396 



MAGNETIC METHOD 



[Chap. 8 



For a vertical dike of infinite depth extent, the transverse magnetization 

 may be neglected and the anomalies are : 



AH = 2kZo log, 



r2 

 n 



AZ = 2kZ, 



o<p 



(8-616) 



(see Fig. 8-52). The horizontal intensity is proportional to the gravity 

 gradient, has a maximum in the south, and is zero above and at a minimum 



-0 *x 



■® 



^ 



¥r 



■*x 



7/q^ 



J. .3 



2' 'f 



Fig. 8-52. Angles and distances on two-dimensional bodies (from left to right, 

 top row first): cylinder, vertical fault, infinite vertical dike, finite vertical dike, 

 slope, inclined dike, anticline, syncline. 



north of the dike. The vertical intensity is proportional to the negative 

 curvature and has a maximum above the dike.^° 



In the case of a vertical dike of limited depth extent, the transverse mag- 

 netization is likewise negligible and the anomalies 



'" Formulas (8-61i>) were given in the following form by Smyth as early as 1899: 



AZ 



(P+ (x + a)2 

 AH = C log .. . , — — t: and 



d^ + (x- a)2 



= 2C( 



X + a X — 



tan~i — : tan~' 



d 



-■■ 



where 2a is the width of the dike, C a constant, d the depth to the upper surface, 

 and X the horizontal surface distance from center. 



