728 ELECTRICAL METHODS [Chap. 10 



vice versa. Examples are given below in section f. In some instances it 

 is possible (especially with the help of borings) to represent the lateral 

 variations of apparent resistivity on such a scale that they may be trans- 

 lated directly into changes of depth of formations of different resistivity 

 (bedrock profiles, and the like). Qualitative methods are also frequentlj^ 

 used in a preliminary interpretation of resistivity depth curves although, 

 as stated below, complete reliance on such methods may lead to serious 

 misinterpretation, since the apparent resistivity continues to change with 

 electrode separation long after the true resistivities have ceased to change 

 with depth. 



2. Quantitative interpretation (analytical) . Analytical, direct methods of 

 depth interpretation are primarily applieable to simple two- and three- 

 layer conditions. One most frequently used is known as Tagg's method. 

 This method establishes a number of simultaneous equations, giving depth 

 h as & function of resistivity factor k. Hence, a family of curves giving 

 Ps/pi as a function of h/a must be prepared (see Fig. 10-62). Since the 

 apparent resistivity, for a given electrode separation, is only a function of 

 the depth and the k value of a contact, theoretically two resistivity values 

 for two electrode separations are sufficient to obtain both h and k. In 

 practice, several equations are set up for various electrode separations, and 

 depths are calculated numerically or graphically. It is convenient to use 

 two diagrams : one for resistivity ratios (when the resistivity of the under- 

 layer is less than that of the upper layer) and the other for conductivity 

 ratios (when the resistivity of the underlay er is greater). Each diagram 

 contains ten curves for k from —0.1 to —1 and from 0.1 to 1. Since a is 

 known, h values as functions of k may be tabulated or plotted for each 

 electrode separation. The correct depth is indicated by the intersection 

 of the curves or by h values, which do not vary with k (see example). 

 From the k value thus determined, the resistivity of the lower layer is ob- 

 tained from p2 = pi(k -{- 1) / (1 — k) . If necessary, field curves are smoothed 

 out for small electrode separations in order to obtain a reasonable average 

 value for the surface resistivity. 



The results in Table 71*^ were obtained from Fig. 10-63a to determine 

 depth to limestone, overlain by loam, sand, and clay. For separations of 

 less than 70 feet, the resistivities were averaged, obtaining a surface 

 resistivity of pi = 6703 ohm-in. 



Since p,/pi > 1, the "conductivity" curves will be used for interpreta- 

 tion. In Table 72 the vertical columns contain ten values of h/a for 10 

 values of k. This is repeated for all electrode separations and correspond- 

 ing at/ffi values. 



" Tasg, •?. eit. 



