266 



GRAVITATIONAL METHODS 



[Chap. 7 



for sixteen azimuths, they may readily be modified for fewer directions by 

 changing the azimuth factor in eq. (7-88). These diagrams are particu- 

 larly suited for the calculation of salt domes, cap rocks, irregular ore 

 bodies, mine cavings, and the like. Certain two-dimensional diagrams 

 are applicable to such geologic features as domes or anticlines if a definite 

 variation of strike extent with depth of the elements (Barton) is 

 incorporated. 



u: 



u. 



'JCZ 



Fig. 7-100. Orientation of two-dimensional interpretation diagram (Fig. 7-796) for 

 gradients and curvatures (after Jung). 



Diagrams for two-dimensional bodies are readily calculated, since their 

 surface effects depend on section only. Calculations are a minimum with 

 cylindrical coordinates. Integration of eq. (7-91c) gives 



Ux'z = -k8 loge °^' (cos 2<pja+i " COS 2<p^) 



Ua' = -kS log, -^' (sin 2^nj+i - sin 2<pjJ 



' (7-956) 



for an element bounded by radii r^ and ?'„+! and angles v?ni find <pja+i (as 

 in Fig. 7-796). A comparison of these equations with the last two in eq. 

 7-86 shows that the curvature terrain diagram of Fig. 7-796 maj^ be used 

 for calculations of gradients and curvatures of two-dimensional masses. 

 Eq. (7-956) indicates 45° symmetry and therefore the orientation for 

 gradients and curvatures differs by 45°, as shown in Fig. 7-100. The unit 

 effect is f E.U. For evaluating horizontal or nearly horizontal forma- 

 tions, it is more convenient to arrange the mass elements along horizontal 

 lines and therefore base the calculations on formula (7-94c). In a form 



