transform subroutine called NLOGN, written by Robinson (1967), is contained 

 in the appendix. This program was used to design the simulated surveys for 

 testing the cubic spline algorithms. 



B. Development of a Point-Mass Model Field 



To provide a reference surface for determining quantitative estimates of 

 interpolation accuracy and to ensure that the data used in the interpolations are 

 error free, gravity model data were generated from a random distribution of 

 point masses as follows. 



Consider a point (P) on the surface of a sphere (Figure 3) with spherical 

 coordinates (0, X), and a point mass located at depth d beneath the surface with 

 coordinates (0', X'). The gravitational potential at P(0, X) due to the point mass is 



•km 



v p = 



(29) 



where m is mass, k is the universal gravitational constant, and r is the distance 

 between the point mass and the point (P). 



P(©,X) 



(©',X') 



POINT MASS 



FIGURE 3. GEOMETRY FOR COMPUTING THE GRAVITATIONAL 

 POTENTIAL DUE TO A POINT MASS. 



