Figure 23 compares the histograms of the errors generated by the cubic spline 

 and Lagrange algorithms. Figures 24-26 show that simular results are obtained 

 with the cubic spline and Lagrange methods when they were applied to a con- 

 ventional shipboard gravity survey simulated by the test model 4 previously 

 described. 



In order to determine if the increased computing time necessary for 

 producing mean anomalies by integrating the bicubic spline surface was justified, 

 the algorithm was applied to the one-minute grid values generated by application 

 of the cubic spline to the model -3 survey data. A histogram of the errors 

 resulting from this technique is shown in Figure 27. A comparison of Figures 

 23 and 27 clearly indicates that the unique capabilities of the bicubic spline 

 approach are wasted in so far as the computation of mean anomalies is concerned. 



CONCLUSIONS 



After evaluating the results obtained from this series of tests, the 

 following conclusions may be drawn: 



1 . The cubic spline algorithm for gridding track-type survey data and 

 for computing mean gravity anomalies is accurate and computationaly efficient 

 in comparison with the other techniques which were tested. 



2. The significant improvement achieved by the model-3 survey in 

 comparison to the model-1 survey illustrates the concept of the sampling 

 theorem embodied in equation (23), i.e., the accuracy of mathematical 

 interpolation, and in particular the spline method, is highly dependent on 

 the density of the survey data points relative to the frequency content of the 

 anomalies. The results obtained by models 3 and 4 show that, if a survey is 

 well designed, highly accurate interpolation may be anticipated by use of the 

 spline procedure. Implicit in this conclusion is the requirement that the survey 

 data itself be of high quality. 



43 



