Chap. 10] 



ELECTRICAL METHODS 



709 



B. Electrode Arrangements 



If, at the surface of the (homogeneous and isotropic) ground of the 

 conductivity <r, an electric current / is introduced by means of two point 

 electrodes, A and B, and if the current flows from A to B, the potential 



at any point P on the surface is Vp = - — (l/n — l/r2), where ri and r2 



2ira 



are the distances of a point P from the electrodes A and B, respectively. 

 The potential difference between two points P and R, which have the dis- 

 tances ri , Ti , and Ri and R2 , respectively, from the electrodes is 



Hence, the resistivity 



2ir<T Vi ra Ri R2/ 



1 9 ^ 

 p = - = 2ir 





1 



Ri 



+ 



R2/ 



(10-31a) 



(10-316) 



This equation holds for any position of the current electrodes A and B 

 and the search electrodes P and R, and does not change when current and 

 potential electrodes are interchanged. Differences in the position of the 

 search electrodes with respect to the current electrodes give rise to various 

 resistivity methods. By selecting definite dispositions, it is possible to 

 simplify the field procedure or to give the expression for resistivity a form 

 that will simplify the interpretation of the results. 



Seven different electrode systems are discussed below. They may be 

 classified as follows: 



Group I 

 Electrode Arrangements with Finite Distance of Power Electrodes 



Group II 

 Measurements Near One Power Electrode; Second Power Electrode in Infinity 



Double equidistant probe 

 method 



Double probe method with 

 unequal probe spacing 



Single probe method 



