On the numerical solution of direct and inverse problems of geoelectromagnetic exploration

Numerical methods for the solution of direct and inverse problems of above-ground, surface and underground electromagnetic exploration geophysics are considered. Approximations of two-dimensional and three-dimensional boundary value problems are made by finite volume methods of high accuracy. The systems of linear algebraic equations with high order sparse matrices are solved by fast incomplete factorization algorithms with acceleration by conjugate gradients. The questions of computing apparent resistivity and sensitivity of characteristics fields to variations of geometric and material properties of media are described. The solution of inverse problems are implemented by optimization approaches including the interior point methods, the Lagrange multipliers and application of sequential quadratic programming.