Papers - Electrical Methods - Interpretation of Resistivity Measurements (With Discussion)

Earth-resistivity measurements are often of service in obtaining information regarding geological formations, particularly when applied to structural problems. In such problems the masses of the various bodies are large, and have a corresponding effect on the average resistivity of the soil. Much work has been done using such measurements, but in general the method of interpretation employed is empirical. Since certain simple cases can be investigated mathematically, it appears to be quite sound to endeavor to apply the mathematical solutions to the practical results, in order to deduce from the latter such unknown quantities as depth. This paper deals with such a method of interpretation for the simple case of a single horizontal stratum. In the method described by Wennerl for measuring earth resistivity, four stake electrodes are driven into the earth in a straight line as shown in Fig. 1. A current I amperes is passed between the two outer stakes and the potential difference V volts between the two inner stakes is measured. Then if a is the electrode separation, the specific resistance of the soil, which is assumed to be homogeneous, is given by the formula P = 2?v/1 [1] v or if v/1 is called a resistance R ohms, p = 2?aR [2] If a is in inches, p will be in ohms per inch cube, or ohm-inches, and if a is in centimeters, p will be in ohms per centimeter cube or ohm-centimeters. As stated above, this formula is true only if the earth is homogeneous, and when this is not the case an application of one of these formulas