Stanley H. Ward

ELECTROMAGNETIC FIELDS ABOUT A LOOP SOURCE OF CURRENT

Integral expressions for the electromagnetic field components produced by a horizontal loop, carrying a current Ieiωt 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 e. 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 ellips...

Three-dimensional mise-a-la-masse modeling applied to mapping fracture zones

A numerical scheme applying the method of volume integral equations has been developed for borehole‐to‐borehole and borehole‐to‐surface modeling of the apparent resistivity response of a thin conductive body in a half‐space; the inhomogeneity simulates a fracture zone in a geothermal system. The algorithm is applicable for the direct‐current case when the buried electrode is either inside (mise‐a‐la‐masse) or outside (near‐miss) the body. In implementing the scheme, the integral equation is transformed into a matrix equation as a result of discretizing the inhomogeneity into rectangular cells. All physical properties are assumed constant within each cell. The rectangular cells are used through‐out execution of the algorithm. The computed surface and subsurface apparent resistivity responses are examined for bodies of similar shape and size but with different orientations: (1) vertical, (2) horizontal, (3) dipping at 60 degrees, and (4) dipping at 30 degrees. The four bodies produce apparent resistivity cr...

UNIQUE DETERMINATION OF CONDUCTIVITY, SUSCEPTIBILITY, SIZE, AND DEPTH IN MULTIFREQUENCY ELECTROMAGNETIC EXPLORATION*

The response of a conductive, magnetic sphere in a uniform, alternating magnetic field is a function of the conductivity, permeability, and radius of the sphere and of the frequency of the alternations. Over one range of frequencies, eddy‐current density in any given sphere and secondary magnetic fields of the sphere are relatively constant and high. Over a much lower range of frequencies eddy currents are negligible, but the secondary magnetic fields may be of large constant amplitude but of polarity reversed to that of the higher frequency range. At some intermediate frequency the secondary magnetic fields will be entirely quadrature with respect to the inducing field. Utilization of this peculiar frequency dependence and of the geometry of the secondary magnetic fields permits unique determination of the conductivity, permeability, radius, and depth to the center of a buried sphere. The procedure for obtaining these variables is described in this article. As an added feature, it is shown that by comple...

THE INVERSION OF VERTICAL MAGNETIC DIPOLE SOUNDING DATA

It is demonstrated that the generalized linear inverse theory may be applied to vertical magnetic dipole sounding problems. An analysis of inversion of theoretical data for a two‐layer model illustrates the method and indicates certain features not inherent in the commonly practiced curve‐matching method of interpretation. In particular, the standard deviations of the layered model parameters may be estimated. Also the data may contain varying degrees of information about individual model parameters. Indeed, the information density matrix may be used to optimize the data information distribution by choosing only data that contributes information above some minimal level. The relative importance of the information distribution to the determination of individual model parameters may be assessed using both the structure of the information density matrix and the size of the estimated parameter standard deviations. Data may be removed until the estimated standard deviations of the parameters exceed some critic...

INDUCTIVE SOUNDING OF A LAYERED EARTH WITH A HORIZONTAL MAGNETIC DIPOLE

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 laye...

Evaluation of the measurement of induced electrical polarization with an inductive system

The induced polarization (IP) technique is based on the observation that variations of earth conductivity with frequency may be indicative of buried metallic mineralization. Conventional IP involves the use of grounded electrodes, the installation of which can be quite time consuming. However, the electromagnetic fields about an oscillating magnetic dipole also depend on ground conductivity. Thus, it is conceivable that we might be able to detect IP anomalies with an inductive system, thereby eliminating the need for grounded electrodes. An airborne induced polarization method is a theoretical possibility.Theoretical calculations based on a conductivity model determined experimentally at frequencies less than 30 hz suggest that the effect of polarizable material on electromagnetic response is quite small.In order to check the theory and to determine experimentally whether inductive IP is feasible, field tests were conducted in two areas in Nevada which exhibit strong conventional IP anomalies. The field tests consisted of measurements of the amplitudes of the electric and magnetic fields about a horizontal loop of wire carrying current at frequencies ranging from 15 hz to 1500 hz. The presence of the polarizable material is not evident in the inductive data; in fact, the observations can be fitted to theoretical curves for nonpolarizable models.Hence, on the basis of both theory and field tests, it is concluded that inductive IP based on amplitude measurements is not a practical exploration tool for environments such as that of the southwestern United States.

ELECTROMAGNETIC DEPTH SOUNDING EXPERIMENT ACROSS SANTA CLARA VALLEY

An electromagnetic depth sounding experiment with a horizontal loop carrying an oscillating current was carried out in Santa Clara Valley, California. The field data are interpreted in terms of the polarization parameters of the magnetic polarization ellipse. The chosen parameters are tilt‐angle, ellipticity, and the modulus of wavetilt. The electrical discontinuities deduced are in general agreement with well data and with a geologic section based on resistivity soundings. The results clearly reveal an intermediate, highly resistive layer, which is a permeable stratum for groundwater recharge. It is concluded that a portable electromagnetic sounding system, measuring only tilt‐angle and ellipticity, should easily locate highly resistive gravel deposits bounded by conductive clay beds. It is theoretically obvious that the system is useful in those regions where it is extremely difficult to inject current into the ground.

On induced electrical polarization and groundwater

Clay horizons and other clay‐bearing unconsolidated sediments are potential sources of induced‐polarization anomalies. If such anomalies may be detected above system noise, the induced‐polarization method may be of value for in‐situ classification of unconsolidated sediments encountered in hydrological projects. One such project exists in Santa Clara County where near‐surface unconsolidated sediments are frequently considered as potential recharge areas. Of four areas surveyed with induced‐polarization apparatus in Santa Clara County, only two yielded significant frequency‐effect anomalies, and in each of these two the frequency effects were of the order of 3 percent. These anomalous frequency effects may be related to clayey gravels. The dipole‐dipole array, with spreads of 10 ft and 20 ft, was typically used in the study.

Magnetotelluric models of the Roosevelt hot springs thermal area, Utah.

The Roosevelt Hot Springs (RHS) thermal area, which includes a hotwater-dominated fracture zone prospect, near the eastern margin of the Basin-Range tectonic province, conceivably possesses a whole family of resistivity structures that includes the following: deep hot brine reservoirs, deep-seated partially molten heat sources in the crust or upper mantle that drive the convective system, near-surface hydrothermal alteration zones, wet sedimentary fill in valleys, and a regional, apparently one-dimensional resistivity profile of the crust and upper mantle. This complex resistivity makeup, particular to RHS but probably similar to that at other geothermal areas in the Great Basin, must be treated as being fully three-dimensional (3-D). In an attempt to understand these structures, broadband (10/sup -3/ to 10/sup -2/ Hz) tensor magnetotelluric (MT) data were obtained including apparent resistivities (rho/sub a/), impedance phases (phi) and vertical magnetic field transfer functions for 93 sites in the vicinity of this resource area.

Recommendations for IP Research

The John S. Sumner Memorial International Workshop on Induced Polarization in Mining and the Environment was held 17–19 October 1994 in Tucson, Arizona. The event, dedicated to the memory of an IP pioneer, attracted 175 people from 18 countries. An objective was to get recommendations for geologic, geochemical, and geophysical research from IP users and practitioners for IP applications to mining and environmental problems. Conventional IP, as well as IP effects in EM and GPR, were considered. These measurements include complex conductivity, complex dielectric permittivity, and complex magnetic permeability in the frequency range 10−3–109 Hz in multidimensional earths.