The apparent resistivity from a helicopter-borne frequency-domain electromagnetic (EM) system is typically obtained from the in-phase and quadrature responses arising from the flow of conduction currents in the earth. The most commonly used resistivity algorithms, derived from half-space models and using single-frequency data, do not account for magnetic polarization and consequently do not yield a reliable value for apparent resistivity in highly magnetic areas. This is because magnetic polarization modifies the EM response, causing the computed resistivity to be erroneously high. The impact of magnetic permeability on the EM response is much greater for the in-phase component than for the quadrature component. If magnetic polarization is to be ignored, the calculation of the apparent resistivity using the quadrature component at two frequencies (the quad-quad algorithm) is less subject to error from magnetic polarization than if the in-phase and quadrature responses at a single frequency are used (the in-phase–quad algorithm). The quad-quad algorithm, however, can display undesirable behavior for large induction numbers, i.e., when conductivities and frequencies are large. Determining which algorithm is optimum is a data-dependent choice, which, of course, is area dependent.
We have studied the behavior of the quad–quad (apparent) resistivity and its comparison to in-phase–quad resistivity to determine the conditions under which the use of quad-quad resistivity is appropriate. For a two-layer earth, the behavior of the quad-quad resistivity depends mainly upon the ratio of the lower frequency fL to the upper-layer resistivity ρ1. If this ratio is low, the quad–quad resistivity will behave well. In areas yielding a high value of the ratio fL/ρ1, the quad–quad resistivity may lie outside of the range of the true resistivities of the earth and therefore provide misleading information. Our studies therefore suggest that the quad–quad resistivity algorithm should be avoided in areas where the ratio is large, i.e., when using high frequencies in conductive areas. The term large is relative. For a two-layer case, for example, the use of quad–quad resistivity is only recommended for magnetic areas where fL/ρ1 < 500 Hz/ohm-m, when conductive cover exists, and where fL/ρ1 <50 Hz/ohm-m when a conductive basement underlies resistive cover. In spite of these limitations, quad-quad resistivity is often preferable to in-phase-quad resistivity in highly magnetic areas.