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The article is devoted to earthquake-prone areas recognition with M ≥ 6.0 in the Caucasus and in the Altai–Sayan–Baikal region. A new approach to the classification of intersections of morphostructural lineaments using the definition of a fuzzy set is proposed. The latter enables an integral interpretation of a single result (composition) of high seismicity zones recognition performed by the Barrier-3 and Kora-3 algorithms.

We present a collection of magnetic field absolute measurements performed by the early Soviet magnetic satellite missions Kosmos-49 (1964) and Kosmos-321 (1970). A total of 17 300 measured values are available for the Kosmos-49 mission, covering homogeneously 75 % of the Earth's surface between 49∘ latitude north and south. About 5000 measured values are available for the Kosmos-321 mission, covering homogeneously 94 % of the Earth's surface between 71∘ latitude north and south. The data are available at PANGAEA (Krasnoperov et al., 2020, https://doi.org/10.1594/PANGAEA.907927).

—The paper addresses almost half a century’s development of pattern recognition algorithms’ application for solving the problem of determination of strong earthquake-prone areas. This approach was named Earthquake-Prone Areas (EPA). The pattern recognition algorithms applied for this purpose, the studied regions, and the methods for assessing the reliability of the obtained results including the theory of dynamic and limit recognition problems are considered. A recently developed alternative method for solving the problem by identifying the clusters of earthquake epicenters is also presented. This method is based on the approaches of the Discrete Mathematical Analysis (DMA) and implemented in the form of the algorithmic system named Formalized Clustering and Zoning (FCAZ). The comparison of the results obtained by the EPA approach and FCAZ system shows their good consistency which provides an additional argument in favor of their reliability. The possibilities for further development and joint application of the EPA approach and FCAZ system and creating, on this basis, an integrated method for systems analysis with the inclusion of artificial intelligence are outlined. In case of success, this method is expected to be used in seismic hazard assessment and planning of earthquake-resistant construction.

The main objective of this study is to apply Discrete Mathematical Analysis (DMA) to the development of the methodology of cyclostratigraphy. This aim is supported by exploring the magnetic properties of rocks, the lithology of sediments and obtained geochronological reference definitions. The analysis was based on measurements of the variability of the magnetic susceptibility of rocks, which reflects climate variations. Astronomical cycles are global; this makes it possible to carry out a correlation analysis over a large area and on different facial types of sediments, considering their lithology and other sedimentary features. The introduction of modern methods of mathematical processing of geological data is one of the prospective areas for investigation and development in geoscience. Astronomical cycles can be revealed from measurements of scalar magnetic parameters of rocks (magnetic susceptibility as presented by the authors). Specific software developed by the authors allows the processing of measurement data and assessment of the presence of stable oscillation cycles based on the obtained measurement base. The present study attempts to apply mathematical methods to magnetic data using the existing PAST program, which allows spectral analysis of primary data with the construction of Lomb-Scargle and REDFIT periodograms. We interpret the spectral analysis data based on paleomagnetic determinations, considering the available dates for the boundaries of direct and reverse polarity chrons on a general stratigraphic scale.

A new version of the Barrier algorithm is proposed for recognition of strong-earthquake prone regions based on training over a single reliable training class. The modification of the algorithm consists in creating blocks that reveal the geological–geophysical features (attributes) characteristic of the recognized highly seismic objects and provide their quantitative estimates. The recognition of the areas prone to earthquakes with M ≥ 6.0 is carried out for the Altai–Sayan–Baikal region. The results of the recognition are used for assessing the effect of the remote earthquakes that occurred in the Altai–Sayan orogenic region on the stability of structural-tectonic crustal blocks in the contact zone of the West Siberian platform and the Siberian plate.

Proper seismic hazard assessment is the most important scientific problem of seismology, and geophysics in general. With the development of the world economy, the importance of the problem grows and acquires global significance.Strong earthquakes (M ≥ M0, M0 is the magnitude threshold starting from which earthquakes in the studied region are considered strong), as a rule, do not occur over the entire territory of the seismic region. Accordingly, the recognition of areas prone to future strong earthquakes is an urgent fundamental direction in research on the assessment of seismic hazard. Identification of potentially high seismicity zones in seismically active regions is important from both theoretical, and practical points of view. The currently available methods for recognition of high seismicity zones do not allow repeatedly correcting their results over time due to the invariability of the used set of recognition objects. In this work, a new system-analytical approach FCAZ (Formalized Clustering And Zoning) to the problem has been created. It uses the epicenters of rather weak earthquakes (M ≥ MR, MR is a certain magnitude threshold of weak earthquakes) as objects of recognition. This makes it possible to develop the recognition result of zones with increased seismic hazard after the appearance of new earthquake epicenters. The latter makes FCAZ a method of systems analysis.The system-analytical method for analyzing geophysical data developed by the authors has led to the successful recognition of areas prone to the strongest, strong, and most significant earthquakes on the continents of North, and South America, Eurasia, and in the subduction zones of the Pacific Rim. At the same time, in particular, for the classical approach of strong earthquake-prone areas recognition EPA (Earthquake-Prone Areas), a new paradigm for recognition of high seismicity disjunctive nodes, and lineament intersections with training by one “reliable” class was created in the work.In the regions studied in this work, FCAZ zones occupy a relatively small area compared to the field of general seismicity – 30% – 40% of the area of all seismicity, and 50% – 65% of the area where earthquakes with M ≥ MR occur. This illustrates the spatial nontriviality of the FCAZ results obtained in this work. The results of the work also show that weak seismicity can actually “manifest” the properties of geophysical fields, which in the classical EPA approach are used directly as characteristics of recognition objects (disjunctive nodes or intersections of the axes of morphostructural lineaments).The reported study was funded by RFBR, project number 20-35-70054 «Systems approach to recognition algorithms for seismic hazard assessment».

Disaster maps are more and more used to prevent and reduce the concentration of exposure to potential hazards and future risks. We present a novel approach, the so-called Formalized Clustering And Zoning (FCAZ) which forms the maps of earthquake risks using pattern recognition of highly seismic zones. It is applied to the Andes, Caucasus and other regions. FCAZ allows carrying out the recognition of significant, strong and strongest earthquake-prone areas based on a predefined set of earthquake epicenters in the studied region. FCAZ has rapidly become a new efficient systems analysis tool for recognition of the zones prone to the occurrence of earthquakes with a certain magnitude level. Furthermore, FCAZ possesses artificial intelligence elements. Two case studies show how areas where strong earthquakes may occur can be identified using FCAZ. These areas include the mountain belt of the Andes in South America and the Caucasus.

This paper shows that the number of aftershocks with a relative magnitude does not depend on the magnitude of the main shock, and, in global and regional consideration, it is characterized by an exponential distribution that is similar to the Gutenberg–Richter repeatability law. This type of distribution makes it possible to give a simple and adequate interpretation of Bath’s law.

This paper continues the series of our works on recognizing the areas prone to the strongest, strong, and significant earthquakes in different mountain countries with the use of the algorithmic Formalized Clustering And Zoning (FCAZ) system. In the paper, for the first time from this standpoint, we study the joint Altai–Sayan region, in which areas prone to significant earthquakes are recognized. A geological description of the concerned region is presented.

The paper continues the series of our works on recognizing the areas prone to the strongest, strong, and significant earthquakes with the use of the Formalized Clustering And Zoning (FCAZ) intellectual clustering system. We recognized the zones prone to the probable emergence of epicenters of the strongest (M ≥ 74/3) earthquakes on the Pacific Coast of Kamchatka. The FCAZ-zones are compared to the zones that were recognized in 1984 by the classical recognition method for Earthquake-Prone Areas (EPA) by transferring the criteria of high seismicity from the Andes mountain belt to the territory of Kamchatka. The FCAZ recognition was carried out with two-dimensional and three-dimensional objects of recognition.

This report continues a series of works by the authors on earthquake-prone areas recognition by the algorithmic system FCAZ. For the first time, successive earthquake-prone areas recognition for several magnitude thresholds in the same seismic region is conducted. This can be done by iteratively narrowing the set of recognition objects of the FCAZ system. Earthquake-prone areas for a given magnitude threshold are recognized within zones already recognized as dangerous for a smaller threshold magnitude. The reproducibility of the study is ensured by the fact that at all stages the recognition algorithm remains unchanged. Earthquakeprone areas with magnitude thresholds of М ≥ 5.5, М ≥ 5.75, and М ≥ 6.0 in the Baikal–Transbaikal region are studied successively.

Typically, strong earthquakes do not occur over the entire territory of the seismically active region. Recognition of areas where they may occur is a critical step in seismic hazard assessment studies. For half a century, the Earthquake-Prone Areas (EPA) approach, developed by the famous Soviet academicians I.M. Gelfand and V.I. Keilis-Borok, was used to recognize areas prone to strong earthquakes. For the modern development of ideas that form the basis of the EPA method, new mathematical methods of pattern recognition are proposed. They were developed by the authors to overcome the difficulties that arise today when using the EPA approach in its classic version. So, firstly, a scheme for the recognition of high seismicity disjunctive nodes and the vicinities of axis intersections of the morphostructural lineaments was created with only one high seismicity learning class. Secondly, the system-analytical method FCAZ (Formalized Clustering and Zoning) has been developed. It uses the epicenters of fairly weak earthquakes as recognition objects. This makes it possible to develop the recognition result of areas prone to strong earthquakes after the appearance of epicenters of new weak earthquakes and, thereby, to repeatedly correct the results over time. It is shown that the creation of the FCAZ method for the first time made it possible to consider the classical problem of earthquake-prone areas recognition from the point of view of advanced systems analysis. The new mathematical recognition methods proposed in the article have made it possible to successfully identify earthquake-prone areas on the continents of North and South America, Eurasia, and in the subduction zones of the Pacific Rim.

This article presents a new Barrier recognition algorithm with learning, designed for recognition of earthquake-prone areas. In comparison to the Crust (Kora) algorithm, used by the classical EPA approach, the Barrier algorithm proceeds with learning just on one “pure” high-seismic class. The new algorithm operates in the space of absolute values of the geological–geophysical parameters of the objects. The algorithm is used for recognition of earthquake-prone areas with М ≥ 6.0 in the Caucasus region. Comparative analysis of the Crust and Barrier algorithms justifies their productive coherence.

With the use of the modified version of the original algorithmic Formalized Clustering and Zoning (FCAZ) system, the areas prone to the probable emergence of the epicenters of significant earthquakes are recognized in the joint region of the Crimea and western part of the Northern Caucasus. The selection of this region is justified by the tectonic structure and the presence of the active junction zone of the meganticlinoria. The reliability of the obtained recognition is substantiated by the comparative analysis of the actual and random FCAZ-recognition. For the first time, the problem of recognizing the locations of the probable emergence of the earthquakes' epicenters is solved for two different magnitude thresholds. This allows us to interpret the areas prone to the probable emergence of the epicenters of significant earthquakes as fuzzy sets.

Preliminary work on the creation of a method for monitoring of seismic activity, on the basis of discrete mathematical analysis for further seismic hazard assessment of a territory, is presented. The method developed is tested for the territory of California and adjacent areas of the United States. The results obtained are analyzed for the period of 1980–2015. The nonrandomness of the results is shown by means of an error chart.

We present the collection of magnetic field absolute measurements performed by early Soviet magnetic satellite missions Kosmos-49 (1964) and Kosmos-321 (1970). Totally 17300 measured values are available for Kosmos-49 mission, covering homogeneously 75 % of the Earth's surface between 49° north and south latitude. About 5000 measured values are available for Kosmos-321 mission, covering homogeneously 94 % of the Earth's surface between 71° north and south latitude.

The fuzzy clustering and zoning method (FCAZm) of systems analysis is suggested for recognizing the areas of the probable generation of the epicenters of significant, strong, and the strongest earthquakes. FCAZm is a modified version of the previous FCAZ algorithmic system, which is advanced by the creation of the blocks of artificial intelligence that develop the system-forming algorithms. FCAZm has been applied for recognizing areas where the epicenters of the strongest (M ≥ 73/4) earthquakes within the Andes mountain belt in the South America and significant earthquakes (M ≥ 5) in the Caucasus can emerge. The reliability of the obtained results was assessed by the seismic-history type control experiments. The recognized highly seismic zones were compared with the ones previously recognized by the EPA method and by the initial version of the FCAZ system. The modified FCAZm system enabled us to pass from simple pattern recognition in the problem of recognizing the locations of the probable emergence of strong earthquakes to systems analysis. In particular, using FCAZm we managed to uniquely recognize a subsystem of highly seismically active zones from the nonempty complement using the exact boundary.

Microseismic sounding along the profile in the Ossetian sector of the Greater Caucasus revealed two domains with characteristic properties and morphology deep beneath the mountain system. One subvertical domain is marked with low velocities and the other, also subvertical, has high velocities. The high-velocity zone is largely located beneath the northern limb and axial part of the Greater Caucasus mega-anticlinorium, whereas the low velocity zone projects on the southern limb. Almost throughout the entire structure of the block part of the northern limb of mega-anticlinorium, the top of the high-velocity zone beneath it is consistently horizontal at a depth of ∼10 km. This pattern is violated by the apparent steep rise of the top of the high-velocity zone to the surface in the southern direction, which starts approximately from the main thrust. Beneath the southern limb, the top boundary can also be guessed at a depth of ∼10 km, although less reliably. The roots of the low-velocity zone stretch to a depth of ∼50–60 km and narrow with the depth. The weak regional seismicity quite distinctly maps onto the high-velocity zone. In the depth interval of 10 to 25 km, weak seismicity abruptly drops northwards at the transition to the low-velocity zone. The independent magnetotelluric data show that electric resistivity of the low-velocity zone significantly exceeds the resistivity of the hosting rocks. The model of a medium filled with isolated fractures with mineralized fluid is suggested for the low-velocity zone. According to a series of features, the low-velocity zone tends to float up; in particular, there is a high lateral correlation between the most elevated part of the mountain relief, morphology, and age of the rocks, on one hand, and the position of the low-velocity zone, on the other hand.

Clustering the epicenters of Caucasian earthquakes with magnitudes M ≥ 3.0 is carried out, and the epicentral zones of the probable earthquakes with M ≥ 5.0 areas where epicenters of earthquakes with M ≤ 5.0 may occur are recognized by the Fuzzy Clustering and Zoning (FCAZ) algorithmic system developed by the authors at the Geophysical Center of the Russian Academy of Sciences. These zones correspond well to the locations of the epicenters of earthquakes with M ≥ 5.0. The zones recognized in this study are compared with the zones previously recognized by A.D. Gvishiani et al. in 1988 by the Earthquake-Prone Areas Recognition (EPA) technique. The comparison shows that the zones identified by FCAZ are mainly located inside the EPA-zones. The FCAZ-zones are also compared with the zones previously recognized using gravimetric and geological data. The results obtained by different methods closely agree.