) FCAZ zones prone to earthquakes with \(M\geq 7.75\) and the epicenters of earthquakes with \(M\geq 7.75\). The DPS clustering of the epicenters of earthquakes, which represent FCAZ recognition objects, was performed as follows. Initially, the DPS algorithm was employed with density level \(\alpha_{1}(\beta_{1})\). The obtained dense set of objects \(W_{1}(\alpha_{1}(\beta_{1}))\) was excluded from further consideration and the algorithm was applied for the second time to the remaining subset with density level \(\alpha_{2}(\beta_{2})\). This allowed obtaining new DPS clusters \(W_{2}(\alpha_{2}(\beta_{2}))\), where \(W_{2}=W\backslash W_{1}(\alpha_{1}(\beta_{1}))\). Subsequent iterations were performed similarly. All connected components forming part of \(W_{1}(\alpha_{1}(\beta_{1}))\cup W_{2}(\alpha_{2}(\beta_{2}))\cup\ldots\cup W_ {k}(\alpha_{k}(\beta_{k}))\) were declared as sought DPS clusters. Four iterations of DPS clustering were performed in the mountain belt of the South American Andes; two iterations, in Kamchatka; and three, in the Kuril Islands. The optimal values of the \(\beta\) parameter--the maximality level of density of DPS clusters--were computed automatically using the artificial intelligence block.