variable being distance along track from some arbitrary starting point, and 

 the dependent variable being of course the adjusted data values. 



3. Utilizing the mapped data, the cubic spline, equation (6), is 

 determined for each track. This equation may then be used to interpolate 

 data values at the intersections of the straight least -squares track lines and a 

 set of parallel lines whose spacing is equal to the desired final grid spacing. 

 If the direction of the survey tracks is predominately east-west then the 

 direction of the set of parallel lines is north-south. Similarly, for north- 

 south tracks, the lines are run east-west. The computer program, contained 

 in the appendix, is designed to operate on tracks in any direction except 

 exactly north-south. The direction of the set of parallel grid lines is controlled 

 by the direction of track line number one. Since the track number designation 

 is arbitrary, this feature allows the user to determine the desired orientation 

 (N-S or E-W) of the parallel grid lines in order to obtain as many intersections 

 as possible. 



4. The interpolated data values generated in step 3 may be regarded 



as unequally-spaced digital samples from a function whose independent variable 

 is distance along each of these parallel lines. Application of the spline pro- 

 cedure in this cross-track direction produces the final interpolated values at 

 the desired grid points. If mean anomalies are desired, grid points are generated 

 at one-half the final grid spacing and the resulting nine points are averaged to 

 produce the mean value for each grid cell . 



THE BICUBIC SPLINE ALGORITHM FOR THE GENERATION OF 

 MEAN ANOMALIES 



In the previous development (Step 4) the mean value of the function 

 is obtained by averaging the nine interpolated values located within the region 

 in which the mean is desired. The accuracy of this method will, of course, 

 depend on the spacing of the points used in the averaging process relative to 



10 



