# Development of the Algorithmic Basis of the FCAZ Method for Earthquake-Prone Area Recognition  
[PERSON]  
1 Geophysical Center of the Russian Academy of Sciences, 119296 Moscow, Russia 1, [PERSON]  
1 Gophysical Center of the Russian Academy of Sciences, 119296 Moscow, Russia 1, [PERSON]  
1 Gophysical Center of the Russian Academy of Sciences, 119296 Moscow, Russia 1, [PERSON]  
1 Gophysical Center of the Russian Academy of Sciences, 119296 Moscow, Russia 1, [PERSON]  
pattern recognition methods [21; 22; 23; 24], makes it possible to create effective preventive seismic hazard maps. The fundamental possibility of using methods and algorithms of pattern recognition for earthquake-prone area recognition was first substantiated by the eminent mathematician [PERSON] et al. in 1972 [25]. The formalized approach developed by them was subsequently called earthquake-prone areas (EPA) [21; 22; 23]. Over the past 50 years, since its inception, EPA has been used to recognize strong earthquake-prone areas in a number of mountainous countries in the world. A posteriori estimates of the recognition reliability that were obtained based on the analysis of the locations of the epicenters of strong earthquakes that occurred in the considered regions after receiving results for them became a confirmation of the effectiveness of using pattern recognition to identify territories with potentially high seismicity [24]. The authors of [21; 26] described in detail the still-existing significant difficulties of applying EPA in practice. The latter served as the fundamental basis for the beginning of research at the Geophysical Center of the Russian Academy of Sciences, dedicated to the development of the ideological, system-mathematical, and computational base for earthquake-prone area recognition. As part of these studies, the algorithmic system of formalized clustering and zoning (FCAZ) [27; 28] was developed, which is an unsupervised pattern recognition method. FCAZ is based on the classification of recognition objects by clustering. The epicenters of weak earthquakes are used as recognition objects. Note that clustering is an important tool in the mining of geophysical data [29]. Clustering studies on earthquake epicenters [30; 31; 32; 33; 34; 35] have been actively developed since the early 1990s [36]. As a rule, they are aimed at achieving two goals: revealing the characteristics of clusters and their relationship with the physical properties of the Earth's crust [37; 38; 39; 40] and the declustering [29; 31] of earthquake catalogs [41]. The analysis of earthquake epicenters with classical clustering algorithms is associated with difficulties [29; 36]. It turns out that algorithms that take into account the \"density\" of the locations of objects are effective due to their ability to find clusters of an arbitrary shape even with significant data noise [29]. Within the framework of the scientific direction of discrete mathematical analysis (DMA) [42; 43; 44], created and developed at the Geophysical Center of the Russian Academy of Sciences, based on fuzzy mathematics and fuzzy logic under the general name DPS clustering, a complex of topological filtering algorithms is being developed that takes into account the density of the objects being classified [45; 46; 47]. It should be noted that DPS clustering algorithms are actively and effectively used in various geological and geophysical studies (analysis of earthquake catalogs, searching for signals on geophysical records, the problem of radioactive waste disposal, etc. [26; 47; 48; 49; 50]). DPS clustering is the algorithmic core of the FCAZ method [28]. FCAZ makes it possible to effectively recognize earthquake-prone areas (with a magnitude \(M\geq M_{0}\)) based on the clustering study of the catalog of seismic events [21]. In its original form, FCAZ was a sequential application of DPS clustering algorithms and the Ext algorithm [26]. The fundamental difference between FCAZ and its predecessors, particularly EPA, is the presence of a formalized block (algorithm) Ext.