GRAVITATIONAL METHODS 343 



Hence Equation 105 reduces to 



T= — mhl (t/yzcosa — Uxzsina) (106) 



Introducing the relation 



T = Td 



where 6 is the angular deflection and t the torsion constant of the torsion wire, 

 Equation 106 may be written in the form : 



e= (^Uyz cos a— Ux2 sin a) (107) 



T 



Replacing 6 by its value in terms of th.e scale readings iia and tio and the distance / 

 (expressed in scale divisions) between scale and mirror 



(108) 



2/ 

 Hence, the fundamental equation of the gradiometer becomes : 



Wa — no= -^^(Uyzcosa — Uxzsina) (109) 



T 



This equation states that the gradiometer deflection in any azimuth a is directly pro- 

 portional to the horizontal gravity gradient {Uyz cos a — Ux, sin a), (cf. derivation 

 for torsion balance, page 308, noting the one difference that h was measured down and 

 2 = -{- h; thus the difference in sign.) 



Interpretation of Gravity Gradient and Curvature Data 



The technique of interpreting gravity gradient and curvature data is 

 complex and cannot be described in a standardized "step-by-step" method. 

 Every survey involves a large number of variable factors, each contributing 

 its effect to the gravity value measurable at the surface of the earth. 



Generally, the first step in the interpretation consists in plotting the 

 gravity gradient and curvature values on a map or on two separate maps. 

 In some cases, these maps can be used to interpret the data directly. In 

 other cases, field gradient and curvature maps alone are inadequate and 

 it is necessary to draw isanomalic contours and profiles and utilize the 

 isanomalic curves in the interpretation. 



Curvature maps have a somewhat limited application in extended 

 structural surveys for oil, because curvature values are influenced by 

 topographic irregularities to a larger degree than the gravity gradients. In 

 many reconnaissance surveys the curvature values are neither computed 

 nor plotted. 



The relationship between the gradient of gravity and the curvature 

 quantity, as measured by the torsion balance, and the configuration of sub- 

 surface heavy masses has been discussed. Certain examples were presented 

 in Figures 141 to 150 inclusive. Although these examples were simplified 

 and quite elementary, they form the background for the interpretation of 

 torsion balance results. 



In like manner, the profiles of gravity anomaly (Ag) over similar 

 subsurface structures, as shown in Figures 126 to 129, are fundamental. 



