Vertical and horizontal resistive limit formulas for a rectangular-loop source on a conductive half-space

We derived analytic expressions for the time integrals of vertical and horizontal transient B-field responses on a conductive half-space excited by a rectangular-loop source. These formulas were applied in two ways in a fast transient electromagnetic (TEM) inversion scheme. Indefinite integrals were used to extrapolate measured TEM decays to early and late time to convert the observed data to resistive limits. Definite integrals over all time provided estimates for the resistive limit response of host-rock. An apparent conductivity of the host was calculated from the resistive limits via a simple least-squares formulation. These applications of the formulas were tested on synthetic and real TEM data. © 2012 Society of Exploration Geophysicists.