BORE-HOLE INVESTIGATIONS 1027 



operations above the water table and to drill holes filled with non-con- 

 ducting fluids, such as oil, etc. 



The expression for the resistivity may be calculated from the funda- 

 mental relations expressing the flow of current in an infinite medium. The 

 derivation for an arrangement in which the four electrodes lie in a line and 

 are equidistantly spaced is as follows : 



Assume that the electrodes A, M, N and B are located in a straight line 

 and at distances of 0, a, 2a, and Za, respectively, from A. Let / denote the 

 measured current passing out of the electrode A and into the electrode B. 

 The potential at M due to the source A and the sink B, is * 



^^ A^\a 2a) 

 and the potential at N due to A and B is 



^"^ " 4^;^ \2^ ~ ~v) 



Hence, 



En — Em = AE 



47ra 

 or 



47raAE 

 P- 1 



(6) 



It is evident from Equation 6 that the resistivity p may be determined from 

 the observed values of the potential drop AE, the current /, and the electrode 

 spacing a. 



Huber t has described a method for obtaining two resistivity curves 

 simultaneously. One curve shows the variations in the resistivities of the 

 strata in the immediate vicinity of the moving current source, and the 

 other curve shows the variations in the resistivities of the strata at an 

 appreciable distance from the moving electrode. Thus, this method yields 

 a direct comparison of the variations in electrical resistivity close to the 

 bore hole where the formation may be permeated with the fluid of the bore 

 hole, and the variations in electrical resistivity at a distance from the bore 

 hole, the distance in question being greater than the distance of penetration 

 of the bore-hole fluid. 



Apparent Resistivity 



Up to this point a homogeneous medium has been assumed, and the 

 basic exploring devices have been described on this basis. It is obvious, 



* The expression for Em is a modified form of Equation 5, p. 473. 



t F. W. Huber. "Methods of and Apparatus for Electrically Exploring Earth Formations," 

 U. S. Patent 2,072,950, issued March 9. 1937. 



