698 



ELECTRICAL METHODS 



[Chap. 10 



with X = r cos 6, andE = ipi . If the resistivity ratio A; = pi/pg , the factor 



k- 1 



c = 



P2 ~ Pi 

 2p2 + Pi 



A;+"2 



(10-28/) 



expresses the effect of good or poor conductors imbedded in another medium 

 on the surface potential (see Fig. 10-40). A "saturation effect" occurs 

 since, for poor conductors, one-half of the maximum effect is reached for a 

 (inverse) conductivity ratio of 2.5, whereas for good conductors one-half 

 of the maximum effect occurs already at a ratio of 4. 



Fig. 10-40. Saturation effect in potential methods, for poor and good (approximately 



spherical) conductors. 



These relations hold for spherical or nearly spherical bodies. For elon- 

 gated bodies the effect depends essentially on the extent of the body in the 

 direction of current flow compared with the extent at right angles thereto. 

 For elliptical bodies of various ratios of major /minor axis (e = a/b) 

 traversed by current in the direction of the major axis, Hummel^^ has 

 calculated the ratio of current density in the body to that in undisturbed 

 ground (Fig. 10-41). Only in a body which is very extended in the direc- 

 tion of current is the current density ratio equal to the resistivity ratio. 



It is noted in eq. (10-28e) that the anomalous potential of a sphere is 

 inversely proportional to. the cube of its distance, and that it increases in 



" J. N. Hummel, Zeit. Geophys., 4(2), 73 (1928). 



