MAGNETIC METHODS 



199 



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Fig. 89. — Anomalies due to a thin layer ter- 

 minated by a horizontal plane. Curve 1 is the 

 vertical component of the end effect (Equation 

 84); curve 2 is the vertical component due to 

 magnetization of the layer by the field at right 

 angles to its surface (Equation 85), and curve 3 

 is the resultant vertical anomaly. 



if the surface of the layer were perpendicular to the total magnetic field 

 of the earth, the end effect would be zero ; on the other hand, if the sur- 

 face of the layer were parallel to the total magnetic field, the end effect 

 alone would be present. In the general case, both effects are present, 

 and the magnitude of each depends 

 on the components of the magnetic 

 field. The end effect depends on l\ 

 (which is equal to the susceptibility 

 k of the layer times the component 

 of the magnetic field normal to the 

 end of the layer), and the cross- 

 magnetization effect depends upon 

 1 2 (which is equal to k times the 

 component of the magnetic field 

 normal to the layer).* 



The vertical anomalies due to 

 the two effects are plotted in Fig- 

 ure 89 for the case that the layer 

 makes an angle of about 32° with 

 the vertical component of the 

 earth's magnetic field. It should 

 be emphasized that the end effect 



can be either positive or negative. That is, the sign, as well as the magni- 

 tude of this effect, depends upon the orientation of the layer. For example, 

 if the layer in Figure 89 were horizontal (^i = 7r/2), the direction of 

 the vertical component due to the end effect would be opposite to that of the 

 vertical component of the earth's field; that is, the end effect would be 

 negative. Thus, in some cases, the presence of a magnetic low may indi- 

 cate that a layer of strongly ferromagnetic material lies heloiv the surface. 

 In general, the end of the layer does not lie directly under the maximum 

 point of the magnetic anomaly, and the depth to the layer can be estimated 

 only if its orientation relative to the earth's resultant field is taken into 

 account. 



Curves 1, 2 and 3 in Figure 89 also represent the horizontal anomalies. 

 Curve 1 is the horizontal anomaly due to cross magnetization, curve 2 is 

 the horizontal anomaly due to the end effect, and curve 3 is the total hori- 

 zontal anomaly. 



Effects Due to a Thick Layer. — Consider the effect produced at a 

 point P (.«'o3;o) by a magnetized strip which is perpendicular to the plane of 

 the paper. (Figure 90.) The magnetized strip corresponds essentially to 

 a linear distribution. Hence, the potential at an external point due to a 

 magnetized strip of thickness dx is given by Equation 79; that is, dV = 



* It is assumed here that the susceptibility of the surrounding medium is negligible. 



