Quasi‐static Transient Response of a Conducting Permeable Sphere

Abstract

When a conducting body is immersed in a time‐varying magnetic field, eddy currents are induced. These, in turn, produce a secondary magnetic field which may be detected by an observer external to the sphere. It has been demonstrated that a measurement of the external field can be used to estimate the conductivity of the body if certain assumptions are valid. For example, Ward (1953) has shown that the conductivity and permeability of geological core specimens from diamond drill holes may be determined by examining the frequency dependence of the time‐harmonic response of the specimen. In principle, the same information should also be available from the time response of the specimen for a suddenly applied magnetic field (Wait, 1951). In this paper, we wish to discuss the transient solution when a homogeneous conducting sphere is under the influence of a transient magnetic field. Also, as suggested earlier by Wait (1951), the actual time‐domain electromagnetic response of a massive sulfide body should exhibit features akin to this transient solution. Thus, the results should have application in mining geophysics. We consider both a nonpermeable and a permeable sphere, using a different approach for each. Because the former is a special case of the latter, a consistency check is obtained.

Time Domain Response of a Sphere in the Field of a Coil: Theory And Experiment

“…The method used in Section II-A to derive this step response is similar to that of Wait and Spies [9]. In this method a time-0196-2892/84/0700-0360$01.00 © 1984 Canadian Crown Copyright harmonic solution is derived first and then Laplace transform techniques are used to obtain time-domain solutions.…”

“…Since X(jico) is the only frequency dependent factor in (4), time dependence of the step response can be derived from it. Following the procedure used by Wait and others [9], [I 1], the time-dependent part gn(t) of the anomalous potential due to a unit current step u(t) applied at t = 0 can be found by applying the inverse Laplace transform definition In order to obtain a simple decaying step response without oscillations, snm must lie on the negative real axis of the s-plane.…”

“…This work was supported by the Chief Research A considerable amount of related work has been done in geophysics [9]- [11] and nondestructive testing [3], [12], [13]. However, work done in geophysics usually uses a uniform or dipole primary field and calculates the object's magnetic field response only.…”

Parametric Forms and the Inductive Response of a Permeable Conducting Sphere

“…for t > 0, where δ n are the positive solutions of (Wait and Spies, 1969). Coefficients δ n are spaced roughly π apart, with…”

Phenomenology and Signal Processing for UXO/Clutter Discrimination

“…They are normalized by the transmitter current. The dashed line shows a fit of the data to the expected TEM response for a permeable sphere [7], using a conductivity of 3.2×10 6 S/m and a relative permeability of 62.5, values which are within the expected range for carbon steel [8]. Figure 3 Signature data on 996 clutter items were collected with the MTADS TEM array.…”