Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 71113 10.2205/2023ES000889 phvzcv ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Regression Derivatives and Their Application in the Study of Magnetic Storms Regression Derivatives and Their Application in the Study of Magnetic Storms https://orcid.org/0000-0003-3710-1246 Агаян Сергей Мартикович Agayan S M s.agayan@gcras.ru https://orcid.org/0000-0002-3171-5768 Богоутдинов Шамиль Рафекович Bogoutdinov Shamil Rafekovich shm@gcras.ru https://orcid.org/0000-0003-2615-4326 Сидоров Роман Викторович Sidorov Roman Viktorovich r.sidorov@gcras.ru https://orcid.org/0000-0002-6476-9471 Соловьев Анатолий Александрович Soloviev Anatoly A https://orcid.org/0000-0002-9287-8042 Камаев Дмитрий Альфредович Kamaev Dmitry Al'fredovich post@typhoon.obninsk.ru Алексанян Андрон Олегович Aleksanyan Andron Olegovich a.alexanyan@itresume.ru https://orcid.org/0000-0003-3427-0634 Дзеранов Борис Витальевич Dzeranov B. V. Геофизический центр Российской Академии Наук RU Geophysical Center of the Russian Academy of Sciences RU Геофизический центр РАН Россия Geophysical Center RAS Russian Federation Институт физики Земли им. О. Ю. Шмидта РАН Россия Schmidt institute of physics of the Earth of the RAS Russian Federation Геофизический центр РАН Россия Geophysical Center RAS Russian Federation Геофизический центр РАН Россия Geophysical Center RAS Russian Federation Институт физики Земли им. О. Ю. Шмидта РАН Россия Schmidt institute of physics of the Earth of the RAS Russian Federation НПО "Тайфун" Россия RPA “Typhoon” Russian Federation Обнинский институт атомной энергетики Россия Obninsk Institute for Nuclear Power Engineering Russian Federation Геофизический центр Российской Академии Наук Россия Geophysical Center of the Russian Academy of Sciences Russian Federation Владикавказский научный центр РАН Россия Vladikavkaz Scientific Center RAS Russian Federation 30 12 2023 30 12 2023 23 6 1 22 25 10 2023 28 12 2023 https://rjes.ru/en/nauka/article/71113/view

Discrete Mathematical Analysis (DMA) is a data analysis method that uses fuzzy mathematics and fuzzy logic. DMA involves the active participation of the researcher in the study of records, offering technologies and algorithms for analyzing records through the properties of interest to the researcher. In the present work, such properties are related to regression derivatives, and the results obtained are applied to magnetic records. The possibilities of the method in the morphological analysis of geomagnetic storms are demonstrated on the example of three strongest storms that have occurred since the beginning of the current 25th solar cycle.

Discrete Mathematical Analysis (DMA) is a data analysis method that uses fuzzy mathematics and fuzzy logic. DMA involves the active participation of the researcher in the study of records, offering technologies and algorithms for analyzing records through the properties of interest to the researcher. In the present work, such properties are related to regression derivatives, and the results obtained are applied to magnetic records. The possibilities of the method in the morphological analysis of geomagnetic storms are demonstrated on the example of three strongest storms that have occurred since the beginning of the current 25th solar cycle.

 Proximity measure regression derivation regression smoothing measures of activity. multi-scale measures of activitys Proximity measure regression derivation regression smoothing measures of activity. multi-scale measures of activitys This work was conducted in the framework of budgetary funding of the Geophysical Center of RAS, adopted by the Ministry of Science and Higher Education of the Russian Federation (grant number 075-00443-24-00). The results presented in this paper rely on data collected at magnetic observatories. We thank the national institutes that support them and INTERMAGNET for promoting high standards of magnetic observatory practice (http://www.intermagnet.org/). This work employed facilities and data provided by the Shared Research Facility “Analytical Geomagnetic Data Center” of the Geophysical Center of RAS (http://ckp.gcras.ru/).

Agayan, S., S. Bogoutdinov, A. Soloviev, and R. Sidorov (2016), The Study of Time Series Using the DMA Methods and Geophysical Applications, Data Science Journal, 15, https://doi.org/10.5334/dsj-2016-016. Agayan, S., S. Bogoutdinov, A. Soloviev, and R. Sidorov (2016), The Study of Time Series Using the DMA Methods and Geophysical Applications, Data Science Journal, 15, https://doi.org/10.5334/dsj-2016-016. Agayan, S., S. Bogoutdinov, D. Kamaev, V. Kaftan, M. Osipov, and V. Tatarinov (2021a), Theoretical Framework for Determination of Linear Structures in Multidimensional Geodynamic Data Arrays, Applied Sciences, 11(24), 11,606, https://doi.org/10.3390/app112411606. Agayan, S., S. Bogoutdinov, D. Kamaev, V. Kaftan, M. Osipov, and V. Tatarinov (2021a), Theoretical Framework for Determination of Linear Structures in Multidimensional Geodynamic Data Arrays, Applied Sciences, 11(24), 11,606, https://doi.org/10.3390/app112411606. Agayan, S., S. Bogoutdinov, R. Krasnoperov, and R. Sidorov (2021b), A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures, Applied Sciences, 11(24), 12,120, https://doi.org/10.3390/app112412120. Agayan, S., S. Bogoutdinov, R. Krasnoperov, and R. Sidorov (2021b), A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures, Applied Sciences, 11(24), 12,120, https://doi.org/10.3390/app112412120. Agayan, S. M., S. R. Bogoutdinov, and R. I. Krasnoperov (2018), Short introduction into DMA, Russian Journal of Earth Sciences, 18(2), 1-10, https://doi.org/10.2205/2018es000618. Agayan, S. M., S. R. Bogoutdinov, and R. I. Krasnoperov (2018), Short introduction into DMA, Russian Journal of Earth Sciences, 18(2), 1-10, https://doi.org/10.2205/2018es000618. Agayan, S. M., A. A. Soloviev, S. R. Bogoutdinov, and Y. I. Nikolova (2019), Regression Derivatives and Their Application to the Study of Geomagnetic Jerks, Geomagnetism and Aeronomy, 59(3), 359-367, https://doi.org/10.1134/s0016793219030022. Agayan, S. M., A. A. Soloviev, S. R. Bogoutdinov, and Y. I. Nikolova (2019), Regression Derivatives and Their Application to the Study of Geomagnetic Jerks, Geomagnetism and Aeronomy, 59(3), 359-367, https://doi.org/10.1134/s0016793219030022. Agayan, S. M., V. N. Tatarinov, A. D. Gvishiani, S. R. Bogoutdinov, and I. O. Belov (2020), FDPS algorithm in stability assessment of the Earth’s crust structural tectonic blocks, Russian Journal of Earth Sciences, 20(6), 1-14, https://doi.org/10.2205/2020es000752. Agayan, S. M., V. N. Tatarinov, A. D. Gvishiani, S. R. Bogoutdinov, and I. O. Belov (2020), FDPS algorithm in stability assessment of the Earth’s crust structural tectonic blocks, Russian Journal of Earth Sciences, 20(6), 1-14, https://doi.org/10.2205/2020es000752. Agayan, S. M., S. R. Bogoutdinov, B. A. Dzeboev, B. V. Dzeranov, D. A. Kamaev, and M. O. Osipov (2022), DPS clustering: New results, Applied Sciences, 12(18), 9335, https://doi.org/10.3390/app12189335. Agayan, S. M., S. R. Bogoutdinov, B. A. Dzeboev, B. V. Dzeranov, D. A. Kamaev, and M. O. Osipov (2022), DPS clustering: New results, Applied Sciences, 12(18), 9335, https://doi.org/10.3390/app12189335. Akasofu, S.-I., and S. Chapman (1963), The development of the main phase of magnetic storms, Journal of Geophysical Research, 68(1), 125-129, https://doi.org/10.1029/jz068i001p00125. Akasofu, S.-I., and S. Chapman (1963), The development of the main phase of magnetic storms, Journal of Geophysical Research, 68(1), 125-129, https://doi.org/10.1029/jz068i001p00125. Batyrshin, I. Z., A. O. Nedosekin, and A. A. Stetsko (2007), Fuzzy hybrid systems. Theory and practice, 207 pp., Fizmatlit. Batyrshin, I. Z., A. O. Nedosekin, and A. A. Stetsko (2007), Fuzzy hybrid systems. Theory and practice, 207 pp., Fizmatlit. Boroev, R. N., and M. S. Vasiliev (2017), Relationship between Indexes of Geomagnetic Activity on the Main Phase of a Magnetic Storm for Various Types of Solar Wind, Science and Education, 1, 67-70, in Russian. Boroev, R. N., and M. S. Vasiliev (2017), Relationship between Indexes of Geomagnetic Activity on the Main Phase of a Magnetic Storm for Various Types of Solar Wind, Science and Education, 1, 67-70, in Russian. Gromova, L. I., N. G. Kleimenova, A. E. Levitin, S. V. Gromov, L. A. Dremukhina, and N. R. Zelinskii (2016), Daytime geomagnetic disturbances at high latitudes during a strong magnetic storm of June 21-23, 2015: The storm initial phase, Geomagnetism and Aeronomy, 56(3), 281-292, https://doi.org/10.1134/s0016793216030051. Gromova, L. I., N. G. Kleimenova, A. E. Levitin, S. V. Gromov, L. A. Dremukhina, and N. R. Zelinskii (2016), Daytime geomagnetic disturbances at high latitudes during a strong magnetic storm of June 21-23, 2015: The storm initial phase, Geomagnetism and Aeronomy, 56(3), 281-292, https://doi.org/10.1134/s0016793216030051. Gvishiani, A., A. Soloviev, R. Krasnoperov, and R. Lukianova (2016a), Automated Hardware and Software System for Monitoring the Earth’s Magnetic Environment, Data Science Journal, 15, https://doi.org/10.5334/dsj-2016-018. Gvishiani, A., A. Soloviev, R. Krasnoperov, and R. Lukianova (2016a), Automated Hardware and Software System for Monitoring the Earth’s Magnetic Environment, Data Science Journal, 15, https://doi.org/10.5334/dsj-2016-018. Gvishiani, A. D., R. V. Sidorov, R. Y. Lukianova, and A. A. Soloviev (2016b), Geomagnetic activity during St. Patrick's Day storm inferred from global and local indicators, Russian Journal of Earth Sciences, 16(6), 1-8, https://doi.org/10.2205/2016es000593. Gvishiani, A. D., R. V. Sidorov, R. Y. Lukianova, and A. A. Soloviev (2016b), Geomagnetic activity during St. Patrick's Day storm inferred from global and local indicators, Russian Journal of Earth Sciences, 16(6), 1-8, https://doi.org/10.2205/2016es000593. Intermagnet (2023), International Real-time Magnetic Observatory Network, https://intermagnet.org, accesed on 1 November 2023. Intermagnet (2023), International Real-time Magnetic Observatory Network, https://intermagnet.org, accesed on 1 November 2023. ISGI (2023), International service of geomagnetic indices, https://isgi.unistra.fr, accesed on 1 November 2023. ISGI (2023), International service of geomagnetic indices, https://isgi.unistra.fr, accesed on 1 November 2023. Kacprzyk, J., A. Wilbik, and S. Zadrożny (2007), Linguistic Summarization of Time Series by Using the Choquet Integral, in Lecture Notes in Computer Science, pp. 284-294, Springer Berlin Heidelberg, https://doi.org/10.1007/978-3-540-72950-1_29. Kacprzyk, J., A. Wilbik, and S. Zadrożny (2007), Linguistic Summarization of Time Series by Using the Choquet Integral, in Lecture Notes in Computer Science, pp. 284-294, Springer Berlin Heidelberg, https://doi.org/10.1007/978-3-540-72950-1_29. Kovalev, S. M. (2007), Hybrid fuzzy-temporal models of time series in problems of analysis and identification of weakly formalized processes, in Integrated Models and Soft Computing in Artificial Intelligence. Proceedings of the IVth International Scientific and Practical Conference (Kolomna, May 28-30, 2007), Moscow: Fizmatlit., vol. 1, pp. 26-41. Kovalev, S. M. (2007), Hybrid fuzzy-temporal models of time series in problems of analysis and identification of weakly formalized processes, in Integrated Models and Soft Computing in Artificial Intelligence. Proceedings of the IVth International Scientific and Practical Conference (Kolomna, May 28-30, 2007), Moscow: Fizmatlit., vol. 1, pp. 26-41. Lazutin, L. L. (2012), Global and polar magnetic storms, 214 pp., Moscow State University, in Russian. Lazutin, L. L. (2012), Global and polar magnetic storms, 214 pp., Moscow State University, in Russian. Mishin, V. M., M. Foerster, T. I. Saifudinova, A. D. Bazarzhapov, Y. A. Karavaev, L. A. Sapronova, and S. I. Solovyev (2007), Spontaneous substorms and ordered type of magnetospheric disturbances during the superstorm of November 20, 2003, Geomagnetism and Aeronomy, 47(4), 429-441, https://doi.org/10.1134/s0016793207040032. Mishin, V. M., M. Foerster, T. I. Saifudinova, A. D. Bazarzhapov, Y. A. Karavaev, L. A. Sapronova, and S. I. Solovyev (2007), Spontaneous substorms and ordered type of magnetospheric disturbances during the superstorm of November 20, 2003, Geomagnetism and Aeronomy, 47(4), 429-441, https://doi.org/10.1134/s0016793207040032. NOAA (2023), National Oceanic and Atmospheric Administartion, https://www.noaa.gov, accesed on 1 November 2023. NOAA (2023), National Oceanic and Atmospheric Administartion, https://www.noaa.gov, accesed on 1 November 2023. OMNI (2023), OMNIWeb Plus, https://omniweb.gsfc.nasa.gov, accesed on 01 November 2023. OMNI (2023), OMNIWeb Plus, https://omniweb.gsfc.nasa.gov, accesed on 01 November 2023. Oshchenko, A. A., R. V. Sidorov, A. A. Soloviev, and E. N. Solovieva (2020), Overview of anomality measure application for estimating geomagnetic activity, Geophysical research, 21(4), 51-69, https://doi.org/10.21455/gr2020.4-4. Oshchenko, A. A., R. V. Sidorov, A. A. Soloviev, and E. N. Solovieva (2020), Overview of anomality measure application for estimating geomagnetic activity, Geophysical research, 21(4), 51-69, https://doi.org/10.21455/gr2020.4-4. Pandey, S. K., and S. C. Dubey (2009), Characteristic features of large geomagnetic storms observed during solar cycle 23, Indian Journal of Radio & Space Physics, 38(6), 305-312. Pandey, S. K., and S. C. Dubey (2009), Characteristic features of large geomagnetic storms observed during solar cycle 23, Indian Journal of Radio & Space Physics, 38(6), 305-312. Pedrycz, W., and M. Smith (1999), Granular correlation analysis in data mining, in FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems.Conference Proceedings (Cat. No.99CH36315), IEEE, https://doi.org/10.1109/fuzzy.1999.790078. Pedrycz, W., and M. Smith (1999), Granular correlation analysis in data mining, in FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems.Conference Proceedings (Cat. No.99CH36315), IEEE, https://doi.org/10.1109/fuzzy.1999.790078. Soloviev, A., S. Agayan, and S. Bogoutdinov (2017), Estimation of geomagnetic activity using measure of anomalousness, Annals of Geophysics, 59(6), https://doi.org/10.4401/ag-7116. Soloviev, A., S. Agayan, and S. Bogoutdinov (2017), Estimation of geomagnetic activity using measure of anomalousness, Annals of Geophysics, 59(6), https://doi.org/10.4401/ag-7116. Soloviev, A., A. Smirnov, A. Gvishiani, J. Karapetyan, and A. Simonyan (2019), Quantification of Sq parameters in 2008 based on geomagnetic observatory data, Advances in Space Research, 64(11), 2305-2320, https://doi.org/10.1016/j.asr.2019.08.038. Soloviev, A., A. Smirnov, A. Gvishiani, J. Karapetyan, and A. Simonyan (2019), Quantification of Sq parameters in 2008 based on geomagnetic observatory data, Advances in Space Research, 64(11), 2305-2320, https://doi.org/10.1016/j.asr.2019.08.038. Tanaka, H., S. Uejima, and K. Asai (1982), Linear Regression Analysis with Fuzzy Model, IEEE Transactions on Systems, Man, and Cybernetics, 12(6), 903-907, https://doi.org/10.1109/tsmc.1982.4308925. Tanaka, H., S. Uejima, and K. Asai (1982), Linear Regression Analysis with Fuzzy Model, IEEE Transactions on Systems, Man, and Cybernetics, 12(6), 903-907, https://doi.org/10.1109/tsmc.1982.4308925. WDC (2023), World Data Center for Geomagnetism, Kyoto, https://wdc.kugi.kyoto-u.ac.jp, accesed on 1 November 2023. WDC (2023), World Data Center for Geomagnetism, Kyoto, https://wdc.kugi.kyoto-u.ac.jp, accesed on 1 November 2023. Yarushkina, N. G. (2004), Fundamentals of the theory of fuzzy and hybrid systems, 320 pp., Finansy i statistika. Yarushkina, N. G. (2004), Fundamentals of the theory of fuzzy and hybrid systems, 320 pp., Finansy i statistika. Yarushkina, N. G., T. R. Yunusov, and T. V. Afanasyeva (2007), Terminal-server traffic modeling based on fuzzy time series trend analysis, Program products and systems, (4), 15-19. Yarushkina, N. G., T. R. Yunusov, and T. V. Afanasyeva (2007), Terminal-server traffic modeling based on fuzzy time series trend analysis, Program products and systems, (4), 15-19. Yermolaev, Y. I., I. G. Lodkina, N. S. Nikolaeva, and M. Y. Yermolaev (2012), Recovery phase of magnetic storms induced by different interplanetary drivers, Journal of Geophysical Research: Space Physics, 117(A8), A08,207, https://doi.org/10.1029/2012ja017716. Yermolaev, Y. I., I. G. Lodkina, N. S. Nikolaeva, and M. Y. Yermolaev (2012), Recovery phase of magnetic storms induced by different interplanetary drivers, Journal of Geophysical Research: Space Physics, 117(A8), A08,207, https://doi.org/10.1029/2012ja017716. Yermolaev, Y. I., I. G. Lodkina, N. S. Nikolaeva, and M. Y. Yermolaev (2014), Influence of the interplanetary driver type on the durations of the main and recovery phases of magnetic storms, Journal of Geophysical Research: Space Physics, 119(10), 8126-8136, https://doi.org/10.1002/2014ja019826. Yermolaev, Y. I., I. G. Lodkina, N. S. Nikolaeva, and M. Y. Yermolaev (2014), Influence of the interplanetary driver type on the durations of the main and recovery phases of magnetic storms, Journal of Geophysical Research: Space Physics, 119(10), 8126-8136, https://doi.org/10.1002/2014ja019826. Yokoyama, N., and Y. Kamide (1997), Statistical nature of geomagnetic storms, Journal of Geophysical Research: Space Physics, 102(A7), 14,215-14,222, https://doi.org/10.1029/97ja00903. Yokoyama, N., and Y. Kamide (1997), Statistical nature of geomagnetic storms, Journal of Geophysical Research: Space Physics, 102(A7), 14,215-14,222, https://doi.org/10.1029/97ja00903. Zhang, G.-L. (1992), Interplanetary disturbance structures and geomagnetic storm, in AIP Conference Proceedings, AIP, https://doi.org/10.1063/1.41724. Zhang, G.-L. (1992), Interplanetary disturbance structures and geomagnetic storm, in AIP Conference Proceedings, AIP, https://doi.org/10.1063/1.41724.