The E Perpendicular Polarization Response of a Two-Dimensional Heterogeneous Layer Modeled by Two Thin Sheets in a Horizontally Stratified Half-Space

The thin sheet approximation is a useful tool for modeling heterogeneous geoelectric structures that are large in horizontal extent as compared with their vertical extent. The primary restriction introduced by the thin-sheet method is the requirement that the anomalous region being modeled with a thin sheet must be electrically thin at the frequency of operation. I have expanded the flexibility of the thin-sheet technique to model two-dimensional structures by analyzing the response to E perpendicular polarization, also known as the transverse magnetic (TM) mode, when a heterogeneous Earth is modeled by two thin sheets over a horizontally stratified half-space. Numerical results are obtained for a representative model using both one and two thin sheets, and the results are compared. At frequencies where the anomalous layer is no longer electrically thin, the percentage phase error in the magnetotelluric impedance that results from the single thin sheet model is much more severe than the percentage magnitude error. If the contribution of the induced vertical current density to the horizontal electric field is neglected, the additional computational effort required by the addition of a second thin sheet can be significantly reduced. Numerical results are obtained using this approximation and compared to the results obtained when the vertical contribution is not neglected. The error generated by this approximate technique is very small except near sharp conductance boundaries.