EXPLORATION GEOPHYSICS 



make use of the expression for Vo. Evidently, 



oo 



jy OOP . X"" oMzk 



00 





-^a (\ + 0^[ ^— + V n + QOQ:''"Q. n 



- 4^ Px (1 + 00 |^f^. + ^jH + 2^y+ {2kd-zyV^j 



In particular, at the boundary between layers and I {z — Q) 



-4^Px(l + Qx)|^^ + 2^ [r^+(2^d)^]v. J (1^) 



Equation 13 is the general solution for the potential produced by the current source 

 .So at the boundary separating layers and I. 



When medium is air, po = co • Also, 



1- ^ 1- ^ 



Hence, Va can be written as follows : 



r.=- 



po pi £o_ 



El 

 po 



Q^^ ^t^^i— i^ = ^ = =1 



Po -r pi 1 + ^ 1 + -^ 



L, fi +2 V —Ql—~\ 



!00 



(14) 



Equation 14 expresses the potential at any point on the surface of the ground due 

 to a current source So* 



If a sink of strength — So is now added at a distance x ^= L where x is measured 

 along the line passing through the source and sink (Figure 292), the potential Vo' 

 produced by the sink at any point on the x axis is : 



i oo 



The total potential produced by the source and sink is obtained by adding Vo and Vo'. 



In the Roman tables, values of W^= 7 Q'' \ 7 ~~ , ^^z^' are given for the 



arguments Q and a. 



* For calculations involving this formula it is convenient to use the tables given 

 by Irwin Roman in an article entitled "How to Compute Tables for Determining 

 Electrical Resistivity of Underlying Beds and Their Application to Geophysical 

 Problems." (Technical Paper 502 U. S. Department of Commerce.) 



