Research of stress-strain state of geo-environment by emanation methods on the example of $\alpha$(t)-model of radon transport

D. A. Tvyordyj ; E. O. Makarov ; R. I. Parovik

Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 44 (2023) no. 3, pp. 86-104

Résumé

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.

Détail

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