insures that the proper and sufficient number of points have 

 been extracted from the MSQLOC area. Additional tracks of data 

 can be created at this time, if required by the complexity of 

 the submarine topography. SYNCHEX requires a control card that 

 is in reality the first data card. The format for this card is 

 given in figure 9. If no further corrections or additions are 

 to be made to the data deck, the MSQLOC area is ready for 

 conversion to gridded bathymetry. 



The SYNGRID program is fundamental to the structuring phase 

 of SYNBAPS. SYNGRID transforms the synthetic track line data 

 into gridded bathymetric data. The mathematical foundation and 

 philosophy behind the one-dimensional cubic spline used to 

 structure the gridded data is fully explained by' Davis and Kontis 

 (1970) . SYNGRID is a modification by Davis of his original 

 program (SPLINT) to handle bathymetric data instead of gravity 

 data. SYNGRID is very flexible as it grids track-line-point 

 data on either a Mercator projection or a Cartesian coordinate 

 system and can compute mean data for various size cells on either 

 system. Summarizing Davis and Kontis (1970) , the value of this 

 method lies not only in its ability to fit the observed data 

 values but to retain the continuity of the first and second 

 derivatives. This method might be considered the mathematical 

 analog of the draftsman's plastic spline. 



Because the cubic spline is a function of only one independent 

 variable, the data obtained along a synthetic track line must be 

 adjusted to lie on a straight line. Under most conditions this 

 creates no problem as the data are digitized along straight lines. 

 The interpolation formula used by Davis fits each data exactly, 

 has continuous first and second derivations, and is a simple cubic 

 polynomial in x within the interval between each pair of data 

 points. The distance along the track line then may be interpreted 

 as the independent variable. Therefore, taking the data from one 

 track at a time, the position of the data points are converted 

 into X, y coordinates and a least squares straight line is fitted 

 to these locations. Because no statistical significance is 

 attached to this operation, either x or y may be considered the 

 independent variable. The computer program listed in appendix B 

 considers x the equivalent longitude as the independent variable. 

 If the survey tracks happen to run exactly north-south, the 

 program should be modified to consider y as the independent 

 variable. 



The perpendicular distance between the least squares straight 

 line and each data point is determined and used to project the 

 points orthogonally onto the line with an adjusted data value 

 (based on an estimate of the local gradient) assumed to be a 

 function of distance only. If the perpendicular distance between 

 this point and the least squares line is less than predetermined 



15 



