ELECTRICAL METHODS 



477 



Fig. 284.- — Vertical section of equipotential 

 surfaces surrounding current electrodes S\ and 

 ^2. (Curve A shows the variation of potential 

 along the surface of the ground.) 



Equation 8 may be used to describe the distribution of potential and 

 current in some detail. The variation of potential along the line through the 

 electrodes Si and Si is plotted in Figure 283. Two features of this curve 

 should be noted: (1) the large drop of potential that occurs near each 

 electrode due to the high current densities in the immediate vicinity of the 

 electrodes and (2) the fairly flat 

 portion of the curve midway be- 

 tween the electrodes.* 



The vertical section of the 

 equipotential surfaces is shown in 

 Figure 284 and the distribution 

 of potential in the boundary plane 

 containing the electrodes is 

 shown in Figure 285. 



Figure 286 shows the current 

 per sq. cm. flowing through a ver- 

 tical plane Q which intersects the 

 line joining the two energizing 

 electrodes at its midpoint M as a 

 function of the ratio of the depth 

 d to the electrode separation. Fig- 

 ure 287 shows the fraction of the 

 total current which penetrates 

 below a plane C located at a depth 

 of d units as a function of the 

 ratio of the depth d to the elec- 

 trode separation, f 



The equations needed for plot- 

 ting Figures 286 and 287 may be 

 derived as follows : 



Let ri and r2 be the distances of a point on a vertical plane Q from ^i 

 and ^2 respectively. Since the vertical plane Q is located midway between 

 Sx and So, the distance ro is equal in magnitude to the distance rx. The 

 current at the point {vi, ^2) is 



Fig. 285. — Distribution of potential in a plane P 

 which contains a source 6"i and a sink ^o. 



or 



P d-^ 

 P d-r 



p d 

 SL 



X \rx ri)~ p \r^ r-? ) 



where L = distance between Sx and S^- 



* Field work is usually planned so that the observational points (points at which 

 the probe or potential electrodes are inserted into the ground) lie in the flat portion 

 of the curve. 



t See also W. Weaver, "Certain Applications of the Surface Potential Method," A.l.M.E. Geo- 

 physical Prospecting, 1929, p. 70. 



