Chap. 10] 



ELECTRICAL METHODS 



791 



lower edges. When the sheet is short, the lower current concentration is 

 efifective. If we place the zero point of the system of coordinates above 

 the upper edge of the ore body, we have, with the notations of. Fig. 10-1 10, 



(di d2\ , /di 2a sin i + di\ 



and 



(V 6\ /y , 2a cos i — y\ 

 -2 - -2 1 = 2/i( -2 + — — 2 -)• (10-55d) 



In structural and stratigraphic investigations, both fixed loops and ex- 

 panding loops are applied. The former procedure is known as the Sund- 

 berg inductive, and the latter as the central ring induction (Koenigsberger) 

 method. Interpretation theory in the first is based on an evaluation of 

 the fields of thin layers of good 



W/r<iv//y^ 





ConduchVt 

 Shtef 



ry 



fi lilt II nil 



CaNt imoqt 



Fig. 10-in. Electromagnetic field in P 

 resulting from cable and cable image. 



conductivity in a section con- 

 sidered a poor conductor. In the 

 second, the effect of a section of 

 progressively increasing thickness 

 is evaluated as the radius of the 

 primary loop is expanded. The 

 theory of the first method has 

 been developed by Levi-Civita, 

 Sundberg, Rostagni, Hummel, 

 Hedstrom, Focken, and others. 

 A list of pertinent literature is 

 found in Focken's article. 



Assume that a long cable is laid 

 out on the ground surface in the x direction (Fig. 10-111). A formation, 

 whose thickness s is small compared with its depth d, is parallel to the 

 surface and extends to infinity in the x and y directions. The electro- 

 magnetic field is measured at a point P, whose horizontal distance from 

 the cable is y and whose vertical distance from the sheet is z. If the point 

 P is sensibly in the surface and if no sheet is present, a horizontal compon- 

 ent does not exist and the vertical component is due only to the primary 

 cable. The action of a sheet of very good conductivity is to reflect the cable 

 and to produce, at twice the depth of the sheet, an image current concen- 

 tration with a phase shift of 180°. In that case, the total vector at P 

 can be readily calculated (see below). Its vertical component is sub- 

 tracted from the component due to the primary cable; its horizontal corn- 



's Colo. Sch. Mines Quart., 32(1), 225-252 (Jan., 1937). 



