204 



EXPLORATION GEOPHYSICS 



and X. (Figure 96. )t The components of the magnetic field in the direc- 

 tion of increasing r and 6 are (see p. 87, position III of Gauss). 





2Mr 



Me 



(96) 



respectively, where Mr and Mg are the components of ikf in the r and 6 

 directions, respectively. 



The horizontal and vertical 

 components of the magnetic an- 

 omaly at a point P on the surface 

 of the earth may be obtained by 

 resolving the magnetic moment 

 M of the sphere into the com- 

 ponents Ma and Mg. (Figure 

 96(a). 



The components of the field in 

 the directions of increasing r and 

 6 due to Ma are 



Fig. 96. 



(a) Sketch illustrating method for resolving mag- 

 netic moment M into components M^ and M^, 



(b) Sketch illustrating method for determining 

 horizontal and vertical magnetic anomalies 

 due to magnetic moment M . 



and 



(AH,), 



(AH,).= 



2M^ cos 6 2M^x 



Mx sin 6 M^d 



The net x component (AH) 3, of these fields is 



(AH),= 



2M,x^ MJ^ 



and the net s component (AZ)j, is 



. „, 2M^xd ^ M^xd 

 (AZ)^= - +— r~ 



SMrxd 



In a similar manner it may be shown that the net x component (AH)^ 

 of the fields due to Mg is 



_ SMgxd 

 iAH),= -T— 



and the net s component (AZ)^ is 



(AZ),= 



M.X' 2MJ^ 



t Compare Starling, loc. cit., p. 16. 



