720 



ELECTRICAL METHODS 



[Chap. 10 



Ca . Similar conditions apply to the potential at P2 , so that 



V = i. L 1^1 4- -A—\ + p^(^ - 1) ] 



' 2x L \a "^ 2d + 2a/ "^ 2a J 

 Then the apparent resistivity becomes 



(10^0^) 



Pi 



1 - k 



k.^- 



\-\-k^ -k 



a 



l-^- 

 a" 



(10-40A) 



{d) In case 4 (three electrodes in second medium) we have for the ap- 

 parent resistivity 



Pi 



k + 1 

 1 - k 



^-H\-^ 



+ 



1 



+ 1 ^ + 2 



a a J 



(10-40t) 



(e) In case 5 (four electrodes in second medium) it is 



d d 



I ^ 

 1 + k 



P» = Pi 



1 + k 



1 - k 





rf2 



- 1 



(10-40i) 



Figs. 10-56a and 10-566 show curves of apparent resistivity on contacts 

 calculated for various k values. These curves are valid for the four- 

 terminal Wenner-Gish-Rooney electrode arrangement, and they express 

 the observed quantities as a function of spread distance from fault plane. 

 It is seen that the apparent i^esistivities approach the true resistivities as 

 the distances of the arrangement from the fault plane increase. Abrupt 

 changes occur when d/a = 0.5 and 1.5, that is, when electrodes cross the 

 contact plane. 



An application of the above theory is made in electrical logging. This 

 method involves the location of formation boundaries in wells by means 

 of a system of fixed spacing electrodes (see Chapter 11). 



When the electrode arrangement is used parallel to the strike of a fault, 

 formula (10-33) may be applied to the contact (p2 , pi), so that 



2t \_a s/W^^^ 



2k 



y/Ad^ + 4a2. 



(10-41a) 



