**3. Results**

#### *3.1. Variable EPA Method*

Figure 2 shows the MSZ map of Altai–Sayan–Baikal region. The result of earthquakeprone areas recognition with *M* ≥ 6.0 by Barrier-3 algorithm is shown in Figure 2 using ellipses with blue boundaries. Upon the completion of recognition, 32 out of 97 objects are identified as high seismicity class *B*. The totality of vicinities of these objects (circles used to compute the values of characteristics) [5] determines the areas prone to earthquakes with *M* ≥ 6.0.

**Figure 2.** The morphostructural zoning map of the Altai–Sayan–Baikal region. Thick black lines—rank I lineaments; medium gray lines—rank II; thin black lines—rank III; solid lines—longitudinal lineaments; dotted line—transverse ones [36,37], areas prone to earthquakes with *M* ≥ 6.0 (ellipses with blue boundaries—Barrier-3 [16], white ellipses—Cora-3 [37], white ellipses with blue boundaries—both the algorithms). Red circles designate the epicenters of crustal earthquakes with *M* ≥ 6.0 (1900–2012) used to form the learning set *B*0, red star refers to the epicenter of crustal earthquake (11 January 2021 with *M* = 6.7) that occurred after the completion of recognition.

Figure 3a shows a bar diagram characterizing the medium contribution of characteristics in recognition using the Barrier-3 algorithm of a sought high seismicity set of objects. Figure 3b shows the contribution of characteristics expressed through attribution to the Top 3 rankings. The *y* axis in Figure 3a shows the average number of "attributions" of characteristics in the recognition of a set *<sup>P</sup>*Π(*<sup>B</sup>*0) (see above), in Figure 3b, the number of attributions to the three "strongest" characteristics (Top 3 ranking).

**Figure 3.** The contribution of characteristics to recognition using the Barrier-3 algorithm of a high seismicity set of objects in the Altai–Sayan–Baikal region: (**a**) average contribution of characteristics; (**b**) the contribution of characteristics expressed through their attribution to the "strongest" threes.

It can be seen from Figure 3 that in the recognition of strong earthquake-prone areas in the Altai–Sayan–Baikal region using the Barrier-3 algorithm, the most significant characteristics include gravity anomalies (Bmax and Bmin), a combination of relief types (Top) and the distance to the nearest lineament of rank II (R2). The intersections of lineaments classified as high seismicity ones against the background of the entire set of objects in their vicinities are characterized by low values of gravity anomalies (mostly Bmax ≤ −160 mGal and Bmin ≤ −220 mGal) and contrasting combinations of relief types—mountains/foothill and mountains/mountains. These are characterized by high values of magnetic anomaly (MOmax), the concentration of dB around 60 mGal and 120 mGal, and the concentration of Hmin less than −1000 m and more than 1000 m.

It can be seen from Figure 3 that lithospheric magnetic field anomalies contribute to the result of recognition in the Altai–Sayan–Baikal region. It can thus be concluded that the vicinities of high seismicity intersections of lineaments are characterized by a high degree of tectonic breaks, the existing deep density heterogeneity, as well as specific structure and composition of the Earth's crust. It would be natural to interpret these signs as the criteria of high seismicity in the studied region.

A comparative analysis of results, obtained independently using the Barrier-3 algorithm and the Cora-3 dichotomy algorithm, which is most common in the EPA [38,39], shows that they are well aligned with each other (Figure 2). The Barrier-3 algorithm recognized as high seismicity ones 32 intersections of morphostructural lineaments and Cora-3 33 intersections [36,37]. That said, 25 objects were attributed by both algorithms to class *B*.

The Barrier-3 algorithm classified as hazardous 6 out of 51 objects of the learning set of a low seismicity class of dichotomy; Cora-3 3 out of 51; both algorithms, 2 intersections. Consequently, 44 learning objects of class *H* were recognized by both algorithms as nonhazardous for magnitude *M* ≥ 6.0. It means that the key differences in the classification belongs to a set of objects initially not attributed to learning sets (20 objects are classified identically by the algorithms and 10 are classified differently). It should be noted that the epicenters of earthquakes with *M* ≥ 6.0, used to form the learning set *B*0 (red circles in Figure 1) are located strictly within the vicinities of objects classified by both algorithms as high seismicity ones [16,37].

It is noteworthy that the Barrier-3 algorithm is structured in such a way that learning objects in the final classification always belong to class *B*. In turn, in recognition using dichotomy algorithms (particularly Cora-3 algorithm), learning objects are broadly speaking, not obliged to retain their attribution to the relevant class [4,7].

The red star in Figure 2 shows the epicenter of the crustal earthquake, which occurred on 11 January 2021, with *M* = 6.7. This earthquake occurred after the completion of the independent recognitions described herein using the Barrier-3 and Cora-3 algorithms, thus representing the material for a pure examination for them. It can be seen from Figure 2 that the epicenter is located outside of the vicinities (with a radius of 25 km) of the intersections of lineaments recognized as high seismicity ones by both algorithms. At the same time, it is located 42 km away from the nearest recognition object attributed to class *B* by both algorithms. It was believed in the formation of learning material that the epicenter is confined to the intersection if it is located at a distance of no more than 50 km. Accordingly, the epicenter of the earthquake that occurred on 11 January 2021, is confined to the intersection of lineaments attributed to class *B* by both algorithms, ye<sup>t</sup> is located outside of the 25 km of vicinities used to compute the values of its characteristics.

The recognition results of the areas prone to earthquakes with *M* ≥ 6.0 in the Altai– Sayan–Baikal region, obtained using the Barrier-3 (one learning class) [16] and Cora-3 algorithms (two learning classes) [36,37], are well aligned with each other. On the one hand, this evidences the reliability of both results since recognition was performed independently. On the other hand, in the interpretation of differences (15.5% of the total number of objects) in the outcomes, preference should be given to the classification using the Barrier-3 algorithm since it was performed with learning containing no protentional errors.

The recognition result of the areas prone to strong earthquakes in the Caucasus, obtained using the Barrier-3 algorithm as the EPA recognition block, is shown in Figure 4 as ellipses with blue boundaries. Barrier-3 attributed 108 out of 237 intersections of lineaments to high seismicity class *B*.

Figure 5 shows the bar diagrams demonstrating the contribution of object characteristics to the recognition, by Barrier-3 algorithm, of the intersections of lineaments, in whose vicinities strong earthquakes can occur in the Caucasus. As it can be seen, the greatest contribution is made by the characteristics that are responsible for relief heights (Hmax and Hmin), the area of quaternary rocks (Q), the highest rank of lineament (HR), the number of lineaments in the vicinities (NLC), and the distances to the nearest lineaments of ranks I (R1) and II (R2).

**Figure 4.** The morphostructural zoning map of the Caucasus (legends as in Figure 2) [40], areas prone to earthquakes with *M* ≥ 6.0 (ellipses with blue boundaries—Barrier-3 [17], white ellipses—Cora-3 [41], white ellipses with blue boundaries— both algorithms) and the epicenters of earthquakes with *M* ≥ 6.0 (brown circles—before 1900, red circles—in the period from 1900 to 1992 (used to form the learning set *B*0), dark green circles—since 1993 (material for a pure exam)) [42].

**Figure 5.** The contribution of characteristics to the recognition, using the "Barrier-3" algorithm, of a high seismicity set of objects in the Caucasus: (**a**) average contribution of characteristics; (**b**) the contribution of characteristics expressed through their attribution to the "strongest" threes.

In the Caucasus, the intersections of lineaments recognized as hazardous ones for *M* ≥ 6.0 against the background of the entire set of recognition objects in their vicinities are characterized by high values of the maximum and minimum heights (Hmax ≥ 2500 m and Hmin ≥ 600 m) and a small area of quaternary rocks (Q ≤ 30%). They are made up of three or more lineaments of ranks II or III (NLC ≥ 3, HR = 2 or HR = 3, R2 ≤ 30 km) and located at a relatively short distance away from the lineaments of rank I (0 < R1 ≤ 50 km).

The joint analysis of Figures 3 and 5 shows that in both regions for the Barrier-3 algorithm, a significant contribution to the formation of a high seismicity set of objects is made by the distance to the nearest lineament of rank II. Namely, the characteristic R2 is important for the Barrier-3 algorithm and invariable relative to the selection out of two regions considered.

Figure 4 illustrates a comparison of the classification of lineament intersections in the Caucasus, obtained with the help of Barrier-3 and Cora-3 algorithms. The first one recognized as high seismicity ones 108 intersections of lineaments [17]; the second one, 107 [41], both algorithms simultaneously recognized 73. The Barrier-3 algorithm classified as hazardous 24 out of 71 objects of the learning set of low seismicity class from Cora-3; Cora3, 22; both algorithms simultaneously, 16. In total, 41 learning objects of a low seismicity class were recognized by both algorithms as non-hazardous. Out of the intersections set not initially classified as the learning sets of Cora-3, the algorithms classified identically 95 objects and classified differently 55 objects [17,41].

It can be seen from Figure 4 that the objects located on the longitudinal lineaments of rank II and classified by both algorithms as high seismicity ones make up extensive zones along the axis of the Main Ridge in the Central and Southeastern Segments of the Greater Caucasus. A good coincidence of recognition results can be seen in the eastern sector of the Lesser Caucasus and the Armenian Volcanic Plateau [43]. A totality of the objects located on the transverse lineaments of rank II and attributed by the Barrier-3 and Cora-3 algorithms to class *B* make up an extensive submeridional zone within the Trans-Caucasian Transverse Elevation, combining the areas prone to strong earthquakes in the Greater and Lesser Caucasus. A fairly good alignment of high seismicity areas can also be seen near the Talysh mountains. It is noteworthy that most earthquakes known in the Caucasus with *M* ≥ 6.0 occurred in the vicinities of the objects making up the zones described above.

The analysis of Figure 4 showed that all 17 epicenters of earthquakes with *M* ≥ 6.0 (red circles), which formed the learning set of high seismicity class of both algorithms, are located inside the *B* zones recognized by both algorithms. Out of 42 epicenters of strong earthquakes, which occurred before 1900 (brown circles), 7 and 8 epicenters, respectively, are located outside of the zones recognized by the Barrier-3 and Cora-3 algorithms. Half of them are located within a short distance from the potentially high seismicity areas recognized by the algorithms.

Dark green circles in Figure 4 refer to the epicenters of strong earthquakes, which have occurred in the Caucasus since 1993. Information about them has not been used, in any manner whatsoever, in the formation of learning sets; thus these earthquakes represent material for a pure examination. Two of the three epicenters are located strictly within the high seismicity zones recognized by both algorithms. The latter represents a significant argumen<sup>t</sup> in favor of the reliability of the result demonstrated by Figure 4.

The replacement of a dichotomy algorithm with the original Barrier-3 algorithm, undertaken in this paper, is an attempt to open a new page in the development of the EPA approach. As shown above, the Barrier-3 algorithm proved itself to be good in the recognition of strong earthquake-prone areas with one learning class in the Caucasus and the Altai–Sayan–Baikal region. This fact strengthens the assumptions that the approach toward the recognition of potentially high seismicity zones based on the only high seismicity learning class through its expansion is adequate to the classical setting of the EPA problem.

The positive variants for recognition obtained using the Barrier-3 and Cora-3 algorithms make them control experiments for each other. Due to the relative proximity of results, these control experiments should be recognized as successful. This enhances the assessment of the reliability of the above results.

The studied regions serve as a basis for the proposed joint interpretation of the strong earthquake-prone areas recognized for one and two learning classes. The interpretation relies on the composition of unclear set construction [44] and the results obtained independently using the Barrier-3 algorithm and the Cora-3 dichotomy [45].

Let *W* still represent a set of intersections of lineaments, and a fuzzy set of high seismicity objects is defined as a set of pairs:

$$B = \{ w, \,\mu\_B(w) | w \in \mathcal{W} \}. \tag{16}$$

That said, membership function *μB*(*w*) is:

$$\mu\_{\mathcal{B}}(w) = \mu\_{\mathcal{B}\_1, \mathcal{B}\_2}(w) = \begin{cases} 1, \ w \in B\_1 \cap B\_2 \\ 0.5, \ w \in B\_1 \Delta B\_2 \\ 0, \ w \notin B\_1 \cup B\_2 \end{cases} = (B\_1 \cup B\_2) \backslash (B\_1 \cap B\_2), \tag{17}$$

where *B*1 and *B*2 are the sets of objects recognized as high seismicity ones by the Barrier-3 and Cora-3 algorithms, respectively. Then high seismicity objects in the integral result are the intersections for which *μB*(*w*) > 0.

Figure 6 provides the example of an interpretation of results for strong earthquakeprone areas recognition with *M* ≥ 6.0 in the Caucasus and the Altai–Sayan–Baikal region using a fuzzy set construction (16–17). In the Altai–Sayan–Baikal region in line with the obtained independent results of recognition (Figure 2), all considered epicenters of strong earthquakes are located in the vicinities of objects attributed to class *B* by both algorithms. Whether or not the epicenter of the 2021 earthquake should be treated as a "missed target" error, the number of missed recognition targets in cases where a fuzzy function is used (Figure 6a) is the same for each algorithm (Figure 2). In this case, recognition using the Formulas (16) and (17) only increases the number of sought high seismicity objects, where strong earthquakes have not been recorded until the present.

**Figure 6.** Presentation of a joint result of earthquake-prone areas recognition with *M* ≥ 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* ≥ 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* ≥ 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 *μ* = 1; in blue, *μ* = 0.5; in green, *μ* = 0. The function *μ* is determined by the formula (17).

The situation in the Caucasus is different. The fuzzy function approach a priori improves the quality of the result here. In Figure 4, out of 62 epicenters of the considered earthquakes with *M* ≥ 6.0, 8, and 9 epicenters, respectively, lie outside of the high seismicity areas recognized by the Barrier-3 and Cora-3 algorithms. That said, as few as 4 epicenters are located outside of the zones identified as high seismicity ones (red and blue ellipses in Figure 6b) based on the Formulas (16) and (17).

The integral result (Figure 6) identifies 41.2% of objects in the Altai–Sayan–Baikal region and 59.9% in the Caucasus as high seismicity ones. That said, for the studied EPA problem, the result is typically treated as nontrivial if not more than 60% of objects are classified as high seismicity ones [4]. The recognition obtained based on the Formulas (16) and (17) meets this condition for both regions. At the same time, this allows obtaining a new nontrivial result for both regions and halving the number of missed targets in the Caucasus.

The improvement of recognition result when construction (16–17) is used derives from the fact that the employment of fuzzy mathematics enables integrating the criteria of two independent recognitions performed by the Barrier-3 and Cora-3 algorithms. This allows, to some extent, compensating incomplete and sometimes defective input data [45].

#### *3.2. 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* ≥ 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

used as recognition objects. To select the magnitude threshold *M*R, starting from which the epicenters were used as recognition objects, completeness magnitude *M*c was assessed in the catalogs [46–48]. Taking into account *M*c assessment, it was decided to use as FCAZ recognition objects in the Andes the earthquake epicenters with *M* ≥ *M*R = 4.5 (16,556 epicenters) [21]; in Kamchatka, *M* ≥ *M*R = 3.5 (44,113 epicenters) [49–51]; in the Kuril Islands, *M* ≥ *M*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.

**Figure 7.** Mountain belt of the Andes: (**a**) FCAZ recognition objects—the epicenters of earthquakes with *M* ≥ 4.5 and recognized DPS clusters; (**b**) FCAZ zones prone to earthquakes with *M* ≥ 7.75 and the epicenters of earthquakes with *M* ≥ 7.75.

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* ≥ 7.75 are shown in Figures 7b and 8.

**Figure 8.** FCAZ zones prone to earthquakes with *M* ≥ 7.75 and the epicenters of earthquakes with *M* ≥ 7.75: Pacific Coast (**a**) of the Kamchatka Peninsula; (**b**) of the Kuril Islands.

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 *<sup>α</sup>*1(*β*1). The obtained dense set of objects *<sup>W</sup>*1(*<sup>α</sup>*1(*β*1)) was excluded from further consideration and the algorithm was applied for the second time to the remaining subset with density level *<sup>α</sup>*2(*β*2). This allowed obtaining new DPS clusters *<sup>W</sup>*2(*<sup>α</sup>*2(*β*2)), where *W*2 = *<sup>W</sup>*\*<sup>W</sup>*1(*<sup>α</sup>*1(*β*1)). Subsequent iterations were performed similarly. All connected components forming part of *<sup>W</sup>*1(*<sup>α</sup>*1(*β*1)) ∪ *<sup>W</sup>*2(*<sup>α</sup>*2(*β*2)) ∪ ... ∪ *Wk*(*<sup>α</sup>k*(*βk*)) 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 *β* parameter—the maximality level of density of DPS clusters—were computed automatically using the artificial intelligence block. It should be noted that 67% of recognition objects in the mountain belt of the Andes were included in the recognized DPS clusters; 73.3%, in Kamchatka; 77.5%, in the Kuril Islands. DPS clusters are highlighted in green in Figures 7 and 8.

In each of the three regions, the E2XT algorithm was applied to DPS clusters. The optimal values of its input parameters *ω* and *v* were computed using the artificial intelligence block. That said, a regular geographical graticule and connection type *C*8 was used. In Figures 7b and 8, the totality of green and red colors shows mapped FCAZ zones.

Figures 7b and 8 show that FCAZ zones are well aligned with the location of the epicenters of the known strongest earthquakes. Out of 24 earthquakes with *M* ≥ 7.75 in the mountain belt of the Andes, only one epicenter (4.2%) is located outside of FCAZ zones (Figure 7b) and creates a missed target error. This is an epicenter of the earthquake which occurred on 24 May 1940, more than 20 years before the commencement of systemic instrumental seismological observations in the region. Accordingly, the location of the epicenter can be distorted and this only error can be irrelevant.

Out of the eight strongest earthquakes considered in the Pacific Coast of the Kamchatka Peninsula, the epicenter of just one (12.5%) does not belong to the recognized FCAZ zones (Figure 8a). This is an epicenter of the Ozernovskiy earthquake with *M* = 7.75 in Koryakia, which occurred on 22 November 1969, in the north of the considered region.

In 2006 the Olyutorskoye earthquake occurred in Koryakia to the north of the border of the considered region, its magnitude was similar to the Ozernovskoye (Figure 8a). The missed target error of the Ozernovskoye earthquake and non-inclusion of the Olyutorskoye earthquake area in the considered region is caused by the fact that their epicenters are located outside of today's subduction zone. The conditions for the occurrence of these earthquakes outside of the subduction zone are dramatically different from the remaining considered strongest earthquakes in the region. This is also justified by the fact that the epicenters of both earthquakes lie outside of the territory in respect of which work is underway to make a long-term forecast of the strongest earthquakes using the method of Academician of RAS S.A. Fedotov [53]. Accordingly, the epicenter of the Ozernovskoye earthquake is possibly not a missed target error.

On the Pacific Coast of the Kuril Islands (Figure 8b), the epicenter of just one (9%) out of 11 known earthquakes with *M* ≥ 7.75 is a missed target error (the earthquake dated 1 May 1915, with *M* = 8.3). Let us note here that the identification of the areas prone to earthquakes on the Pacific Coast of the Kuril Islands using pattern recognition methods has not been previously performed. It is undertaken in this paper for the first time.

It is noteworthy that the FCAZ zones recognized in the mountain belt of the South American Andes contain 69% of earthquake epicenters with *M* ≥ 5.0 from among those present in the instrumental catalog used for recognition purposes. That said, they occupy approximately half of the area of the seismically active mountain belt of the Andes and the active subduction zone. FCAZ zones on the Kamchatka coast contain 73% of the epicenters of earthquakes, with *M* ≥ 4.0 among those present in the instrumental catalog and occupying 40% of the area of seismically active Kuril-Kamchatka and Aleutian Arcs falling within the boundaries of the considered region. On the coast of the Kuril Islands, FCAZ zones contain 81% of the earthquake epicenters with *M* ≥ 5.0 among those present in the catalog. The aforesaid allows interpreting, with a high degree of reliability, the recognized FCAZ zones (Figures 7b and 8) as the areas prone to earthquakes with *M* ≥ 7.75 in the mountain belt of the Andes and on the Pacific Coast of the Kamchatka Peninsula and the Kuril Islands.

The recognized zones prone to the strongest earthquakes in Kamchatka and on the Kuril Islands are well aligned with the results of a long-term seismic forecast for IX 2013– VIII 2018, using the method of Academician of RAS S.A. Fedotov. In [53], earthquakes with *M =* 5.7–7.2 were expected throughout the Pacific Coast of Kamchatka with a varying probability level. That said, during the above-mentioned time interval, earthquakes with *M* ≥ 7.7 were expected in the coastal zone of the Avacha Bay and near the shores of Southern Kamchatka. Fairly big FCAZ zones are situated in these areas as well (Figure 8a).

The best justification for the reliability of recognition results is a pure experiment, i.e., the analysis of the alignment of FCAZ zones and the location of the epicenters of earthquakes (with *M* ≥ *M*0) that occurred after the end of the instrumental catalog used for recognition purposes. For instance, three earthquakes with *M* ≥ 7.75 occurred in the mountain belt of the South American Andes after 2013: on 1 April 2014, with *M* = 8.2 (northwest of the Chili coast), on 16 September 2015, with *M* = 8.3 (Chili coast), and on 16 April 2016, with *M* = 7.8 (Ecuador). Information about these strongest earthquakes was not used for recognition purposes in any manner whatsoever.

The epicenters of earthquakes of 2014, 2015, and 2016 are shown in Figure 7b using black, purple, and blue stars, respectively. The first two epicenters are located strictly inside the FCAZ zones. The third one is a short distance away from the boundaries of the recognized zones. This allowed obtaining an argumen<sup>t</sup> in favor of the reliability of the completed FCAZ recognition, both weighty and independent from research results.

Summarizing the results obtained, an important achievement should be noted. For the first time, the strongest earthquake-prone areas were successfully recognized based on the objective classification without involving morphostructural zoning and the formation of learning sets. That said, the results are generally well aligned with those previously obtained independently using the EPA method (for details, see below). Accordingly, it is shown that FCAZ method is applicable to the system observation of regions with a very high seismicity level.

#### *3.3. FCAZ Recognition of the Areas Prone to Strong and Significant Earthquakes for One and Several Threshold Magnitudes*

The regions with a lower seismicity level than in the previous section of the article: California, the Altai–Sayan region and the Baikal–Transbaikal region, the Caucasus, as well as the Crimean Peninsula, and the northwestern Caucasus are considered. The sets of recognition objects were formed based on the epicenters of crustal earthquakes

from the following catalogs: ANSS (1960−2012, California), Earthquakes in the USSR and Earthquakes of Northern Eurasia (1962–2008, the Caucasus; 1962–2008, Crimea and northwestern Caucasus; 1962–2009, the Altai–Sayan region; and 1962–2010, the Baikal– Transbaikal region). Based on the assessment of *M*c, it was decided to use the epicenters of earthquakes with *M* ≥ *M*R = 3.0 (31,874 epicenters) as recognition objects in California [54–56]; in the Altai–Sayan region, *M* ≥ *M*R = 2.8 (3647 epicenters) [57]; in the Caucasus, *M* ≥ *M*R = 3.0 (6980 epicenters) [21,22,58,59]; in Crimea and northwestern Caucasus, *M* ≥ *M*R = 2.0 (2398 epicenters) [60,61]; and in the Baikal–Transbaikal region, *M* ≥ *M*R = 2.7 (11,297 epicenters) [35].

In Figure 9, the totality of green and red colors shows the recognized FCAZ zones prone to strong earthquakes in California (*M* ≥ 6.5) and significant earthquakes in the Altai–Sayan region (*M* ≥ 5.5), in the Caucasus (*M* ≥ 5.0), and in the Crimean Peninsula and northwestern Caucasus (*M* ≥ 4.5).

**Figure 9.** FCAZ zones prone to earthquakes: (**a**) California, *M* ≥ 6.5 (black stars—epicenters of earthquakes with *M* ≥ 6.5 from 1836 through 2010; blue and white stars—*M* ≥ 6.5, since 2014); (**b**) the Caucasus, *M* ≥ 5.0 (black stars–*M* ≥ 5.0 for the period of 650–2008; blue stars—*M* ≥ 5.0, since 2009); (**c**) the Altai–Sayan region, *M* ≥ 5.5 (blue stars—*M* ≥ 5.5 for the period of 1902–2008; yellow stars—*M* ≥ 5.5, since 2011); (**d**) Crimea and the northwestern Caucasus, *M* ≥ 4.5 (black stars—*M* ≥ 4.5 for the period of 1900–2008; blue stars—*M* ≥ 4.5, since 2009).

At first sight, out of 33 strong earthquakes with *M* ≥ 6.5 (1836–2010) in California, the epicenters of 5 (15%) do not fall within the FCAZ zones (Figure 9a). It should be noted that three of them are located offshore in the Pacific Ocean at a grea<sup>t</sup> distance from the coast and are thus not caused by the tectonics of the studied region. Two other earthquakes occurred in 1857 and 1906 a long time before the commencement of systematized instrumental observations in the region. If thus these special cases are excluded from consideration, we will see that, in fact, the result contains no missed target errors [54].

It should be noted that in California, FCAZ zones contain 83% events with *M* ≥ 4.5 among those present in the instrumental catalog. After the end of the catalog used to select recognition objects, two strong earthquakes occurred (Figure 9a). The epicenters of both lie strictly within the FCAZ zones. Accordingly, we have grounds to believe that recognition resulted in building sought areas prone to strong earthquakes with *M* ≥ 6.5 in California.

In the Altai–Sayan region, out of 48 (1902–2008) significant earthquakes with *M* ≥ 5.5, only 7 epicenters (15%) are located outside of the recognized FCAZ zones (Figure 9c). It should be noted that 6 of them occurred before the commencement of active seismological observations. That said, 3 epicenters are situated in Mongolia, 2 are located in the south of the Krasnoyarsk region, where a small number of seismic stations now function.

FCAZ zones contain 67% of the earthquake epicenters with *M* ≥ 4.0 from among those present in the catalog. After the end of the used instrumental catalog, five significant earthquakes occurred in the region (Figure 9c). Of them, four epicenters are located strictly inside FCAZ zones. Summing it up, the totality of provided arguments allows stating that the results of FCAZ recognition in the Altai–Sayan region shown in Figure 9c have a high degree of reliability [57].

In FCAZ research in the Altai–Sayan region, an attempt was also made to recognize zones with the lowest possible number of missed target errors. For this purpose, localization radius *rq*(*W*) was varied in DPS clustering through changes in a preset interval of values of parameter *q*. Of all obtained recognition variants, an optimal one was selected, i.e., having the lowest number of omissions of significant earthquake epicenters. This variant had two missed targets less than the main variant of FCAZ zones (Figure 9c).

The epicenters of these two significant earthquakes, which make up the difference in the number of missed target errors, are located within and at the border of Mongolia. That said, the resulting area of optimal zones was 1.5 times higher than in the main recognition variant (Figure 9c). Accordingly, in the case of optimal FCAZ zones, the number of false alarms grows inevitably, adversely affecting the reliability of recognition. In this regard, the final choice was made in favor of the main recognition variant (Figure 9c) [57].

In the Caucasus, out of 106 (650–2008) significant earthquakes with *M* ≥ 5.0, the epicenters of 8 (7.5%) are located outside of FCAZ zones (Figure 9b). Explaining these missed targets, note that three earthquakes occurred in 957, 1250, and 1667 long before the commencement of systemized instrumental observations in the region. Three more unrecognized epicenters are situated at a grea<sup>t</sup> distance from seismic networks based on which the catalogs used for recognition were created. This casts doubt on the fact that these earthquakes are real missed targets. Accordingly, certain missed targets are two epicenters of significant earthquakes.

It should be noted that FCAZ zones contain 68% of the epicenters of earthquakes with *M* ≥ 4.0 among those present in the instrumental catalog. The epicenters of all three significant earthquakes which occurred after the end of the used instrumental catalog are located strictly inside of FCAZ zones (Figure 9b). This is an argumen<sup>t</sup> in favor of the reliability of the FCAZ recognition results [22].

It should be noted that the subregion in the northwestern part of the Caucasus (white triangle in Figure 9b) was excluded from consideration due to the lack of earthquake epicenters representing recognition objects in this region. FCAZ recognition in this subregion turns out to be impossible. This area forms part of the united region Crimea—northwestern Caucasus, in which FCAZ recognition was performed for *M*0 = 4.5 [21].

The number of earthquakes with *M* ≥ *M*0 must be sufficient to assess the level of their alignment with the recognized FCAZ zones. In the instrumental catalog of earthquakes of the Crimea and northwestern Caucasus region, there are just 5 events with *M* ≥ 5.0 and 17, since 1900. That said, the magnitudes of earthquakes of the early 20th century can be overstated. For that reason, two different magnitude thresholds of the earthquake locations being recognized *M*0 = 4.5 and *M*0 = 5.0 were considered in the region.

As can be seen from Figure 9d, FCAZ zones are well aligned with the location of the epicenters of significant earthquakes (1900–2008) with *M* ≥ 4.5. Only 5 (11.4%) out of 44 epicenters are situated outside of recognized zones. It should be noted that all missed earthquakes occurred before the commencement of the used instrumental catalog. That said, 3 earthquakes have magnitudes *M* = 4.5–4.7 identified to a precision of ±0.5. For the threshold *M*0 = 4.5, it is fairly safe to say that there are only two missed targets. FCAZ zones contain 67% of the earthquake epicenters, with *M* ≥ 3.5 among those present in the catalog.

The recognized FCAZ zones (Figure 9d) turn out to be connected with the events of higher magnitude threshold *M*0 = 5.0. At the moment of recognition, there are 17 known earthquakes with *M* ≥ 5.0 in the region. The epicenters of 15 (88.2%) of them are located within or at the boundaries of FCAZ zones. Accordingly, if we consider earthquakes with *M* ≥ 5.0, then FCAZ zones can be interpreted as areas prone to the same events. That said, two missed targets are the same two Black Sea earthquakes as in the previous reasoning about the threshold *M*0 = 4.5.

Nine earthquakes with *M* ≥ 4.5 occurred in the considered region after the end of the used instrumental catalog. The epicenters of eight of them lie strictly within FCAZ zones. The only missed target error is the epicenter of the earthquake, with *M* = 4.6 located offshore in the Black Sea.

The considered Crimea–Caucasus region is the first one for which FCAZ zones were interpreted for two different magnitude thresholds. In other words, in the recognition problem of the areas prone to earthquakes, there was variation in the magnitude threshold *M*0 [60].

The above statistical data allows, to a grea<sup>t</sup> extent of reliability, interpreting FCAZ zones (Figure 9) as the areas prone to strong earthquakes in California and the areas prone to significant earthquakes in the Altai–Sayan region, the Caucasus, as well as in the Crimean Peninsula and the northwestern Caucasus.

The description of the first-ever successive recognition of the areas prone to earthquakes for several magnitude thresholds in the same region is given further. This recognition was performed using the SFCAZ method mentioned above, which further develops FCAZ. Successively studied were the areas prone to earthquakes with *M* ≥ 5.5, *M* ≥ 5.75, and *M* ≥ 6.0 in the Baikal–Transbaikal region [35].

Phase one of the research entailed the solution of a classical problem of recognizing the areas prone to significant earthquakes ( *M* ≥ *M*0 = 5.5). Figure 10a shows the recognized zones that are well aligned with the earthquake epicenters with *M* ≥ 5.5. Out of 71 such earthquakes, the epicenters of two (2.8%) are located outside of recognized zones, thus creating missed target errors. These two earthquakes occurred before the commencement of active instrumental observations in the region (1929 and 1957) and have a magnitude *M* = 5.6, identified to a precision of ±0.5 [52], and their epicenters are located outside of the Russian Federation. Accordingly, their actual magnitude can be lower than the threshold *M*0 = 5.5 and the completed recognition is likely to have no missed targets.

Totally new are the second and third phases of successive recognition. Phase two entailed studying the areas prone to significant earthquakes with *M* ≥ 5.75 in the same Baikal–Transbaikal region. To that end, only the epicenters that were included in DPS clusters during phase one were used as recognition objects. Accordingly, inside the DPS clusters that define high seismicity zones for *M* ≥ 5.5, subclusters and morphogenetic areas prone to stronger significant earthquakes were recognized.

**Figure 10.** Baikal–Transbaikal region: (**a**) zones prone to earthquakes with *M* ≥ 5.5 and the epicenters of earthquakes with *M* ≥ 5.5; (**b**) zones prone to earthquakes with *M* ≥ 5.75 and the epicenters of earthquakes with *M* ≥ 5.75; (**c**) zones prone to earthquakes with *M* ≥ 6.0 and the epicenters of earthquakes with *M* ≥ 6.0.

The zones recognized in this way are well aligned with the earthquake epicenters with *M*≥ 5.75 (Figure 10b). The epicenters of just 3 (10%) of 30 such significant earthquakes lie

outside of their boundaries. These are the epicenters of earthquakes with a fairly inaccurate identification of magnitude: *M* = 5.8 ± 0.5 and *M* = 5.8 ± 0.2 [52]. The magnitude of the third earthquake was recalculated from the energy class. The magnitudes of these three earthquakes are highly likely to have the values of *M* < 5.75, and the earthquakes themselves are highly unlikely to constitute the subject matter of research. It should be noted that the recognized territories form part of high seismicity zones for the magnitude threshold *M*0 = 5.5, identified during phase one of the research.

Phase three entailed recognizing the areas prone to strong earthquakes with *M* ≥ 6.0. The epicenters of earthquakes included in the DPS clusters during phase two have already been used as recognition objects. Out of 17 earthquakes with *M* ≥ 6.0, the epicenters of just two (11.7%) are located outside of recognized zones (Figure 10c). The first one is the epicenter of the 1939 earthquake with *M* = 6.0 ± 0.3 [52]; the second one which occurred in 2008, with *M* = 6.3, is located at the distance of 0.15◦ of the mapped zones.

After 2010, 3 earthquakes with *M* ≥ 5.5 occurred in the considered region. The epicenters of two of them lie strictly within the zones corresponding to their magnitudes, which is an argumen<sup>t</sup> in favor of the reliability of SFCAZ recognition results.

Successive recognition using the SFCAZ method made it possible to obtain a chain of high seismicity areas, in which the zones for greater threshold magnitudes are inserted in the relevant zones for smaller ones. Accordingly, the results of successive recognition can be used in practical seismic zoning. The results of completed successive recognition allow us to argue that the performed transition from FCAZ to SFCAZ does not impair the quality of obtained results [35].

After the end of the used instrumental catalogs, 22 earthquakes with *M* ≥ *M*0 occurred in 5 considered regions. These events allowed conducting a pure experiment. It should be noted that 19 epicenters (86.3%) are located within high seismicity zones. Such a result of a pure experiment should be recognized as successful. This yielded an objective argumen<sup>t</sup> in favor of result reliability for completed FCAZ recognition.

The earthquake with *M* = 7.1, which occurred in California on 6 July 2019 (white star in Figure 9a), deserves a separate mention. The epicenter of this earthquake is located inside FCAZ zones in the territory with no prior strong earthquakes. It should be noted that this epicenter is located outside of the zones recognized by the EPA method [62].
