Numerical modeling of borehole-surface electromagnetic responses with 3-D finite difference method and comparison with physical simulations

Borehole-surface electromagnetic method (BSEM) is a high-accuracy electromagnetic prospecting method that uses AC-powered vertical finite line source as the excitation source. The observed surface electromagnetic field is inverted for the subsurface conductivity structure. In this paper, the total field is separated into a primary part, due to a horizontally layered host medium, and a secondary part due to 3-D heterogeneities. After solving for the primary field with an analytical method, the frequency-domain second-order differential equation for the secondary field is discretized by finite differences. A sparse matrix storage scheme is employed and a BiCGSSTAB(m) method with a diagonal matrix preconditioner is used to obtain the secondary field as well as the 3-D BSEM response of the model. We compare the result of anomalous responses of three-layered medium derived by 3-D forward modeling with the result of semi-analytical solution. We also perform physical simulation and 3-D numerical forward modeling based on similarity criterion. As a result, the shape of both anomalous response curves are the same, which validates the 3-D numerical simulation method. The anomalous fields of 3-D numerical forward and physical simulation share similar anomalous feature of symmetric bimodal structure that is consistent with its harmonic response curve. It demonstrates that borehole-surface electromagnetic method can be used not only for prospection by employing a multi-frequency response, but also can provide multi-angle information about subsurface anomaly by varying relative depths of vertical finite line source in the borehole.