Chap. 10] 



ELECTRICAL METHODS 



745 



method is also superior in resolving power because potential differences 

 are not measured absolutely but in the form of a ratio of successive dif- 

 ferences. However, this increase in precision frequently results in in- 

 creased near-surface interference, and special precautions are necessary 

 to reduce it. P.D.R. arrangements consist essentially of Wheatstone 

 bridge circuits with adjacent stake intervals in two arms, known resist- 

 ances in the other two arms, and an indicating instrument in the center 

 arm, connected to the center stake (see Fig. 10-82). Hence, for a D.C. 

 circuit, the ratio of the two voltage differences is equal to the ratio of the 

 two resistances when adjusted for balance. 



B. Theory 



1. Horizontal layers. In all applications of P.D.R. method for the ex- 

 ploration of stratified ground, measurements are made outside the elec- 



T 



r 



o- 



J^ 



b 

 b 



Fig. 10-77a. Electrode arrangement for constant spacing. 



trode basis and usually at right angles to it. By this means the effect of 

 the second electrode is virtually eliminated (Fig. 10-77a). For two layers 

 of arbitrary conductivity ratio, with a lower layer of infinite depth extent, 

 the P.D.R. may be calculated from the potentials at three surface points, 

 using the equations previously derived. According to eq. (10-35a), in 

 the vicinity of one power electrode 



F. = ;p I i + 2 E ' 



2'K\r 



ix Vr^+ (2n/i)2j" 



Applying this to three equidistant points with the interval h, and with a 

 center distance r from the power electrode (see Fig. 10-77a), we get 



k"" 1 



Va = 



Vc 



2ir\_r- 

 2x1^4 

 2Tlr 



n=oo 



, +2E "77= 

 — h n=i V{r 



hy -\- {2nhy_ 



U2Z 



k"" 



=1 Vr^ + (2n/i)2. 



(10-42a) 



