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 $\alpha$(t)-model a good agreement with experimental data was obtained. This indicates that the ereditary $\alpha$(t)-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.
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”.
Citation:
D. A. Tvyordyj, E. O. Makarov, R. I. Parovik, “Research of stress-strain state of geo-environment by emanation methods on the example of $\alpha$(t)-model of radon transport”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 44:3 (2023), 86–104
\Bibitem{TvyMakPar23}
\by D.~A.~Tvyordyj, E.~O.~Makarov, R.~I.~Parovik
\paper Research of stress-strain state of geo-environment by emanation methods on the example of $\alpha$(t)-model of radon transport
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2023
\vol 44
\issue 3
\pages 86--104
\mathnet{http://mi.mathnet.ru/vkam613}
\crossref{https://doi.org/10.26117/2079-6641-2023-44-3-86-104}
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https://www.mathnet.ru/eng/vkam613
https://www.mathnet.ru/eng/vkam/v44/i3/p86
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