The frequency-domain electromagnetic response of a confined conductor buried in a resistive host has received much attention, particularly in the context of mineral exploration. In contrast, the problem of the electromagnetic response of a confined resistor buried in a conductive host has been less thoroughly studied. However, resistive targets are important in geotechnical and hydrologic studies, archaeological prospecting, and, more recently, offshore hydrocarbon exploration. I analytically address the problem of the electromagnetic response of a completely resistive cylindrical cavity buried in a conductive host in the presence of a simplified 2D electric dipole source. In contrast to the confined conductor, which channels and induces current systems, the confined resistor deflects current and produces additional eddy current systems in the conductive host. I apply this theory to model the response of a grounded electric dipole-dipole system operating over a range of frequencies from 0 Hz to 10 kHz, in the presence of a horizontal 5-m radius insulating cylinder located 1-m beneath the surface of a uniform earth. This represents a common hazard encountered during mining and civil engineering operations. Results show that such an insulating cavity increases the recorded electric field amplitude and phase delay at all transmitted frequencies. These observations suggest that a broadband electromagnetic prospecting system may provide additional information about the location and extent of a void, over and above a standard dipole-dipole resistivity survey. When the host skin depth is much larger than all other length scales, the response can be approximated by an equivalent single dipole unless the cylinder’s radius is much larger than its distance from the transmitter. This result provids a useful rule of thumb to determine the acceptable range over which a resistive target can be modeled by a distribution of dipoles.
Semiclassical scattering of an electric dipole source inside a spherical particle
