THEORY OF BOREHOLE MAGNETIC SUSCEPTIBILITY MEASUREMENTS WITH COIL PAIRS

Abstract

The boundary value problem for an axially symmetric configuration of a transmitter‐receiver coil pair in a borehole is considered with particular attention to the “quadrature component” of voltage induced at the receiver coil. It has been known from mathematical expressions previously presented in the literature on induction logging that the quadrature voltage is dependent upon the magnetic permeabilities of the formation and borehole media. The purpose of this investigation was to explore the nature of that dependence in sufficient detail to ascertain some features of its potential usefulness for magnetic susceptibility measurements, particularly of the type contemplated in “Project Mohole.” Although that project is no longer being actively pursued, results of the study are of possible interest in magnetic susceptibility measurements for other purposes, such as geologic correlation. Numerical results from a digital computer program show that the quadrature voltage at the receiver coil is essentially independent of changes in borehole or formation conductivity under the conditions for which the computations were performed. Effects of coil size and the spacing between coils on the quadrature receiver coil voltage were used to determine optimum coil geometry. Analytical expressions valid for small ratios of coil diameter to coil spacing confirm the computer results throughout their domain of validity. An investigation of the sensitivity of the method shows that, when coil geometry is optimum, a given percentage change in κ yields a very slightly greater percentage change in receiver coil voltage. With proper coil spacing, the dependence of receiver coil voltage on κ is very well described by an equation of the form [Formula: see text] where γ is a constant nearly equal to one. This result was verified both analytically and numerically by the calculations from the full expression for voltage.