150 



GRAVITATIONAL METHODS 



[Chap. 7 



obtained from the diagram and multiplied by pi). This difference is 

 finally multiplied by AV/27r, to obtain the attraction of a compartment. 



Calculation of the gravity anomalies of subsurface geologic features 

 which are extended in the direction of strike {two-dimensional features) 

 is based on the equations for the logarithmic potential, (7-39e) and 

 (7-39/). For example, application of these formulas to the case of a 



0.00/ 



Microqa/s 



Fig. 7-43. Attraction of cylinders of various length/radius and depth/radius ratios 



(after Wright). 



horizontal cylinder (Fig. 7-44a) gives directly Agr/2A;5 = S-z/r' = 

 S sin (p/r; hence, 



■^ 2TrkbR^ Sirup 



Ag = 2 



irkSz i^-j 



(7-42a) 



Rectangular prisms (Fig. 7-446) represent in approximation such geologic 

 bodies as vertical dikes, ore veins, or horizontally stratified formations^. 

 Their attraction may be calculated by integration of eq. (7-39/). If d 

 is the depth to its upper surface, D the depth to the lower surface, x the 

 distance of the station from the far face, x' the distance from the near 

 face, and 6 the breadth: 



A(7 = 2fc8 / / 



•'0 Jd 



Z'dxdz 



'd z^-\- {x- x'y 



= 2k8 



i ^"^^ l/^ 



" + (a; - x'y 

 -\- (x- x'y 



or 



