1967. "Electrical Methods", Mining Geophysics Volume II, Theory, Don A. Hansen, Walter E. Heinrichs, Jr., Ralph C. Holmer, Robert E. MacDougall, George R. Rogers, John S. Sumner, Stanley H. Ward
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We are concerned in this section with establishing the basic material upon which the subsequent sections of the chapter depend. Thus we must establish the Maxwell field equations and the wave potentials in the unitary system to be utilized (mks)follow this with solutions of the wave equation pertinent to some of the later development. This abbreviated summary of electromagnetic fundamentals then permits us to follow the subsequent presentations of specific problems in electromagnetic theory; the problems chosen are essential to our comprehension of the electrical methods.
Electrical conductivity is the movement of electrical charge from one location to another. Because the charge may be carried by ions or electrons, whose mobilities vary from material to material, there is a full spectrum of conductivities ranging from highly conducting metals to nearly perfect insulators, as illustrated in Figure 1
Electrical conductivity can be derived from the relation where n is the number of charge carriers in a material, e is the charge carried by eachu is the mobility of the carriers. The mobility is defined as the drift velocity per unit electric field. Since the charge carriers may be ions or electrons (or “holes” as we shall see later), we classify conduction in solids as ioncc or electroncc within the range 1 to 10s mho/m. Below this range of conductivity, materials may be semiconductors or insulators. For porous media, such as rocks at the earth’s surface, conductors extend into the range normally covered by solid semiconductors.
Ionic conductivity involves the ordered movement of ions in an electrolyte upon application of an external electric field. In the absence of an electric field, the ions move randomly as a result of thermal agitation and collisions with other ions and atoms. Since both cations and anions are present in an electrolyte, the conductivity can be expressed as where the numbers and mobilities of the positive and negative ions are indicated by superscript signs. A temperature increase results in a conductivity increase since the mobility of both ion species is
Figures & Tables
The relative merits of any geophysical method in a given situation can be predicted by careful study of the expected message-to-noise1 ratio. For example, let us draw or deduce from the subsequent text, the anomaly formulas due to a spherical inhomogeneity in the subsurface and the symbols in each formula are explained in the text. The gravity, magnetic, resistivity, and induced-polarization surveys all are volume dependent, whereas the electromagnetic method is dependent only upon the area of the inhomogeneity, normal to the inducing field. Thus, a thin disk can give nearly the same electromagnetic anomaly as a sphere of the same radius.
If we can make a reasonable estimate of the physical property contrast anticipated to exist between ore and host, we can then predict the anomaly magnitude expected from the sphere, when buried at any given depth, via the geometric factor. Note that from this viewpoint, given the maximum or saturation value of unity for the physical property factor, the magnetic and resistivity methods theoretically give the same percent anomaly due to a sphere. The physical property function M–iN for the electromagnetic method has a maximum value of one half for a sphere while the change with frequency of the electrical resistivity contrast.
Thus, except for a factor of two, the magnetic, resistivity, electromagnetic, and induced-polarization methods should give the same maximum anomaly. Note that the geometry of the anomalous fields for each of these methods is an induced dipole with a resultant fall-off of peak anomaly proportional to the inverse cube of the depth to the center of the sphere below the measuring plane. In contrast, the gravity method exhibits an inverse second power fall-off due to an induced monopole. The density contrast between ore and host sometimes exhibits a maximum value of two. Thus f r om a maximum message viewpoint, one would be inclined to rate the methods in the order given above. However, we need to counter this bias by considering expected values of the physical property factor and the noise for any given geologic situation.
Let us look, then, at iron ore, massive sulfides, and disseminated sulfides, items treated i n Volume I. We should expect the following physical property ranges: A very wide range of properties is evident and hence the prediction of an anomaly magnitude looks hopeless.