Geodesic
Identification of parameters of the mathematical $\alpha$-model of radon transport in the accumulation chamber based on data from the Karymshina site in Kamchatka
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 48 (2024) no. 3, pp. 95-119

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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 $\alpha$, 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 $\lambda$0, 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 $\lambda$0 and $\alpha$ by solving the corresponding inverse problem. As a result of the research it was shown that for the hereditary $\alpha$-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 $\lambda$0 and $\alpha$. 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.
Mots-clés : С
Keywords: мathematical modeling, dynamic processes, radon volume activity, Kamchatka, earthquake precursors, fractional derivatives, Gerasimov-Caputo, memory effect, nonlocality, nonlinear equations, inverse problems, unconditional optimization, Gnuplot.
Mots-clés : Levenberg-Marquardt algorithm 
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     author = {D. A. Tvyordyj and E. O. Makarov and R. I. Parovik},
     title = {Identification of parameters of the mathematical $\alpha$-model of radon transport in the accumulation chamber based on data from the {Karymshina} site in {Kamchatka}},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
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D. A. Tvyordyj; E. O. Makarov; R. I. Parovik. Identification of parameters of the mathematical $\alpha$-model of radon transport in the accumulation chamber based on data from the Karymshina site in Kamchatka. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 48 (2024) no. 3, pp. 95-119. http://geodesic.mathdoc.fr/item/VKAM_2024_48_3_a7/