Inductive Sounding of a Layered Earth With a Horizontal Magnetic Dipole

Abstract

A complete solution of the boundary value problem of a horizontal magnetic dipole over homogeneous and n‐layered half‐spaces is outlined. Quasi‐static expressions for the electric and magnetic fields have been obtained and a comparison of the complete solution with the quasi‐static approximation in practical frequency ranges is made. An analysis of the phases and amplitudes of the magnetic field components and of the polarization parameters of the magnetic field reveals that the phase of the vertical component of the magnetic field and the ellipticity of the magnetic field polarization ellipse are the most sensitive indicators of layering. Amplitude measurements are, in general, less effective than phase measurements for resolution of layered earth structures. Results from both parametric and geometric modes of sounding have been studied in detail for a number of two‐ and three‐layered models of varying thicknesses and conductivity contrasts. Deduction of layering for different thicknesses of the top layer from the measurements of [Formula: see text] and polarization parameters, seems relatively easier when the underlying layer is more conductive than the top layer. For models in which the underlying layer is less conductive than the top layer, the phases of both [Formula: see text] and wave tilt are more diagnostic of changes in layer parameters.

On the Computation of Polarization Ellipse Parameters

“…Dey and Ward (1970) are exactly a factor of fwo larger than would be observed from field measurements. No numerical results are given for this parameter since the relationship is an exact factor of two.…”

“…In addition, we will show an error in ellipse parameters computed by Dey and Ward (1970). Amplitudes of the components of the magnetic field generated by a magnetic dipole source arc commonly normalized with the primary magnetic field or, equivalently, the mutual coupling factor between the source and receiver.…”

“…We will discuss in this section the effects of the use of equation (6) rather than equation (4), which has been used by Dey and Ward (1970) and Ryu et al (1970) for the HMD and VMl) sound ing problems, respectively. In addition, we will show an error in ellipse parameters computed by Dey and Ward (1970).…”

Reconstruction of 1-D conductivity from dual‐loop EM data

“…Ryu et al (1970) present a solution for the forward problem of a horizontal loop that can be adapted easily to the case of a vertical magnetic dipole source. Dey and Ward (1970) and Ward and Hohmann (1988) compute the forward responses of a horizontal magnetic dipole over a layered earth. They show that when the measurements are taken above the earth, the secondary field resulting from the transverse magnetic mode associated with a horizontal magnetic dipole can be ignored.…”

A simple method for calculating apparent resistivity from electromagnetic sounding data

“…This method is accurate and stable but requires a computer or extensive hand calculations, and it is not well suited to field applications. Dey and Ward (1970) briefly discuss how to determine apparent conductivity from horizontal dipole EM sounding data by matching observed data to half-space field curves. Their discussion involves determining the layer conductivities from low-frequency and high-frequency asymptotic approximations and finding the top layer thickness by using twolayer master curves.…”