Very low frequency magnetotelluric and dipole-dipole responses of three-dimensional thin-layer resistivity structure modeled using finite elements

An algorithm to simulate the very low frequency magnetotelluric and dipole-dipole responses of three-dimensional thin-layer inhomogeneity has been developed from an existing finite element program used to simulate resistivity/IP signatures of 2-D earth sections. The 3-D body is confined to and extends uniformly across a thin layer overlain by air and underlain by infinite resistivity. Electric fields are obtained through differentiation of piecewise parabolas fit to nodal voltages while magnetic fields arise from integration of the free-space Green's tensor over secondary current perturbations throughout the thin layer. Dipole-dipole apparent resistivities arise through application to nodal voltages of the logarithmic geometric factors appropriate to continuously grounded line sources of current. Checks on accuracy of the simulation utilize analytic solutions, 2-D AC plane-wave results using finite elements, and a surface integral equations technique.