Mathematical Model of Radon Accumulation in a Storage Chamber Taking Into Account Heredity

Continuous registration of radon volume activity (RVA) is underway on the Kamchatka Peninsula and Sakhalin Island. The analysis of radon monitoring data is one of the methods for searching for earthquake precursors, since RVA is affected by changes in the stress-strain state of the geo-environment preceding seismic events. The aim of the study is to investigate the accumulation of radon in the chamber using mathematical modeling methods and solving inverse problems. The change in the intensity of radon transport due to a change in the state of the geo-environment is described using the fractional differentiation operator of constant real order \(\alpha \) . It is known that radon in a container with sensors is influenced by environmental parameters, in particular the multiplicity of air exchange \(\lambda _0\) , the effect of which must be taken into account in the process model. As a result, it is shown that for the heredity \(\alpha \) -model, the optimal values of the parameters \(\lambda _0\) and \(\alpha \) can be determined by the method of unconditional optimization based on experimental RVA data. The obtained model curves are in good agreement with the RVA data in comparison with the classical model.