Numerical modeling of EM fields over local anomalies with a vertical axis of symmetry

A method for numerical modeling of quasi-stationary electromagnetic fields in axially symmetric media is proposed. It is based on the direct finite-element method and the use of special basis functions. Assuming cylindrical coordinates r, φ, z, the three-dimensional solution is presented as a superposition of fields with the azimuthal dependence exp(inφ). For each case this results in a system of two equations of elliptical type in two scalar functions in the (r, z) plane.

The discretization leads to the conservative nine-points difference scheme. The system of linear equations is solved by means of the LU-decomposition technique, the band structure of the matrix being taken into account.

The program is tested using analytical results (DC asymptote) for a near-surface inhomogeneity. Comparison also is made with 2D results (H-polarization) for the model of a local well conducting inclusion in a three-layered Earth.