Vestnik КRAUNC. Fiz.-Mat. nauki. 2023. vol. 44. no. 3. P. 86-104. ISSN 2079-6641


Research Article

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MSC 34A08, 34A34

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Research of Stress-Strain State of Geo-Environment by Emanation Methods on the Example of \alpha\left(t\right)-Model of Radon Transport

D. A. Tverdyi¹²^\ast, E. O. Makarov²³, R. I. Parovik¹²

¹Institute for Cosmophysical Research and Radio Propagation FEB RAS, 684034, p. Paratunka, Mirnaya st., 7, Russia
²Vitus Bering Kamchatka State University 683032, Petropavlovsk-Kamchatsky, st. Pogranichnaya, 4, Russia
³Kamchatka branch Unified Geophysical Service of the RAS, 683006, Kamchatka Petropavlovsk-Kamchatsky, Piipa boulevard, 9, Russia

Abstract. Continuous monitoring of variations in the volumetric activity of radon in order to search for its anomalous values preceding seismic events is one of the effective techniques for studying the stress-strain state of the geosphere. We propose a Cauchy problem describing the radon transport taking into account its accumulation in the chamber and the presence of the memory effect of the geo-environment. The model equation is a nonlinear differential equation with non-constant coefficients with a derivative in the sense of Gerasimov-Kaputo of fractional variable order. In the course of mathematical modeling, in MATLAB environment, of radon transport by the ereditary \alpha\left(t\right)-model a good agreement with experimental data was obtained. This indicates that the ereditary \alpha\left(t\right)-model of radon transport is more flexible, which allows it to describe various anomalous variations in the values of volumetric activity of radon due to the stress-strain state of the geosphere. It is shown that the order of the fractional derivative can be responsible for the intensity of the radon transfer process associated with the characteristics of the geo-environment. It is shown that due to the order of the fractional derivative, as well as quadratic nonlinearity in the model equation, the results of numerical modeling give a better approximation of the experimental data of radon monitoring than by classical models.

Key words: mathematical modeling, nonlinear equations, saturation effect, fractional equations, fractional derivatives, hereditarity, memory effects, nonlocality in time, radon volumetric activity, stress-strain state, geo-environment, earthquake precursors

Received: 19.10.2023; Revised: 26.10.2023; Accepted: 28.10.2023; First online: 02.11.2023

For citation. Tverdyi D. A., Makarov E. O., Parovik R. I. Research of stress-strain state of geo-environment by emanation methods on the example of \alpha\left(t\right)-model of radon transport. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 44: 3, 86-104. EDN: AOBZGA.

Funding. The research was carried out within the framework of the grant of the President of the Russian Federation
MD-758.2022.1.1 on the topic “Development of mathematical models of fractional dynamics in order to study oscillatory processes and processes with saturation”

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.

^\astCorrespondence: E-mail:

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

© Tverdyi D. A., Makarov E. O., Parovik R. I., 2023

© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)


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Information about authors

Tverdyi Dmitrii Alexsandrovich – Ph. D. (Phys. & Math.), Researcher, laboratory of electromagnetic propogation Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Russia, ORCID 0000-0001-6983-5258.

Makarov Evgeny Olegovich – Ph. D. (Phys. & Math.), Senior Researcher Kamchatka Branch of the Federal State Budgetary Institution of Science Federal Research Center “Unified Geophysical Service of the Russian Academy of Sciences 683023, Kamchatka Petropavlovsk-Kamchatsky, Russia ORCID 0000-0002-0462-3657.

Parovik Roman Ivanovich – D. Sci. (Phys. & Math.), Associate Professor, Leading researcher, laboratory of modeling physical processes Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Head of the International Integrative Research Laboratory of Extreme Phenomena of Kamchatka, Kamchatka State University named after Vitus Bering, Petropavlovsk-Kamchatsky, Russia, ORCID 0000-0002-1576-1860.