184 EXPLORATION GEOPHYSICS 



for inferring the subsurface structure from magnetic data obtained at the 

 surface. 



The theoretical procedure for deducing subsurface structure from mag- 

 netic data is: (1) to assume (a) a geologically plausible configuration of 

 the subsurface formations and (b) probable values of the permeabilities 

 (or susceptibilities) ; (2) to compute the magnetic effects which the as- 

 sumed configuration (and permeabilities) would produce at the surface; 

 (3) to compare the theoretical and observed results; (4) to modify the 

 assumptions until a satisfactory agreement is obtained between the ob- 

 served and theoretical data. 



Three theoretical methods will be considered. The first method is used 

 when the subsurface body has a small cross section relative to its length. 

 The procedure followed in this method is to set up expressions for anom- 

 alies characteristic of a single pole, a vertical magnetic dipole and an 

 inclined dipole, and to compare the theoretical results with the observed 

 anomalies. This method is described in section A below. 



The second method is used for calculating the magnetic anomalies 

 produced by magnetized strata. The theoretical technique for obtaining 

 the magnetic anomalies of magnetized strata may be subdivided into two 

 separate methods. In one, use is made of a functional relation between 

 the magnetic and gravitational effects of magnetic layers in order to obtain 

 the unknown theoretical magnetic anomalies from known theoretical gravi- 

 tational anomalies. In the other, it is postulated that the magnetic effects 

 produced at the surface of the earth by the volume distribution of mag- 

 netization throughout the layers are approximately the same as those 

 produced by surface distributions of magnetic charge located on the upper 

 and lower faces and on vertical contacts of the layers. This method is 

 described in section B below. 



The third method is used to calculate the magnetic effects produced 

 by uniformly magnetized geologic bodies having the shape of spheres, 

 ellipsoids of revolution, etc. In the case of a uniformly magnetized sphere, 

 the theoretical magnetic effects at the surface of the earth may be obtained 

 by replacing the sphere by a bar magnet having a magnetic moment equiv- 

 alent to that of the sphere. This method is described in section C below. 



A. Anomalies Produced by Certain Ore Bodies and Igneous Intru- 

 sions. — Certain ore bodies and igneous intrusions which occur in the form 

 of pipes, shoots, chimneys, etc., and have a small cross section relative to 

 their length may be represented by single poles, provided their depth extent 

 is large enough to warrant neglecting the effect of the accompanying 

 magnetic pole at the lower end of the subsurface body. 



1. Field Due to a Magnetic Pole 



Assume that a pole of strength in exists at a depth d below the surface 

 in a medium of permeability 1. The magnetic field at any point due to this 

 pole may be calculated by computing the derivative of the magnetic poten- 



