Vestnik КRAUNC. Fiz.-Mat. nauki. 2024. vol. 48. no. 3. P. 95 – 119. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2024-48-3-95-119
Research Article
Full text in Russian
MSC 26A33, 86A17, 86A22, 49N45

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Identification of Parameters of the Mathematical α-Model of Radon Transport in the Accumulation Chamber Based on Data from the Karymshina Site in Kamchatka

D. A. Tverdyi^{\ast}¹, E. O. Makarov², R. I. Parovik²

¹Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034, Paratunka village, Mirnaya str., 7, Russia
²Kamchatka Branch of the Federal Research Center «Unified Geophysical Service of the Russian Academy of Sciences», 683023, Petropavlovsk-Kamchatsky, Piipa Boulevard st., 9, Russia

Abstract. Radon is an inert radioactive gas, and studies of its variations in relation to seismicity are considered promising for the development of earthquake prognosis methods. A network of observation points has been deployed on the Kamchatka peninsula, where radon volumetric activity (RVA) is monitored using accumulation chambers with gas-discharge counters. Analysis of RVA data within the framework of radon monitoring is one of the methods of searching for precursors of seismic events. This is due to the fact that changes in the stress-strain state of the geo-environment, through which the gas flows, affect the RVA. The change in radon transport intensity due to changes in the stress-strain state of the geosphere is described by a fractional differentiation operator of constant real order α, which is related to the permeability of the geosphere. It is known that the RVA in the storage tank with sensors is also affected by the air exchange rate λ0, the effect of which should be taken into account in the study of the radon transport process. The aim of the research is to study the accumulation of radon in the chamber, which consists in the identification of the values of the parameters λ0 and α by solving the corresponding inverse problem. As a result of the research it was shown that for the hereditary α-model of radon transport by the Levenberg-Mackwardt method with the involvement of experimental data of RVA it is possible to determine the optimal values of its parameters λ0 and α. The obtained model curves agree well with the RVA data obtained within the framework of the well-known classical model of radon transport in an accumulation chamber.

Key words: мathematical modeling, dynamic processes, radon volume activity, Kamchatka, earthquake precursors, fractional derivatives, Gerasimov-Caputo, memory effect, nonlocality, nonlinear equations, inverse problems, unconditional optimization, Levenberg-Marquardt algorithm, С, Gnuplot.

Received: 27.09.2024; Revised: 30.09.2024; Accepted: 20.10.2024; First online: 20.11.2024

For citation. Tverdyi D. A., Makarov E. O., Parovik R. I. Identification of parameters of the mathematical α-model of radon transport in the accumulation chamber based on data from the Karymshina site in Kamchatka. Vestnik KRAUNC. Fiz.-mat. nauki. 2024, 48: 3, 95-119. EDN: AUYJMD. https://doi.org/10.26117/2079-6641-2024-48-3-95-119.

Funding. The research was funded by a grant from the Russian Science Foundation, project number 22-11-00064, which can be found at https://rscf.ru/project/22-11-00064/. The work was supported by Ministry of Science and Higher Education of the Russian Federation (075-00682-24). The research was funded by a grant from the Russian Science Foundation, project number 23-71-01050, which can be found at https://rscf.ru/project/23-71-01050/

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: tverdyi@ikir.ru

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., 2024

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

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