pivot distance (usually set at 0.2 of a meridional part), the 

 value associated with the data point is unchanged. If this 

 distance is greater than the pivot distance, then the adjusted 

 value associated with the mapped coordinates is computed. 



In the computer program for the cubic spline algorithm 

 (SPLINE) contained in appendix B, the pivot distance is selectable 

 via a control card. This pivot distance is usually equal to 

 the maximum distance which one could move a data point without 

 significantly changing its value. In order to minimize the error 

 associated with the assumption that the gradient correction is 

 independent of direction, continuous synthetic survey tracks 

 which deviate appreciably from a stright line should be broken 

 up into smaller segments with each segment treated as a separate 

 track. The mapped coordinates and adjusted data values may 

 be considered as irregularly spaced digital samples from a 

 function whose independent variable is distance along the track 

 from some arbitrary starting point, and whose dependent variable 

 is the adjusted data values. 



Utilizing the mapped data, the cubic spline is determined 

 for each track. The cubic spline may then be used to interpolate 

 data values at the intersections of the straight least square 

 track lines and a set of parallel lines whose spacing is equal 

 to the desired final grid spacing (5 minutes) . If the direction 

 of the survey tracks is predominantely 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 (app. B) , 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. 



The interpolated data values generated as outlined in the 

 preceding paragraph may be regarded as unequally spaced digital 

 samples from a function whose independent variable is distance 

 along each of the parallel lines. Application of the spline 

 procedure 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 control card formats for SYNGRID are given in figure 10. 

 The output from SYNGRID is a new punched card deck of gridded 

 bathymetry with seven points per card. The printout from SYNGRID 



17 



