Short introduction into DMA

Agayan, S. M.; Богоутдинов, Ш. Р.; Krasnoperov, Roman

doi:10.2205/2018es000618

Cited by 22 publications

(18 citation statements)

References 17 publications

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“…It is necessary to say in conclusion a few words, about the mathematical apparatus of DMA [Agayan et al, 2018]. It is being developed at the Geophysical Center of the Russian Academy of Sciences and forms the basis of the methodology for searching periods in the series of cyclostratigraphic data presented in the article.…”

Section: Discussionmentioning

confidence: 99%

“…The proposed technique is based on DMA [Agayan et al, 2018]. The new method is an original technique for analysing discrete data, developed at the GC RAS.…”

Section: Methodsmentioning

confidence: 99%

“…The final stage is the search for strong minima of the estimate C(f, T). Provided that they exist, we can obtain the necessary periods for the function f using the apparatus of minimality measures [Agayan et al, 2018].…”

Section: Methodsmentioning

confidence: 99%

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Assessment of the influence of astronomical cyclicity on sedimentation processes in Eastern Paratethys based on paleomagnetic measurements using Discrete Mathematical Analysis

Дзебоев

Odintsova

Rybkina

2021

Preprint

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Abstract. 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.

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Section: Discussionmentioning

confidence: 99%

“…The proposed technique is based on DMA [Agayan et al, 2018]. The new method is an original technique for analysing discrete data, developed at the GC RAS.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Assessment of the influence of astronomical cyclicity on sedimentation processes in Eastern Paratethys based on paleomagnetic measurements using Discrete Mathematical Analysis

Дзебоев

Odintsova

Rybkina

2021

Preprint

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“…The said tasks were implemented as a researcher-oriented data analysis approach, which takes an intermediate position between hard math methods and soft combinatoric methods. This is called discrete mathematical analysis (DMA) [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Framework for Determination of Linear Structures in Multidimensional Geodynamic Data Arrays

et al. 2021

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The article addresses the issue of clustering of multidimensional data arrays with a noise using the methods of discrete mathematical analysis (DMA clustering). The theory of DMA clustering through the logical densities calculus is detailed, and the new algorithm Linear Discrete Perfect Sets (LDPS) is described. The main objective of the LDPS algorithm is to identify linearly stretched anomalies in a multidimensional array of geo-spatial data (geophysical fields, geochemistry, satellite images, local topography, maps of recent crustal movements, seismic monitoring data, etc.). These types of anomalies are associated with tectonic structures in the upper part of the Earth’s crust and pose the biggest threat for integrity of the isolation properties of the geological environment, including in regions of high-level radioactive waste disposal. The main advantage of the LDPS algorithm as compared to other cluster analysis algorithms that may be used in arrays with a noise is that it is more focused on searching for clusters that are linear. The LDPS algorithm can apply not only in the analysis of spatial natural objects and fields but also to elongated lineament structures.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

FCAZ-recognition based on declustered earthquake catalogs

Дзебоев¹,

Karapetyan²,

Aronov³

et al. 2020

Russ. J. Earth Sci.

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The article presents the results of FCAZ-recognition of the strongest (≥ 7.75) earthquakeprone areas on the Pacific coast of the Kamchatka Peninsula and strong (≥ 6.5) earthquakeprone areas in California. For the first time, earthquake epicenters from declustered catalogs were used as recognition objects. Based on the example of the considered regions it is shown that the presence of foreshock and aftershock sequences in the earthquake catalogs does not significantly affect the results of FCAZ-recognition based on the clustering study of weak earthquake epicenters.

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Short introduction into DMA

Cited by 22 publications

References 17 publications

Assessment of the influence of astronomical cyclicity on sedimentation processes in Eastern Paratethys based on paleomagnetic measurements using Discrete Mathematical Analysis

Assessment of the influence of astronomical cyclicity on sedimentation processes in Eastern Paratethys based on paleomagnetic measurements using Discrete Mathematical Analysis

Theoretical Framework for Determination of Linear Structures in Multidimensional Geodynamic Data Arrays

FCAZ-recognition based on declustered earthquake catalogs

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