248 



GRAVITATIONAL METHODS 



[Chap. 7 



(a) 



in the —x' direction as negative ordinate. A curvature vector at 0° 

 angle is plotted as positive ordinate (d^U/dXi) and a curvature making 

 an angle of 90° with the profile as negative ordinate. 



5. Calculation of relative gravity, construction of isogams. Since the 

 horizontal gradient of gravity represents the slope of the gravity curve, 

 it is possible to calculate the difference in gravity between two points when 

 the rate is reasonably uniform and the distance between them is small. 

 A number of procedures are in use to accomplish the "mechanical integra- 

 tion" of the gradient curve. For close spacings of stations and uniform 

 gradients it is satisfactory to project the gradient vectors on the profile 

 line, to average the projections at successive stations, and to multiply the 



average by the distance. If 

 gradients are expressed in E.U. 

 and distances in kilometers, 

 the gravity anomaly is ob- 

 tained in tenth milligals. Cal- 

 culation of the projection of 

 the vectors upon a line con- 

 necting the station is facili- 

 tated by the use of a gradu- 

 ated glass scale or transparent 

 graduated paper. Gravity dif- 

 ferences are added from sta- 

 tion to station along closed 

 loops, and the error of closing 

 is distributed at the end. A 

 least square adjustment of the 

 entire net of stations can be 

 made if desired."" 



A second method of calcu- 

 lating gravity differences be- 

 tween stations is based on 

 the construction of tangent polygons (Fig. 7-956), with the assump- 

 tion that the rate given by the gradient at one station prevails half 

 way to the next. Between two stations, A and B, the projections of 

 the vectors Ulz and U'sz are plotted as ordinates against unit distance. 

 This procedure, beginning with A, gives the point D on the "Ag curve" 

 for the half-way point E. Hence, the gradient for the second station, B, 

 is plotted as ordinate against unit distance and the point F is obtained 

 on the gravity curve. The procedure is again applied to several sets of 

 stations arranged in closed loops or polygons. Three stations arranged 



"«D. C. Barton, A.A.P.G. Bull., 13(9), 1168-1181 (Sept., 1929). I. Roman, 

 A.I.M.E. Geophysical Prospecting, 486-503 (1932). 



Fig. 7-94. Projection of gradients and curva- 

 tures on profile direction. 



