**5. Conclusions**

The problem of recognition of the areas prone to strong (with *M* ≥ *M*0) earthquakes [4,5,67,68] is studied in this paper using two methods developed by the authors. Their fundamental difference lies in the selection of recognition objects.

In the first method, objects are vicinities of intersections of lineament axes constructed using a formalized technique of morphostructural zoning. In the second method, objects are constituted by the epicenters of all earthquakes that meet the condition *M* ≥ *MR*, where threshold MR is significantly lower than the magnitude threshold M0 of the recognized earthquake areas.

The methods also differ in the sets of characteristics of object description and the employed pattern recognition algorithms. In the first case, these are geological-geophysical and geomorphologic characteristics and the original Barrier-3 algorithm. In the second case, these are the characteristics of epicenters of weak earthquakes and systems analysis procedure for the objective recognition of dense condensations of FCAZ.

Despite the critical differences between these two original methods, their recognition results are well aligned in the Altai–Sayan–Baikal region and the Caucasus. The territories classified as high seismicity ones by both methods should be viewed as the most hazardous since they are recognized as such by independent methods based on different recognition objects and their characteristics.

The first method allows, from the standpoint of dynamic systems analysis, repeatedly solving the problem of classification of lineament intersections into high and low seismicity ones. This relies on the fact that learning is every time performed only for one high seismicity class, which is easy to form with due regard for new strong earthquakes that have occurred. This, in turn, contributed significantly to the development of the classical EPA approach towards the recognition of high seismicity areas [3–5,67,69,70].

Previously, there was a problem of identification of the learning set of the objects in whose vicinities strong earthquakes cannot occur. This problem is solved in the paper by developing an original method for image recognition called Barrier-3.

This algorithm makes it possible to classify objects into high and low seismicity based on one learning class. Barrier-3, having information about the objects with known epicenters of earthquakes with *M* ≥ *M*0 in their vicinities, enables finding a set of the so-called similar objects.

The recognition of the areas prone to earthquakes is the first developed method to rely on the hypothesis about the association of epicenters of strong earthquakes with the intersections of morphostructural lineaments, which was confirmed in [18]. Accordingly, building the morphostructural zoning map is an important phase of the first method for studying the problem. That said, despite the logical formalization conducted as early as 1977 by a group of mathematicians under the guidance of I.M. Gelfand, the process of morphostructural zoning remains ambiguous. In this regard, a question was pending: Can the recognition of strong earthquake-prone areas be performed without constructing morphostructural zoning model? [22]. This paper answers this question positively based on the use of the systems analysis method FCAZ.

The employment of DMA algorithms in this paper, which use the epicenters of earthquakes as recognition objects, justifies this positive answer. Accordingly, the system FCAZ approach is a new step in the study of a recognition problem of strong earthquake-prone areas.

The recognition process of the high seismicity hazard zones in tectonically active regions represents a complicated system. The condition of the system depends on both spatial coordinates of recognition objects and on time. In this regard, FCAZ recognition is viewed

in this paper from the perspective of the systems analysis. The system–mathematical model of FCAZ recognition as a complicated dynamic system was developed. The space-andtime model T(i) × FCAZ for recognition of the areas prone to the strongest, strong, and significant earthquakes makes it possible to develop a schedule of subsequent iterations for the recognition of high seismicity hazard zones for the regions studied in this paper.

The following regions with varying seismicity levels were studied by Barrier-3 and FCAZ methods in this paper:


The Altai–Sayan–Baikal region, the Pacific Coast of the Kuril Islands, and the Crimean Peninsula were first studied with the employment of methods for the recognition of earthquake-prone areas. Moreover, the Baikal–Transbaikal region was used as an example of the first recognition of earthquake-prone areas for the finite succession of growing magnitude thresholds *M*10 < *M*20 < *M*30. The joint presentation of the recognition results obtained by the Barrier-3 and Cora-3 algorithms in the Caucasus based on their composition with a fuzzy set allowed halving the number of missed targets.

It was shown, using California and the Pacific Coast of the Kamchatka Peninsula as an example, that the existence of foreshock and aftershock sequences in the catalogs of earthquakes does not have a significant impact on the FCAZ recognition results. A totality of control experiments conducted in this paper demonstrates the reliability and reproducibility of the interpretation of FCAZ zones as the areas prone to the strongest, strong, and significant earthquakes.

In the studied regions, FCAZ zones occupy a relatively small area as compared with the total seismicity field, which makes up 30%–40% of the total seismicity space and 50%–65% of the space where earthquakes with *M* ≥ *M*R occur. This illustrates the spatial nontriviality of the obtained results.

Findings from the paper also demonstrate that low seismicity can actually "manifest" the properties of geophysical fields, which in the classical EPA approach are used directly as the characteristics of recognition objects.

**Author Contributions:** Conceptualization, B.A.D. and A.D.G.; data curation, B.A.D.; formal analysis, B.A.D., A.D.G., and S.M.A.; funding acquisition, B.A.D.; investigation, B.A.D. and A.D.G.; methodology, B.A.D., A.D.G., and S.M.A.; project administration, B.A.D.; resources, J.K.K. and B.V.D.; software, B.A.D. and I.O.B.; validation, B.A.D., A.D.G., J.K.K., and B.V.D.; visualization, B.A.D. and Y.V.B.; writing—original draft, B.A.D., A.D.G., B.V.D., and Y.V.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** The reported study was funded by RFBR, project number 20-35-70054 «Systems approach to recognition algorithms for seismic hazard assessment».

**Acknowledgments:** This work employed data provided by the Shared Research Facility «Analytical Geomagnetic Data Center» of the Geophysical Center of RAS (http://ckp.gcras.ru/ access date: 30 July 2021).

**Conflicts of Interest:** The authors declare no conflict of interest.
