Numerical Solution of the One-Dimensional Forward Magnetotelluric Sounding Problem Using a Computational Grid Adaptation Approach

The paper considers an implementation of an adaptive computational grid constructing algorithm in a numerical solution of the one-dimensional forward magnetotelluric sounding problem (the Tikhonov–Cagniard problem). The numerical solution of the problem is realized by a method of local integral equations which was proposed by the authors previously. The adaptive computational grid construction is based on geometrical principles of optimizing a piecewise constant interpolant of the electrical conductivity function to be approximated. Numerical experiments are carried out to study and illustrate the effectiveness of the combined method. The algorithm is tested on the Kato–Kikuchi model with a known exact solution.