Advances in three‐dimensional magnetotelluric modeling using integral equations

Abstract

Recent progress in integral equation modeling of three‐dimensional magnetotelluric responses includes the ability to simulate 3-D structures which outcrop (excluding topography), which transect layer interfaces, and which extend indefinitely in one or more directions. The most important factor in achieving this capability is an accurate treatment of the electric surface charge. In particular, a previous integro‐difference formulation for evaluating charges has been abandoned in favor of true surface integrations over the source cells with potential differencing across the field cells in the 3-D body. The new procedure constitutes a good approximation to Galerkin’s method while preserving internal consistency in terms of pulse basis functions. To verify outcropping structures, juxtaposed conductive and resistive prisms at the surface are simulated and compared to 2-D results. An elongate version of the 3-D model shows good agreement with both transverse electric and transverse magnetic modes of the 2-D response at both high and low frequencies. Apparent finite strike length effects for a short version of the 3-D body are physically reasonable. To verify structures cut by layer interfaces, an elongate tabular conductor at the base of a resistive overburden layer, which is in immediate contact with a tabular resistor at the top of a conductive basal half‐space is considered. All 3-D field components are in good agreement with 2-D transverse electric and transverse magnetic calculations from the surface down through or beside the body into the conductive basement below. The proper discontinuity of the normal component of the electric field across inhomogeneity boundaries is simulated well by the algorithm, but not exactly because of the pulse nature of the basis functions. Finally, outcropping and infinitely extended structures are checked by comparison of an offset basin model with very low frequency, thin‐layer calculation. In general, best results are obtained at cell body centers or face centers, but are not reliable over cell corners. From the offset basin study, we show also that 2-D transverse magnetic mode modeling of corresponding 3-D responses cannot be carried out indiscriminately over arbitrary structures without propagating errors to substantial depths in the 2-D model cross‐section.