190 EXPLORATION GEOPHYSICS 



An alternative method for determining the approximate thickness of 

 the overburden over a dike makes use of vector diagrams, as illustrated 

 in connection with Figure 76. 



B. Theoretical Anomalies Produced by Magnetic Strata. — Two 



methods may be employed to calculate the magnetic effects of two-dimen- 

 sional bodies such as strata. In both methods it is assumed that the 

 difference in susceptibilities between the anomalous body and the adjacent 

 formation is such that demagjietization effects'^ are negligible. 



■** '^''' 



Method Utilizing Functionjal Rel^fion Between Magnetic and 

 Gravitational Anomalies 



As a consequence of a theorem due to Poisson, it may be shown that 

 the following relationships obtain between the magnetic and gravitational 

 anomalies produced by two-dimensional bodies : t 



where 



_ Ak / ^ d^U . yd^U\ 



(77) 



A^ = susceptibility difference of the geologic body relative to the ad- 

 jacent rock. 

 G =■ gravitational constant (6.68 • 10~® c. g. s.) 

 Act = density difference. 

 U = gravitational potential. 

 a = angle between geographical north and the west direction of 



strike. 

 H = horizontal component of earth's field. 

 Z = vertical component of earth's field. 



The applicability of the AH and AZ formulas derives from the fact that 



— — r- , ) have been 



OX^ ox OS / 



evaluated for numerous, two-dimensional geologic bodies. (Compare chap- 

 ter on gravimetric methods.) 



Method Utilizing Equivalence of Volume and Surface Distributions 



of Magnetic Charge 



This method consists in calculating the magnetic effects of a uniformly 

 magnetized formation in terms of its effective surface distribution of mag- 

 netic charge. This method postulates that the magnetic effects at the 

 surface due to a volume distribution of magnetization throughout a stratum 



* A discussion of demagnetization effects is given on p. 203 et scq. 



t R. von Eotvos, "Bestimmung der Gradienten der Schwerekraft und ihrer Niveauflachen mif 

 Hilfe der Drehwage," XV. Allgemeine Konferens der Intern. Erdmessung, Budapest, 1906. See also 

 W. P. Jenny, "Experimental Interpretation of Magnetic and Gravimetric Anomalies," Terr. Mag. 

 40 (No. 1) March 1935, pp. 71-78. 



