For a sphere of radius R, the distance r is 



2 2 1/2 



r = (IT+R' -2RR' cos iff) X 



where R 1 = R - d 



and 



cos \lf = cos cos 1 + Sin Sin 0' cos ( X- X ) . 



The radial (vertical component) "g R of the gravitational force at P is 



9V P km 



% (e ' X)= --aiT =T <*-*■«*). 



r 



For a finite number (N) of point masses situated at various depths and locations 

 beneath the surface of the sphere, we can generate gravity anomalies on the 

 sphere by summing the radial components due to the N point masses, i .e., 



N km. 



? R (9,X) = 2 -j (R-R'j cos +.) . (30) 



i=l r. 

 i 



A computer program to calculate the radial, easterly, and northerly components, 

 in addition to the deflection of the vertical components with respect to a 

 spherical earth of a set of point masses is given in the appendix. 



COMPARISON OF GRIDDING TECHNIQUES AND THE COMPUTATION 

 OF MEAN ANOMALIES USING MODEL DATA 



The accuracy of the spline interpolation method, relative to several 

 other techniques, is now considered in terms of gridding survey data and the 

 computation of mean gravity anomalies by utilizing simulated survey data. 



A set of gravity anomalies, for use as a reference surface, were 

 calculated from equation (30), at one-minute intervals, over an area of 80 x 

 80 square minutes. The anomalies, given in Figure 4, result from 16 point 



19 



