138 



GRAVITATIONAL METHODS 



[Chap. 7 



in radius from 2 m to 22 km, each containing from four to sixteen compart- 

 ments, have been published by Hammer. 



Another procedure uses so-called graticules, or correction diagrams, in 

 which the attraction of each element is the same, regardless of distance or 

 azimuth. They may be prepared for use in plan view (with contour lines) 



or in vertical section (with 

 terrain profiles). A graticule 

 for use with contour lines is 

 calculated in the following 

 manner :^' As indicated in Fig. 





1-Zl^ the surrounding topog- 

 raphy is assumed to be 

 composed of masses which 

 have the shape of cylindrical 

 segments. Hence, the mass 

 of such an element is dm = 

 h-rd*p-dr-dh. Since the po- 

 tential of a mass element at the origin is f/ = /b • dm/r, the potential due 

 to the entire topography surrounding the station is given by 



Fig. 7-37. Terrain sectors. 



U = U I / / 



Jo •'0 •'0 



rdr-d<p-dh 



(7-386) 



The integration is here extended for distances from to infinity. In 

 practice the calculation is carried only to the point where the terrain effect 

 is less than the probable error. The integration may be carried out by 

 introducing a terrain angle ^ = tan"* h/r. Then the vertical component 

 of the attraction follows from a differentiation of eq. (7-386): 



Ag = — = - A;5 f [ (1 - cos ^) dr.d<f. (7-38c) 



dz Jo Jo 



The mass elements are now so dimensioned that within each of them 

 the terrain angle may be assumed to be constant. If each mass element 

 is bouhded by the concentric radii Tj^ and rm+i and by the angles <Pa 

 and ^n+i> 



which is 



Ag = -kSil - cos^) / / dr'd,p, 



A^ = -kSil - COS\l/)(rja+i - 0(^n+i - ^n)- 



(7-38d) 



"S. Hammer, Geophysics, 4(3), 184-194 (July, 1939). 

 ^9 K. Jung, Zeit. Geophys., 3(6), 201-212 (1927). 



