GRAVITATIONAL METHODS 



359 



One of the simple formulas not included in the above list is that for a 

 sloping plane : namely, 



Uxz — 2G IT a m (approximately) (128) 



where in = slope. 



This formula is accurate for gentle dips and is quite useful in computing 

 terrain effects as well as subsurface effects. 



Mathematical Treatment of Geologic Structures and Ore Bodies. 



— To calculate the gravitational effects of actual geologic structures and 

 ore bodies, it usually is necessary to consider the structures as composed 

 of a series of simple bodies for which formulas of the type 115 to 128 are 

 available and not too complicated. The gravity eft'ects are calculated for 

 each of the constituent simple bodies and then summed up to get the effect 



Fig. 208. — Schematic representation of a structural ridge. A 

 shows approximation by four prisms, B by seven prisms. (Barton, 

 A.I.M.E. Geophysical Prospecting, 1929.) 



of the whole body. For example, in certain cases, an irregular ridge may 

 be represented by four prisms (Figure 208A) or by seven rectangular 

 prisms (Figure 208B), and the gravity effects of the ridge can be com- 

 puted as the sum of the effects of the prisms. 



The calculations are obviously quite lengthy, t For example, suppose 

 the structure is split into several infinite horizontal prisms. Each evalua- 

 tion of the appropriate formula would give the gradient for a single 

 rectangular block at a single station. The minimum number of points to 

 determine, approximately, a limited section of profile such as shown in 

 Figure 209 would be five. Good accuracy would require at least nine points. 



For the differential curvature curve, 

 seven points would be the minimum and 

 thirteen, or more, preferable. To obtain 

 the gradient profile corresponding to 

 Figure 208 A, Equation 121 would have 

 to be calculated at least 20 and prefer- 

 ably 36 times ; to obtain the differential 

 curvature, Equation 122 would have to 

 be calculated 28 and preferably 52 times. 



Quantitative Methods: Trial and Error Calculations. — Actually, the 

 geophysicist is interested in the inverse problem of that described above : 

 namely, it is desired to infer from the observed data, the form, dimensions. 



_ Fig. 209. — General type of gradient and 

 differential curvature profiles produced by 

 structural ridges. (Barton, A.I.M.E. Geo- 

 physical Prospecting, 1929.) 



t Barton, loc. cit. 



