Chap. 10] ELECTRICAL METHODS 697 



D. Interpretation 



The interpretation of an equipotential-line survey is empirical and is 

 based largely on previous experience with the method as well as on a satis- 

 factory knowledge of the geological features of the area under consideration. 

 Owing to its speed, this method is of value for general reconnaissance. 

 However, it is advisable to re-examine conductive zones thus located with 

 other electrical methods. In many cases it is relatively simple to make a 

 general qualitative interpretation of an equipotential-line survey by mark- 

 ing off the axes of the conductive zones indicated by the greatest line 

 distortions. 



1. Equipotential-line anomalies of simple geometric bodies. Depth esti- 

 mates are sometimes possible by measuring the displacement of the equi- 

 potential lines from their normal position. What may be expected in the 

 way of displacement may be calculated by assuming, for simplicity, that a 

 subsurface body has the shape of a sphere and is traversed (in the x 

 direction) by a current paralleled to the earth's surface, so that it is equiva- 

 lent to a horizontally polarized doublet. In eq. (10-19a) the potential of 

 a charged sphere at a surface point P was given as Fi = m cos d/r , in 

 which the electrical moment is proportional to the electrical field E so that 

 w = pE and — "^2 = pE cos 6/r . Since the undisturbed potential at the 

 point P is —xE, the resultant total surface potential is 



K=-rEcos^-^^^ (10-28a) 



The value of the factor p may be determined from the boundary conditions 

 at the surface of the sphere, where the current densities (p2 = resistivity 

 of the sphere, pi = resistivity of the surrounding medium) are given by 



i.-^'^l.rf^. ■ (10-28i) 



Pi aR p2 uK 



Since it follows from eq. (10-28a) that at the surface of the sphere (r = R) 



- 7r = E cos 5 (r - 2I-2) , (10-28c) 



substitution of eqs. (10-28a) and (10-28c) in (10-286) gives 



p= P"- P' .R\ (10-28^) 



2p2 4- pi 



Substituting this in eq. (10-28a), 



Vr= - ip. X (\ 4- 1^^ . ^) , (10-28e) 



\ 2p2 -1- pi r / 



