Integral expressions for the electromagnetic field components produced by a horizontal loop, carrying a current [Formula: see text] and placed on or above the surface of an n‐layered half‐space, are deduced in a form such that numerical integration can be performed easily. The expressions are free of approximations and completely general for all frequencies. They are constrained only to the uniformity of current around the transmitting loop. The resulting computed electromagnetic fields are valid for arbitrary values of the electrical parameters σ, μ, and ε. The quasi‐static approximation for the region above the half‐space, wherein the wave equation is replaced by the Laplace equation, can be avoided. Measurements outside the loop constitute induction depth sounding. Induction depth sounding curves of field components and magnetic polarization parameters show good resolution of subsurface layering. In particular, it is suggested that the measurements of tilt angle and/or ellipticity of the magnetic polarization ellipse should be made to determine earth layering because of the rapidity and ease of these measurements in field operation. It is shown that the radius of the loop should, in the general case, be taken into account in theoretical computations. Measurements at the center of the loop constitute central induction sounding. Central induction sounding responses are diagnostic only for layered earth models in which conductivity increases with depth. Measurement of the quadrature part of the vertical magnetic field is particularly promising. Theoretical curves for earth models consisting of one layer overlying a half‐space are given for the quasi‐static case for induction depth sounding, and for the nonquasi‐static (general) case for central induction sounding. In another application, the response from a homogeneous, conductive, magnetic half‐space with the central induction method at low frequencies reveals the feasibility of in‐situ determination of static magnetic permeability. In a final application, it is shown that the effect of ground conductivity should be included in making the normal correction to Turam data whenever the apparent conductivity of the ground is greater than [Formula: see text].
Nonexistence of smooth electromagnetic fields in nonlinear dielectrics: Shock development in a half-space
