Vestnik КRAUNC. Fiz.-Mat. nauki. 2024. vol. 49. no. 4. P. 50 – 64. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2024-49-4-50-64
Research Article
Full text in Russian
MSC 60G22, 37M10, 33E12

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Characteristics of the Deformation Process in the Subduction Zone of the Kuril-Kamchatka Island Arc in the Aftershock Phase Based on a Fractional Model of Deformation Activity

O. V. Sheremetyeva^{\ast}, B. M. Shevtsov

Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034, Kamchatka region, Elizovskiy district, Paratunka, Mirnaya str., 7, Russia

Abstract. The article presents the results of calculations of the values of parameters determining the properties of the deformation process, based on data from the earthquake catalog of the Kamchatka Branch of the Federal Research Center «Geophysical Survey of the Russian Academy of Sciences» (KB FRC GS RAS) for the period from 1 January 1962 to 31 December 2002 for the Kuril-Kamchatka island arc subduction zone (area 46^{\circ}–62^{\circ} N, 158^{\circ}––174^{\circ} E) in the aftershock phase in within the framework of the fractional model of the deformation process previously presented by the authors. The compound power-law Poisson process in fractional time representation is considered as a model. Aftershocks associated with the mainshock of a given energy are determined based on energy, spatial and temporal criteria.To construct an empirical cumulative distribution function (eCDF) for aftershocks of a fixed class depending on the time before the mainshock, the superposed epoch analysis is applied to sequences of aftershocks for all mainshocks of a given energy in the catalog. The eCDF of the aftershock waiting time are approximated by the Mittag-Leffler function based on the fractional model of the deformation process developed by the authors. The results of calculations of the values of the Mittag-Leffler function parameters for the mainshocks of the classes K < 12.5 showed that the deformation process in the considered zone has the properties of nonstationarity and hereditarity. With an increase in the class of the mainshock, the process can be considered non-stationary standard Poisson process.

Key words: aftershocks, approximation, fractional Poisson process, Mittag-Leffler’s function, herediterity, non-stationarity, statistical model, fractional model.

Received: 06.11.2024; Revised: 19.11.2024; Accepted: 26.11.2024; First online: 27.11.2024

For citation. Sheremetyeva O. V., Shevtsov B. M. Characteristics of the deformation process in the subduction zone of the Kuril-Kamchatka Island arc in the aftershock phase based on a fractional model of deformation activity. Vestnik KRAUNC. Fiz.-mat. nauki. 2024, 49: 4, 50-64. EDN: TKITJI. https://doi.org/10.26117/2079-6641-2024-49-4-50-64.

Funding. The work was funded by Russian Science Foundation [grant number 22-11-00064 «Modeling dynamic processes in geospheres taking into account hereditarity»]. https://rscf.ru/project/22-11-00064/.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^{\ast}Correspondence: E-mail: sheremeteva@ikir.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Sheremetyeva O. V., Shevtsov B. M., 2024

© Institute of Cosmophysical Research and Radio Wave Propagation, 2024 (original layout, design, compilation)

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Information about the authors

Sheremetyeva Olga Vladimirovna – Ph. D. (Tech.), Research Scientist, Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Kamchatka, Russia, ORCID 0000-0001-9417-9731.

Shevtsov Boris Mikhaylovich – D. Sci. (Phys. & Math.), Chief Scientific Officer, Laboratory of Electromagnetic Radiation, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Kamchatka, Russia, ORCID 0000-0003-0625-0361.

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