MAGNETIC METHODS 189 



i the dip of the ore body ; x is the distance from the origin to the point of 

 observation. 



Profiles of the horizontal and vertical intensity anomalies in the 

 .r-direction are shown in Figure 81. The curves were plotted for the case: 

 di. = —1, do = —3, m = 2,i = 60°, and / = 2.305 ; that is, 



and 



^^ - + 2 <! ^^.2 + 1)% ^g + ^_^ _ i_i5)2-|3/,| (72a) 



^^"" "^ ^ (.1-2 + 1)'/^ " [9 + (.r- 1.15)-]^/^!' ^""^^^ 



3. Anomalies Due to Long Narrow Dikes 



If the dike is approximately vertical, it is equivalent in its magnetic 

 effects to a vertical magnetized "sheet" of finite thickness. Also, if the 

 depth extent is sufficiently great that the effects due to the induced pole 

 strength at the deep end may be neglected, the magnetic anomalies pro- 

 duced at the surface are essentially the same as would be produced by a 

 linear distribution of magnetic charge. In particular, it may be shown 

 that the maximum value of the vertical intensity anomaly is :t 



AZ.„ = 2f^ (74) 



where m is the magnetic pole strength per unit area, b the width of the 

 dike, and d the depth to the effective linear distribution of magnetic charge. 

 (d is, of course, somewhat greater than the distance from the surface to 

 the top of the dike.)* The anomaly at a point P located at a distance x 

 from the point of maximum anomaly along the line at right angles to the 

 strike is : 



• 7 _ 2mbd .-cs 



^^'-J^+T- (^5) 



If we choose the point P such that AZ = J^AZ^ax and combine the last 

 two equations, we obtain 



2mbd mb .^^, 



(76) 



.v2 + d^ d 

 or 



d = X 



Thus the thickness of the overburden is equal approximately to the distance 

 along the line perpendicular to the strike of the dike at which AZ is equal 



to ^AZmnx. 



t The method outlined here is described by D. A. Keys, "Determining Depth of Magnetic Ore 

 Bodies," A.I.M.E. Geophysical Prospecting, Tech. Pub. 830, p. 5. 



* Equation 74 which gives the maximum value of the vertical anomaly is essentially 

 a particular application of the expression for the field due to a linear distribution of 

 magnetic charge. (Compare p. 191.) 



