Numerical Solutions of the Response of a Two‐dimensional Earth to an Oscillating Magnetic Dipole Source

Abstract

A finite difference formulation is developed for computing the frequency domain electromagnetic fields due to a point source in the presence of two‐dimensional conductivity structures. Computing costs are minimized by reducing the full three‐dimensional problem to a series of two‐dimensional problems. This is accomplished by Fourier transforming the problem into the x-wavenumber [Formula: see text] domain; here the x-direction is parallel to the structural strike. In the [Formula: see text] domain, two coupled partial differential equations for [Formula: see text] and [Formula: see text] are obtained. These equations resemble those of two coupled transmission sheets. For a requisite number of [Formula: see text] values these equations are solved by the finite difference method on a rectangular grid on the y-z plane. Application of the inverse Fourier transform to the solutions thus obtained gives the electric and magnetic fields in the space domain. The formulation is general; complex two‐dimensional structures containing either magnetic or electric dipole sources can be modeled. A quantitative test of accuracy is presented which compares the finite difference results to analytic results for a magnetic dipole on a homogeneous half‐space. In addition, the computed results for a two‐dimensional model are qualitatively compared to published results for a three‐dimensional analog model. Synthetic field data for surveys over several different bodies of anomalous conductivity are presented. Two of these demonstrate the nonuniqueness of single frequency data interpretation. Results also show that the characteristic form of the response given by the anomalous body can be heavily dependent upon the structure of the host medium. This is especially true for horizontal magnetic dipole source surveys.

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Otze - Airborne EM Inversion on Unstructured Model Grids

“…Both types of models can be inverted using either a 1D forward algorithm (Weidelt, 2006) or multidimensional solver based on a FD approach. For a 2D model, the latter would be a 2.5D forward solver (Stoyer and Greenfield, 1976). The 3D solver uses a multigrid preconditioner for efficient simulations (Plessix et al, 2007).…”

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