Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 46647 10.2205/2018ES000618 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Short introduction into DMA Short introduction into DMA Agayan S M Agayan S M Bogoutdinov Sh R Bogoutdinov Sh R Krasnoperov R I Krasnoperov R I The Geophysical Center of RAS ru The Geophysical Center of RAS ru The Geophysical Center of RAS ru The Geophysical Center of RAS ru The Geophysical Center of RAS ru The Geophysical Center of RAS ru 18 2 1 29 10 2021 https://rjes.ru/en/nauka/article/46647/view

Discrete Mathematical Analysis (DMA) is a new approach to data analysis that is being developed at the Geophysical Center of the Russian Academy of Sciences. Multiple papers, which have been published earlier, are mainly devoted to applied research and solving specific problems in various areas of the Earth's sciences, such as detection of geophysical anomalies, monitoring of geophysical processes, seismic zoning, etc. The goal, which the authors pursue in this paper, is, to a certain degree, opposite -- to give a formal mathematical description of principles that form the basis of DMA.

Discrete Mathematical Analysis (DMA) is a new approach to data analysis that is being developed at the Geophysical Center of the Russian Academy of Sciences. Multiple papers, which have been published earlier, are mainly devoted to applied research and solving specific problems in various areas of the Earth's sciences, such as detection of geophysical anomalies, monitoring of geophysical processes, seismic zoning, etc. The goal, which the authors pursue in this paper, is, to a certain degree, opposite -- to give a formal mathematical description of principles that form the basis of DMA.

 Fuzzy mathematics Discrete mathematical analysis discontinuous anomality clusters trends geophysical monitoring Fuzzy mathematics Discrete mathematical analysis discontinuous anomality clusters trends geophysical monitoring

Agayan, S., Bogoutdinov, Sh., Dobrovolsky, M. Discrete Perfect Sets and their application in cluster analysis, // Cybernetics and Systems Analysis, 2014. - v. 50 - no. 2 - p. 176. Agayan, S., Bogoutdinov, Sh., Dobrovolsky, M. Discrete Perfect Sets and their application in cluster analysis, // Cybernetics and Systems Analysis, 2014. - v. 50 - no. 2 - p. 176. Agayan, S., Bogoutdinov, Sh. R., Soloviev, A., et al. The Study of Time Series Using the DMA Methods and Geophysical Applications, // Data Science Journal, 2016. - v. 15 - p. 1. Agayan, S., Bogoutdinov, Sh. R., Soloviev, A., et al. The Study of Time Series Using the DMA Methods and Geophysical Applications, // Data Science Journal, 2016. - v. 15 - p. 1. Bogoutdinov, Sh. R., Gvishiani, A. D., Agayan, S. M., Soloviev, A. A., Kihn, E. Recognition of disturbances with specified morphology in time series. Part 1: Spikes on Magnetograms of the Worldwide INTERMAGNET Network, // Physics of the Solid Earth, 2010. - v. 46 - no. 11 - p. 1004. Bogoutdinov, Sh. R., Gvishiani, A. D., Agayan, S. M., Soloviev, A. A., Kihn, E. Recognition of disturbances with specified morphology in time series. Part 1: Spikes on Magnetograms of the Worldwide INTERMAGNET Network, // Physics of the Solid Earth, 2010. - v. 46 - no. 11 - p. 1004. Gvishiani, A. D., Agayan, S. M., Bogoutdinov, Sh. R. Fuzzy recognition of anomalies in time series, // Doklady Earth Sciences, 2008. - v. 421 - no. 1 - p. 838. Gvishiani, A. D., Agayan, S. M., Bogoutdinov, Sh. R. Fuzzy recognition of anomalies in time series, // Doklady Earth Sciences, 2008. - v. 421 - no. 1 - p. 838. Gvishiani, A. D., Agayan, S. M., Bogoutdinov, Sh. R., Soloviev, A. A. Discrete mathematical analysis and applications geology and geophysics, // Bulletin of KRAESC. Earth Sciences, 2010. - no. 10 - p. 109. Gvishiani, A. D., Agayan, S. M., Bogoutdinov, Sh. R., Soloviev, A. A. Discrete mathematical analysis and applications geology and geophysics, // Bulletin of KRAESC. Earth Sciences, 2010. - no. 10 - p. 109. Gvishiani, A. D., Agayan, S. M., Bogoutdinov, Sh. R., Zlotnicki, J., Bonnin, J. Mathematical methods of geoinformatics. III. Fuzzy comparisons and recognition of anomalies in time series, // Cybernetics and System Analysis, 2008. - v. 44 - no. 3 - p. 309. Gvishiani, A. D., Agayan, S. M., Bogoutdinov, Sh. R., Zlotnicki, J., Bonnin, J. Mathematical methods of geoinformatics. III. Fuzzy comparisons and recognition of anomalies in time series, // Cybernetics and System Analysis, 2008. - v. 44 - no. 3 - p. 309. Gvishiani, A. D., Dobrovolsky, M. N., Agayan, S., Dzeboev, B. Fuzzy-based clustering of epicenters and strong earthquake-prone areas, // Environmental Engineering and Management Journal, 2013. - v. 12 - no. 1 - p. 1. Gvishiani, A. D., Dobrovolsky, M. N., Agayan, S., Dzeboev, B. Fuzzy-based clustering of epicenters and strong earthquake-prone areas, // Environmental Engineering and Management Journal, 2013. - v. 12 - no. 1 - p. 1. Gvishiani, A. D., Dzeboev, B., Agayan, S. M. A new approach to recognition of the strong earthquake-prone areas in the Caucasus, // Izvestiya, Physics of the Solid Earth, 2013. - v. 49 - no. 6 - p. 747. Gvishiani, A. D., Dzeboev, B., Agayan, S. M. A new approach to recognition of the strong earthquake-prone areas in the Caucasus, // Izvestiya, Physics of the Solid Earth, 2013. - v. 49 - no. 6 - p. 747. Gvishiani, A. D., Soloviev, A., Krasnoperov, R., et al. Automated Hardware and Software System for Monitoring the Earth's Magnetic Environment, // Data Science Journal, 2016. - v. 15 - no. 18 - p. 1. Gvishiani, A. D., Soloviev, A., Krasnoperov, R., et al. Automated Hardware and Software System for Monitoring the Earth's Magnetic Environment, // Data Science Journal, 2016. - v. 15 - no. 18 - p. 1. Love, J., Remick, K. J. Magnetic indices In: Gubbins, D and Herrero-Bervera, E (eds.) Encyclopedia of Geomagnetism and Paleomagnetism - New York: Springer., 2007. - 711-713 pp. Love, J., Remick, K. J. Magnetic indices In: Gubbins, D and Herrero-Bervera, E (eds.) Encyclopedia of Geomagnetism and Paleomagnetism - New York: Springer., 2007. - 711-713 pp. Mikhailov, V., et al. Application of artificial intelligence for Euler solutions clustering, // Geophysics, 2003. - v. 68 - no. 1 - p. 168. Mikhailov, V., et al. Application of artificial intelligence for Euler solutions clustering, // Geophysics, 2003. - v. 68 - no. 1 - p. 168. Sidorov, R. V., Soloviev, A. A., Bogoutdinov, Sh. R. Application of the SP algorithm to the INTERMAGNET magnetograms of the disturbed geomagnetic field, // Izvestiya, Physics of the Solid Earth, 2012. - v. 48 - no. 5 - p. 410. Sidorov, R. V., Soloviev, A. A., Bogoutdinov, Sh. R. Application of the SP algorithm to the INTERMAGNET magnetograms of the disturbed geomagnetic field, // Izvestiya, Physics of the Solid Earth, 2012. - v. 48 - no. 5 - p. 410. Soloviev, A., Agayan, S. M., Bogoutdinov, Sh. R. Estimation of geomagnetic activity using measure of anomalousness, // Annals of Geophysics, 2016. - v. 59 - no. 6 - p. 1. Soloviev, A., Agayan, S. M., Bogoutdinov, Sh. R. Estimation of geomagnetic activity using measure of anomalousness, // Annals of Geophysics, 2016. - v. 59 - no. 6 - p. 1. Soloviev, A., Bogoutdinov, Sh. R., Gvishiani, A. D., Kulchinskiy, R., Zlotnicki, J. Mathematical Tools for Geomagnetic Data Monitoring and the INTERMAGNET Russian Segment, // Data Science Journal, 2013. - v. 12 - p. WDS114. Soloviev, A., Bogoutdinov, Sh. R., Gvishiani, A. D., Kulchinskiy, R., Zlotnicki, J. Mathematical Tools for Geomagnetic Data Monitoring and the INTERMAGNET Russian Segment, // Data Science Journal, 2013. - v. 12 - p. WDS114. Soloviev, A., Chulliat, A., Bogoutdinov, Sh. R., et al. Automated recognition of spikes in 1 Hz data recorded at the Easter Island magnetic observatory, // Earth, Planets and Space, 2012. - v. 64 - no. 9 - p. 743. Soloviev, A., Chulliat, A., Bogoutdinov, Sh. R., et al. Automated recognition of spikes in 1 Hz data recorded at the Easter Island magnetic observatory, // Earth, Planets and Space, 2012. - v. 64 - no. 9 - p. 743. Soloviev, A. A., Agayan, S. M., Gvishiani, A. D., et al. Recognition of disturbances with specified morphology in time series. Part 2: Spikes on 1-s magnetograms, // Izvestiya, Physics of the Solid Earth, 2012. - v. 48 - no. 5 - p. 395. Soloviev, A. A., Agayan, S. M., Gvishiani, A. D., et al. Recognition of disturbances with specified morphology in time series. Part 2: Spikes on 1-s magnetograms, // Izvestiya, Physics of the Solid Earth, 2012. - v. 48 - no. 5 - p. 395. Zelinskiy, N. R., Kleimenova, N. G., Kozyreva, O. V., Agayan, S. M., Bogoutdinov, Sh. R., Soloviev, A. A. Algorithm for recognizing Pc3 geomagnetic pulsations in 1-s data from INTERMAGNET equatorial observatories, // Izvestiya, Physics of the Solid Earth, 2014. - v. 50 - no. 2 - p. 240. Zelinskiy, N. R., Kleimenova, N. G., Kozyreva, O. V., Agayan, S. M., Bogoutdinov, Sh. R., Soloviev, A. A. Algorithm for recognizing Pc3 geomagnetic pulsations in 1-s data from INTERMAGNET equatorial observatories, // Izvestiya, Physics of the Solid Earth, 2014. - v. 50 - no. 2 - p. 240. Zadeh, L. A. Fuzzy sets, // Information Control, 1965. - v. 8 - no. 3 - p. 338. Zadeh, L. A. Fuzzy sets, // Information Control, 1965. - v. 8 - no. 3 - p. 338. Zlotnicki, J., LeMouel, J.-L., Gvishiani, A. D., et al. Automatic fuzzy-logic recognition of anomalous activity on long geophysical records. Application to electric signals associated with the volcanic activity of la Fournaise volcano (Reunion Island), // Earth and Planetary Science Letters, 2005. - v. 234 - no. 1-2 - p. 261. Zlotnicki, J., LeMouel, J.-L., Gvishiani, A. D., et al. Automatic fuzzy-logic recognition of anomalous activity on long geophysical records. Application to electric signals associated with the volcanic activity of la Fournaise volcano (Reunion Island), // Earth and Planetary Science Letters, 2005. - v. 234 - no. 1-2 - p. 261. INTERMAGNET, International Real-time Magnetic Observatory Network web-page - Paris: WDCS., 1991. INTERMAGNET, International Real-time Magnetic Observatory Network web-page - Paris: WDCS., 1991. WDC, World Data Center for Geomagnetism, Kyoto - Kyoto: WDCS., 1957. WDC, World Data Center for Geomagnetism, Kyoto - Kyoto: WDCS., 1957.