Numerical solution of the inverse problem of identifying methane consumption rate in soil

Subject of research: a mathematical model of methane consumption in soils. Purpose of research: to develop an algorithm for the numerical solution of the inverse problem of identifying the methane consumption rate in soils. Methods and objects of research: this work addresses the issue of recovering the methane consumption rate in soil based on measured methane concentration data at a set of points. The mathematical model is a second-order ordinary differential equation, and the sought coefficient is the lower-order coefficient in the equation. This equation is based on the MeMo v1.0 model. It is noteworthy that the inverse problem posed had not been theoretically investigated before, and the proposed methods for its solution previously required rather large data sets, unlike the current work. Main results of research: an algorithm for the numerical solution of the problem was obtained, based on the method of steepest descent, which demonstrated good convergence for a set of synthetic data. The error in recovering the methane consumption rate by depth does not exceed 19 %, averaging 16 %. The error in recovering the methane concentration by depth, for a twofold increase in the number of measurement points, is 2.3 %.