Formalized clustering and significant earthquake-prone areas in the Crimean Peninsula and Northwest Caucasus

FCAZ-recognition based on declustered earthquake catalogs

“…In the early 2010s, at the Geophysical Center of the Russian Academy of Sciences, as a result of research by A. D. Gvishiani, S. M. Agayan, and B. A. Dzeboev on the basis of Discrete Mathematical Analysis (DMA) [Gvishiani et al, 2008[Gvishiani et al, , 2010Agayan et al, 2018], the system-analytical [Zgurovsky and Pankratova, 2007] method FCAZ (Formalized Clustering And Zoning) was created [Gvishiani et al, 2013[Gvishiani et al, , 2016. FCAZ makes it possible to effectively recognize areas prone to the strongest, strong, and significant earthquakes based on clustering studies (topological filtration) of the weak earthquake epicenters [Gvishiani et al, 2016[Gvishiani et al, , 2020. Thus, earthquake epicenters starting from a certain magnitude threshold are used as objects for FCAZ-recognition.…”

“…The FCAZ method represents a sequential application of two algorithms: the clustering algorithm/topological filtering algorithm DPS (Discrete Perfect Sets) [Agayan et al, 2014;Gvishiani et al, 2013Gvishiani et al, , 2016 and the E 2 XT algorithm [Gvishiani et al, 2013[Gvishiani et al, , 2016. DPS selects subsets ( ( )) in a finite set of recognition objects with a density level ( ), where is the optimal value of the maximum density of DPS clusters, which allows one to separate dense clusters of objects ( ( )) from their non-empty complement.…”

“…The E 2 XT algorithm implements a formalized single-valued transformation of DPS clusters of earthquake epicenters into nonzero measure flat zones, inside and at the boundaries of which earthquakes can occur. A detailed description of the FCAZ method is given in [Gvishiani et al, 2013[Gvishiani et al, , 2016.…”

On the monitoring of seismic activity using the algorithms of discrete mathematical analysis

“…The seismic process is analyzed by studying its behavior at the nodes of the coordinate grid with a given interval (reference points) and constructing measures of activity. As a measure of activity, we use the value , determined by the algorithm of topological filtration (clustering) DPS Gvishiani and Dzeboev, 2015;Gvishiani et al, 2013aGvishiani et al, , 2013bGvishiani et al, , 2016Gvishiani et al, , 2017c or its adaptive version A-DPS (adaptive discrete perfect set).…”

“…DMA is a series of algorithms aimed at solving the main tasks of data analysis: clustering and tracing in multidimensional arrays Agayan and Soloviev, 2004;Gvishiani et al, 2017bGvishiani et al, , 2017cMikhailov et al, 2003;Soloviev et al, 2016;etc. ], morphological analysis of surface [Gvishiani et al, 1994[Gvishiani et al, , 2008detc.…”