186 



EXPLORATION GEOPHYSICS 



and 



A// = AX = ^ = - 





2x 



^o (l+;i-2)B/, (69a) 



An examination of the expression for AZ reveals that AZ is symmetrical 

 with respect to the ^•-axis, has a maximum for x = o, i.e., directly over the 

 pole and approaches the jt'-axis asymptotically. The expression (69a) 

 for A// shows that A// is an odd function of x. (AH for negative values 

 of X is equal to —AH for the corresponding positive values of x.) AH 

 vanishes for x = o and approaches the ;ir-axis asymptotically for large posi- 

 tive or negative values of x.^ 



Two "depth rules" are readily de- 

 duced from Equations 68 and 69. f ( 1 ) 

 The horizontal distance u from a point 

 directly over the pole to a point where 

 AZ equals ^AZ^ax is approximately 

 equal to % the depth of the pole. (Ti- 

 berg depth rule.) (2) At a horizontal 

 distance u equal to d, AZ = i/sAZmas 

 (approximately). That is, the distance 

 from the origin to a point at which AZ 

 is approximately equal to VsAZmax is 

 equal to the depth of the pole. (Haanel 

 depth rule.) 



An alternative method for obtain- 

 ing an approximate value of thickness 

 of the overburden is to draw the vector 

 diagram of the total anomalies near 

 the point of maximum vertical anomaly, t 



The anomalies in the horizontal and vertical intensities are obtained by 

 subtracting the normal values of the horizontal and vertical intensities 

 in the area under investigation from the observed values. (Compare p. 

 156.) Corresponding values of the horizontal and vertical anomalies are 

 then combined vectorially in or- 

 der to obtain resultant vectors hav- 

 ing the direction of the total anom- 

 aly. Since the resultant vector at 

 any point is tangent to the line of 

 force at that point, the resultant 

 vectors near the point of maximum 

 vertical intensity will intersect very 

 nearly at the pole of the ore body. 

 Figure 77 shows a diagram for the 



* To draw the curves given in Figure 76, it is sufficient to assume four or five values 

 of X and compute AZ and AH from Equations 68a and 69a. 



t Compare C. A. Heiland, A.I.M.E. Geophysical Prospecting, 1932, p. 213. 



t A. S. Eve and D. A. Keys, "Studies of Geophysical Methods," 1930, Department of Mines 

 (Canada), Memoir 170, pp. 36-37. 



_L 



Fig. 76. — Vertical and horizontal inten- 

 sity anomalies produced by an ore body 

 equivalent in its magnetic effects to a single 

 s pole of strength m located at a depth d. 



Fig. 77.— -Vectors of resultant magnetic anom- 

 alies due to ore body. (Eve and Keys, Cana- 

 dian Memoir 170, p. 39.) 



