Restoration of the order of fractional derivative
in the problem of mathematical modelling of radon accumulation
in the excess volume of the storage chamber based
on the data of Petropavlovsk-Kamchatsky geodynamic polygon
Abstract:
The paper researches the issues related to the nonlinear transport of radon gas through the
geosphere, in particular, when describing the variation of volumetric activity (RVA) in an accumulation
chamber with recording sensors. RVA is considered to be an informative and operational precursor to
earthquakes. Based on the assumption that the radon transport process takes place in a permeable geosphere,
an ereditary RVA model based on the Riccati equation with fractional Gerasimov–Kaputo derivative is used
for modelling. The model has been previously validated at the geodynamic test site in PetropavlovskKamchatsky. In the study the identification of the order value of the fractional derivative, which is associated
with such geo-environmental characteristics as porosity and permeability is of most interest. However, we do
not have information about some parameters of the process under consideration to determine this value
accurately enough. But we know additional information obtained from the experiment. This information can
be used to reconstruct the values of interest. Which leads us to the inverse problems. To reconstruct the
order of the fractional derivative, we solve the one-dimensional optimisation problem using the iterative
Levenberg–Marquardt method of Newtonian type. It is shown that this method can be used to reconstruct
some parameters of such a dynamic system as radon transport through geo-environment. It is shown that the
solution of the inverse problem by the Levenberg–Marquardt method gives a more accurate result in a shorter
time than the manual selection of parameter values and types of functions for the model equations.
Fulltext:
PDF file (601 kB)