Numerical solving of the one-dimensional forward magnetotelluric sounding problem using computational grid adaptation approach

The paper considers an implementation of an adaptive computational grid constructing algorithm inside the numerical solution of the one-dimensional forward magnetotelluric sounding problem (the Tikhonov-Cagniard problem). The numerical solution of the problem is realized by the method of local integral equations, which was proposed by authors earlier. An adaptive computational grid construction is based on geometrical principles, which conduct approximation of the electrical conductivity function via optimization of its’ piecewise-constant interpolant. Numerical experiments are carried out to study and illustrate the effectiveness of the combined method. Approbation was realized on the Kato-Kikuchi model with known exact solution.