Chap. 10] 



ELECTRICAL METHODS 



713 



the same points resulting from the source at B and its image at B'. If 

 the electrodes are at equal intervals a in a straight line and at a depth b 

 below the surface, the potential difference is 



-^^) 



where q = b/a. 



AV 



47r \a 



= ^ f 1 . 



4ira \ Vl + 4g2 Vl + q^ 



+ 

 1 + 



► (10-33) 



■i^t 



kVl'k^I 



Fig. 10-51. Image distribution in two-layer potential problem. 



When q is large (depth great compared with the electrode separation), 

 A7 = pi//47ra (potential for an infinite homogeneous medium). When 

 g = (electrodes on ground surface), AF = pi//2xa (potential for the 

 semi-infinite medium). 



2. Two horizontal layers. Assume two semi-infinite media with resis- 

 tivities pi and p2 , as in Fig. 10-51. The upper layer is bounded by air 

 (resistivity po = °o). If current is supplied at two pomts, and 0', 

 the potential distribution at the surface can be calculated by considering 

 a source 7 at 0, a sink —7 at 0', and the images of this source and sink 



