Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 53. no. 4. P. 45 – 58. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2025-53-4-45-58
Research Article
Full text in Russian
MSC 60G22, 37M10, 33E12

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Application of the Fractional Model of Deformation Activity to the Study of the Properties of the Heredity and Non-Stationary of the Seismic Process in the Subduction Zone of the Kuril-Kamchatka Island Arc in the Relaxation Phase

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

Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, 684034, Kamchatka Krai, Paratunka village, Mirnaya str., 7, Russia

Abstract. The study of the properties of the heredity and non-stationary of the seismic process in the relaxation phase is carried out on the basis of data from the earthquakes catalog of the KB FRC GS RAS (01.01.1962−31.12.2002, the subduction zone of the Kuril-Kamchatka island arc). The algorithm used considers events related only to the main event of a given energy as aftershocks based on spatial and time criteria previously developed by the authors in the statistical model of the deformation process. Due to the small samples volume of aftershocks of a given energy for a single main event, the study uses the method of superimposing «epochs» to construct empirical laws of the distribution of aftershocks waiting time. The empirical laws of aftershocks distribution are approximated by the three-parameter Mittag-Leffler function based on the fractional model of the deformation process developed by the authors. A comparative analysis of the obtained calculations results of the values of the parameters of the Mittag-Leffler function with those previously presented on the basis of an algorithm that takes into account the branching of the process is carried out. It is concluded that there are properties of non-stationary and weak heredity of the seismic process in the subduction zone of the Kuril-Kamchatka island arc in the relaxation phase.

Key words: fractional Poisson process, seismic process, Mittag-Leffler’s function, approximation, statistical model, fractional model.

Received: 12.11.2025; Revised: 01.12.2025; Accepted: 02.12.2025; First online: 03.12.2025

For citation. Sheremetyeva O. V., Shevtsov B. M. Application of the fractional model of deformation activity to the study of the properties of the heredity and non-stationary of the seismic process in the subduction zone of the Kuril-Kamchatka Island arc in the relaxation phase. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 53: 4, 45-58. EDN: WNVLGJ. https://doi.org/10.26117/2079-6641-2025-53-4-45-58.

Funding. The work was supported by IKIR FEB RAS State Task (subject registration No. 124012300245-2)

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., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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