INTRODUCTION

Electrical resistivity is a physical property of a material as are density, seismic velocity, magnetic susceptibility and many others. We have seen that seismic velocity is not a good indicator of sediment type. Resistivity, in contrast, is an excellent indicator of sediment type in a given geologic setting.

RESISTANCE OF AN OBJECT

With a simple laboratory experiment we can determine the resistance (ohms) of an object through which a current flows (amperes). The voltage (volts) driving the current equals the product of the current times the resistance. This familiar relationship is called Ohm’s Law.

Any number of objects can have the same resistance depending on the size, shape and materials. Thus resistance depends on a particular object and the experimental set-up; it is not a physical property of a material alone.

RESISTIVITY OF MATERIALS

By standardizing the size and shape of our test object we can define the resistivity of an object. Thus we can say that the resistivity (ohm-meters) of a material is the resistance of a unit cube with current flowing evenly across the cube from one face to the opposite face. Alternatively we can define the resistance of a cylinder as the resistivity times the length divided by the cross-sectional area (for current flowing along the length).

Defined in this way, resistivity is a true physical property of a material. It depends on the solid components, the pore fluid chemistry, the geometry of the solid parts and pores, the temperature and other factors. Before learning how to estimate resistivities of in situ earth materials let’s look at the units of resistivity.

UNIT CONVERSION

In the modern geophysical literature resistivity is expressed in ohm-meters although frequently conductivity is used instead. Conductivity (siemens per meter) is the inverse of resistivity.

To convert units just write out the resistance of a given unit cube in both sets of units. The resistance of the cube in ohms is the same regardless of what units are used for resistivity or lengths of the sides. Thus we see that resistivity in ohm-feet is 3.28 times larger than the same resistivity expressed in ohm-meters.

APPARENT RESISTIVITY

To estimate sensitivities underground we use an array of metal electrodes. Two of these inject electric current into the ground ("current electrodes") and two measure a voltage difference ("potential electrodes"). The use of four electrodes and low-frequency alternating current prevent charge migrations that would invalidate the measurements. In most near-surface earth materials conduction is by ions in the pore water.

The common "Wenner" array aligns the electrodes with a uniform spacing from one to the next in line. By convention the spacing distance is denoted "a". For this array we define an "apparent resistivity" equal to two pi times the voltage difference (between the inner electrodes) times the a-spacing divided by the current (between the two outer electrodes). The apparent resistivity is expressed in ohm-meters. For a truly uniform infinite half-space the apparent resistivity equals the true material resistivity. In the actual world the apparent resistivity is some sort of effective weighted resistivity of all the material through which the injected current flows. We’ll see later how to interpret apparent sensitivities in terms of hypothesized resistivity distributions.

RESISTIVITY PROFILES AND SURVEYS

In these cases apparent resistivities are determined in a line (profile) or on a grid (survey) using a fixed a-spacing. Usually the goal is to find patterns or anomalies that correspond to features of interest. Thus high resistivity areas in New Hampshire might correspond to either dry sand and gravel at the surface or to very shallow bedrock. Very low values might indicate glacial marine muds or perhaps contamination by road salt.

Thus a central issue is that many materials may have similar resitivities and that the same material may have a wide range of sensitivities depending, for example, on the pore fluid. Because the injected currents flow more deeply for a large a-spacing than for a small, the apparent resistivity over a feature depends on the spacing also.

Although we can use mathematical models to invert resistivity data, it is probably more common to just use empirical correlations. Lack of definite information makes the results of modeling very questionable. As we’ll see in the next class we usually do seek mathematical models for resistivity soundings.

READING

Birch, 1989, Northeastern Geology, 11, 124-132.