794 



ELECTRICAL METHODS 



[Chap. 10 



one side and the corresponding maximum is displaced by Ay = 2h sin i, 

 where h is the depth perpendicular to the bed and t the dip. Relations 

 readily understood in their geometric significance may be obtained from 

 Fig. 10-113 by considering a perfectly conductive layer, for which p = 0, 

 q = 00 (see eq. [10-57]). Since the quadrature components cancel, 



4/od ^ rr 8Io(f 



Y = 



4^2 + y' 



and Z = — 



2/(4c^2 + y^) 



(10-59) 



Fig. 10-1 12a. Sundberg interpretation diagram for inductive methods, vertical 

 component, 100 meters from cable. Solid lines represent depth; broken lines, 1/q 

 (reciprocal induction factor). 



These relations follow hkewise by combining the primary field (Fig. 10-113, 

 dotted circle) with the image field (solid circle). At P the horizontal com- 

 ponent of the primary field is zero and that of the secondary field T is 

 Y = 2 /,- d'/r\ With perfect reflection, /.• = h ; d' = 2d; r = 

 f2 = V4d^ + y^; and, therefore, Y = 4/o rf/(4ci!^ + y^). The vertical 

 component of T due to the image is (eq. [10-46a]) Z = 2Iiy/r or, with 

 the present notation, Z = 27o?//(4rf^ + 2/ )• 



same point is Zo = — 2Io/y, since r = 

 component equals 



_^(^ y 



y -' 



y- 



\ 4d' + yy 



or 



The field of the cable at the 

 Hence, the resultant vertical 



-8hd^ 



y(^d^ + y') 



