Chap. 10] ELECTRICAL METHODS 793 



For the field at the earth's surface, where z is always closely enough equal 

 to d in level terrain, 



4/od / . , , 14/-/ 



and 



Y = .^r^ o ( sin cof + iTT' T^i I ""2 ^os '''^ 

 4^2 + 2/2 \ 2rfq 4^2 + 2/2 



> (10-58c) 



Z = - 



( - sin w« - X-* Jl^-| — 2 ^os '^^ ) • 

 \2/ dq 4(^2 _|_ ^2 y J 



4^2 + ^2 

 From eq. (10-58c) the phase shift in the horizontal component is 



tan<^ = ^.^^J-^] (10-58d) 



2dq 4^2 + if- 



and that in the vertical component is 



2 



Their difference is 



tan <^z = -1. —^ . (10-58e) 



dq 4c^^ + 7/2 



tan v^Y — tan (^z = ^ • (10-58/) 



Depth and induction factor of a conductive sheet are calculated by dia- 

 grams as shown in Figs. 10-1 12a and 10-1126. A large loop (about 6000 

 by 2500 feet) is laid out (longitudinal direction parallel with assumed strike) 

 and a number of parallel profiles are run at right angles to the cable. 

 Along each profile the in-phase and quadrature components of both the 

 vertical and the horizontal fields are measured at a number of distances. 

 Theoretically, one distance on each profile is sufficient to calculate both 

 depth and induction factor. Assume this distance to he y = 100 m, for 

 which the diagrams of Fig. 10-112 have been calculated. These diagrams 

 contain, for both vertical and horizontal component, lines of equal depth 

 (solid) and lines of equal reciprocal" induction factor (1/q, dotted). If at 

 100 m distance from the cable one has observed an in-phase vertical com- 

 ponent of 17| microgauss per ampere primary current, and a quadrature 

 component of 1| microgauss, the depth as read from the diagram is 100 m 

 and the induction factor is 100 (meters, since the reciprocal induction factor 

 has the dimension of length). For the horizontal field the in-phase com- 

 ponent would be 7 microgauss per ampere and the out-of-phase component 

 — 2 microgauss per ampere. 



For horizontal beds the in-phase horizontal component has a maximum 

 directly above the cable. For a dipping bed the image point moves to 



