Comparison of integral equation and physical scale modeling of the electromagnetic responses of models with large conductivity contrasts

Abstract

A comparison is made between the results from two different approaches to modeling geophysical electromagnetic responses: a numerical approach based upon the electric-field integral equation and the physical scale modeling approach. The particular implementation of the integral-equation solution was developed recently, and the comparison presented here is essentially a test of this new formulation. The implementation approximates the region of anomalous conductivity by a mesh of uniform cuboidal cells and approximates the total electric field within a cell by a linear combination of bilinear edge-element basis functions. These basis functions give a representation of the electric field that is divergence free but not curl free within a cell, and whose tangential component is continuous between cells. The charge density (which arises from the discontinuity of the normal com-ponent of the electric field across interfaces between cells of different conductivities and between cells and the background) is incorporated in a similar manner to integral equation solutions to dc resistivity modeling. The scenarios considered for the comparison comprise a graphite cube of [Formula: see text] conductivity and 14-cm length in free space and in brine ([Formula: see text] conductivity). The transmitter and receiver were small horizontal loops; measurements and computations were made for various fixed transmitter-receiver separations and various heights of the transmitter-receiver pair for frequencies ranging from [Formula: see text]. The agreement between the numerical results from the integral-equation implementation and the measurements from the physical scale modeling was very good, contributing to the verification of this particular implementation of the integral-equation solution to electromagnetic modeling.