Mutual Coupling of Loops Lying on the Ground

Abstract

The theory of a method to measure electrical ground constants by mutual coupling of loops is outlined. Curves are given in parametric form showing the dependence of the mutual impedance on conductivity, dielectric constant, frequency, and separation. An expression is derived in the appendix for the field of a circular wire loop laid on a homogeneous conducting ground.

Low induction number, ground conductivity meters: A correction procedure in the absence of magnetic effects

“…The electromagnetic solution for an elevated magnetic dipole on or above a homogenous earth was developed by Wait (1954Wait ( , 1955. The model was extended to the 2-layer case by Frischknecht (1967).…”

Rapid computation of electromagnetic fields for high-frequency sounding in the 300 kHz to 30 MHz range over layered media

“…The essence of the new method uses a Q-factor correction for extending a closed-form half-space analytic solution to a layered earth model. Use of the Q-factor in this context was first studied by Wait (1962; p. 53-61). Kraichman (1976) also discusses when the Q-factor method can be used to provide a good approximation to an exact layered earth solution.…”

“…Use of the Q-factor in this context was first studied by Wait (1962; p. 53-61). Kraichman (1976) also discusses when the Q-factor method can be used to provide a good approximation to an exact layered earth solution.According to Wait (1962) and Kraichman (1976), the Q-factor approach may be used if the dipole fields can be approximated by a single normally incident plane wave at the receiver in the top layer. Fortunately, for the high-frequency range of interest with the HFS system, and with moderately conductive and dielectric earth models, the Q-factor method (also called the HFS Q-method) is usually a very good approximation to the exact solution for a layered earth.…”

“…A case history paper on use of the HFS in field applications is also given by Stewart et al (1994). In the latter paper, mention of a quick reconnaissance method of HFS data inversion is given by Anderson (1991), where complex image theory and the Q-factor method was first introduced to obtain fast approximate image solutions for layered models.To obtain improved forward and/or inverse solutions for HFS over a layered earth, I begin with an exact half-space formulation (Wait, 1954) for the magnetic H fields and electric E field components in cylindrical coordinates for a vertical magnetic dipole (VMD) loop source on the earth's surface, with exp(+/otf) time dependence, (5), r is the VMD transmitter and receiver separation, where r > 0 m, and m is the magnetic dipole moment (ampere-m2). The terms 7n(z) and Kn(z) in equation (2) are modified Bessel functions of order n and complex argument z defined in equation (5).…”

“…However, the numerical integration and Hankel transform digital filter obviously begins to break down at about 100 MHz (1 x 108 Hz). Thus, for this example, the HFS Q-method gives superior accuracy over numerical integration at all frequencies, and especially in the extreme gigahertz range.For more examples and a detailed discussion on the range of validity of the Q-factor method to approximate layered model solutions, refer to Wait (1962) and Kraichman (1976). …”