To comprehend the bases and the interpretational techniques of electrical prospecting methods, requires first a knowledge of the tools of electromagnetic theory. The ability to solve a boundary-value problem in electromagnetic theory then becomes the objective. All electromagnetic phenomena are governed by the empirical Maxwell's equations; we must start with them. Maxwell's equations are uncoupled first-order linear differential equations but can be coupled by the empirical constitutive relations which reduce the number of basic vector field functions from five to two. Care must be taken in selecting the form of the constitutive relations pertinent to the earth. In particular, for most earth problems, we assume isotropy, homogeneity, linearity, and temperature-time-pressure independence of the electrical parameters of local regions of the earth. A more complicated earth model is formed by juxtaposition of several such regions.A concept fundamental in electricity and magnetism is that of magnetic and electric polarization. We introduce the polarization vector in a symmetrical sense which demands recognition of, at least, the theoretical existence of magnetic current density and magnetic monopoles, as well as electric current density and electric monopoles. Maxwell's equations are generalized and made more symmetric in the process with a conceptual advantage afforded when we come to deal with scalar and vector potentials. Total vector polarization functions, consisting of the algebraic sums of induced and source parts, frequently facilitate description of a physical problem.Many boundary-value problems can be solved in terms of the vector electric and magneticfield intensity functions. In an earth composed of several juxtaposed homogeneous isotropic linear regions, a solution of a wave equation is postulated for each region. These solutions must be matched at every boundary according to prescribed boundary conditions on two vector field functions or potentials. The wave equation used for each region is derived directly 132 Ward and Hohmann from Maxwell's equations and really represents a compact form of these equations. If the wave equation is homogeneous, no sources are present in that region. If the wave equation is inhomogeneous, sources exist in that region. Often a boundary-value problem is difficult to solve in terms of vector field functions andis easier to solve in terms of vector and/or scalar potential functions from which the vector field functions may be derived. Several different sets of potential functions appear in the literature; we use the Schelkunoff potentials because of their symmetry and because of the ease of relating them to the TE and TM modes of excitation. Any electromagnetic field, in a homogeneous, source-free region, may be decomposed into a part for which the electric field is transverse to some axis (TE mode) and a part for which the magnetic field is transverse to this same axis (TM mode). Mode decomposition simplifies the solution of boundary-value problems. The development of a se...

In‐situ complex resistivity measurements over the frequency range [Formula: see text] to [Formula: see text] have been made on 26 North American massive sulfide, graphite, magnetite, pyrrhotite, and porphyry copper deposits. The results reveal significant differences between the spectral responses of massive sulfides and graphite and present encouragement for their differentiation in the field. There are also differences between the spectra of magnetite and nickeliferrous pyrrhotite mineralization, which may prove useful in attempting to distinguish between these two common IP sources in nickel sulfide exploration. Lastly, there are differences in the spectra typically arising from the economic mineralization and the barren pyrite halo in porphyry copper systems. It appears that all these differences arise mainly from mineral texture, since laboratory studies of different specific mineral‐electrolyte interfaces show relatively small variations. All of the in‐situ spectra may be described by one or two simple Cole‐Cole relaxation models. Since the frequency dependence of these models is typically only about 0.25, and the frequency dependence of inductive electromagnetic coupling is near 1.0, it is possible to recognize and to remove automatically the effects of inductive coupling from IP spectra. The spectral response of small deposits or of deeply buried deposits varies from that of the homogeneous earth response, but these variations may be readily determined from the same “dilution factor” [Formula: see text] currently used to calculate apparent IP effects.

The electromagnetic fields scattered by a three‐dimensional (3-D) inhomogeneity in the earth are affected strongly by boundary charges. Boundary charges cause normalized electric field magnitudes, and thus tensor magnetotelluric (MT) apparent resistivities, to remain anomalous as frequency approaches zero. However, these E‐field distortions below certain frequencies are essentially in‐phase with the incident electric field. Moreover, normalized secondary magnetic field amplitudes over a body ultimately decline in proportion to the plane‐wave impedance of the layered host. It follows that tipper element magnitudes and all MT function phases become minimally affected at low frequencies by an inhomogeneity. Resistivity structure in nature is a collection of inhomogeneities of various scales, and the small structures in this collection can have MT responses as strong locally as those of the large structures. Hence, any telluric distortion in overlying small‐scale extraneous structure can be superimposed to arbitrarily low frequencies upon the apparent resistivities of buried targets. On the other hand, the MT responses of small and large bodies have frequency dependencies that are separated approximately as the square of the geometric scale factor distinguishing the different bodies. Therefore, tipper element magnitudes as well as the phases of all MT functions due to small‐scale extraneous structure will be limited to high frequencies, so that one may “see through” such structure with these functions to target responses occurring at lower frequencies. About a 3-D conductive body near the surface, interpretation using 1-D or 2-D TE modeling routines of the apparent resistivity and impedance phase identified as transverse electric (TE) can imply false low resistivities at depth. This is because these routines do not account for the effects of boundary charges. Furthermore, 3-D bodies in typical layered hosts, with layer resistivities that increase with depth in the upper several kilometers, are even less amenable to 2-D TE interpretation than are similar 3-D bodies in uniform half‐spaces. However, centrally located profiles across geometrically regular, elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic (TM) algorithm, which implicitly includes boundary charges in its formulation. In defining apparent resistivity and impedance phase for TM modeling of such bodies, we recommend a fixed coordinate system derived using tipper‐strike, calculated at the frequency for which tipper magnitude due to the inhomogeneity of interest is large relative to that due to any nearby extraneous structure.

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The finite‐element method can be used to solve the differential equations which describe electrical and electromagnetic (EM) field behavior. The equations are, respectively, Poisson's equation and the vector, damped wave equation. The finite‐element equations are derived, in both cases, using the minimum theorem. While both tetrahedral and hexahedral elements may be used for the modeling of the resistivity problem, only hexahedral elements give satisfactory results for the EM problem. A disadvantage of the relatively simple mesh design used in the approach described here is the presence of long thin elements. Such elements have very poor interpolating properties, and they adversely affect the rate of convergence of the overrelaxation technique used in solving the resulting system of linear equations. For the modeling of resistivity data over an earth with one plane of symmetry, the system of equations typically has about 9000 unknowns. About 50,000 unknowns are needed to give a satisfactory solution to an EM problem where the earth has one plane of symmetry. The advantage of solving these problems with a technique such as the finite‐element method is that earths with an almost arbitrary distribution of conductivity can be modeled. On the other hand, an integral‐equation method can be far more cost effective for small inhomogeneities. The results from the resistivity algorithm show the adverse effect of an irregular, conducting, and polarizable overburden on dipole‐dipole, induced polarization surveys. Modeling of a horizontal loop EM survey illustrates the importance of assessing the host rock conductivity before attempting to interpret inhomogeneity responses.