MAGNETIC METHODS 



187 



resultant magnetic anomaly due to an ore body. In this case the vectors 

 indicate that the pole is about 150 to 175 feet below the surface. This 

 "depth" is of course an approximate value, because vector diagrams in- 

 dicate a point near the center of attraction of the upper pole of the body 

 and do not give the thickness of the overburden, which will always be less 

 than that deduced from the diagram. 



2. Field Due to' a Magnetic 

 Dipole f 



If the depth extent of the sub- 

 surface magnetic feature (ore body, 

 etc.) is too small to permit neglecting 

 the magnetic effect of the pole on the 

 deep end of the ore body, the total 

 effect may be approximated by assum- 

 ing that the ore body is equivalent to 

 a magnetic dipole. (Figure 78.) 



The magnetic anomalies produced by a dipole are calculated by adding 

 the effects of a south and a north pole vectorially. The application of 

 Equations 68 and 69 to the poles — m and + m yields : 



Fig. 78. — Field at P due to a vertical dipole. 



AZ = — m I — 5" 



and 



AH=- 



1 ^^rf ^^6 1 



(70) 

 (71) 



Sketches of the horizontal and vertical intensity anomalies produced 

 by a vertical dipole are shown in Figure 79. The profiles in the .r-direction 



are drawn for the case: m ~2, di = —l, 

 and do =~ 3; that is 



1 3 



AZ = 



AH" 



-2.[- 



1 



(9 + x'^Y'' 

 1 





1 





(l+A--)'/^ (9 + ,r2)'/» 



An approximate depth rule for an ore 

 body which is equivalent in its magnetic 

 effects to a vertical dipole was given by 

 Thalen in 1879. The rule may be stated as 

 follows : The depth d\ to the top of the ore 

 body is equal approximately to 0.7 of the 

 horizontal distance u from a point directly 

 over the dipole to a point where AZ = 0. 



t H. Haalck, Die Magnetischen Verfahren der Angewandten Geophvsik (Gebruder Borntrager), 

 Berlin, 1929. 



A. Nippoldt, Verwertung Magnetischer Messungen (Springer), Berlin, 1930. 



C. A. Heiland, Chapter on Magnetic Prospecting, pp. 136-139. Terrestrial Magnetism and 

 Electricity, edited by J. A. Fleming (McGraw-Hill), 1939. 



Fig. 79. — Vertical and horizontal 

 intensity anomalies for an ore body 

 which is magnetically equivalent to a 

 vertical dipole. 



