the track spacing and surveying at an angle to the trends in the data. Obviously 

 this will not be true in the general case, since the effect of changing any of the 

 survey design parameters will be controlled by the characteristics of the field 

 being measured. 



Survey models 3 and 4 were used to produce data for testing three 

 algorithms for computing mean gravity anomalies. The technique for generating 

 mean anomalies using both a nine point averaging of the gridded data produced 

 by the cubic spline and the two-dimensional integration of the bicubic spline 

 surface have been discussed previously. In addition to these methods, a 

 technique was tested which utilized a one-dimensional Lagrange interpolation 

 (see e.g., Hamming, 1962). This procedure generated mean gravity anomalies 

 on a uniform grid by averaging all of the survey data points falling within a 

 grid interval to form a mean for that interval. Following this, a one-dimensional 

 fourth-degree Lagrange interpolation was applied to these mean values to obtain an 

 estimate of the mean gravity value for each of the grid cells for which no survey 

 data was available. The results of these mean anomaly tests are shown in 

 Figures 21-27. Figure 21 is a contour chart of the differences between the 

 true mean anomalies computed for each one-minute square of the model field 

 via equation (30), and the mean values computed by averaging the 1/2 minute 

 grid values produced by applying the cubic spline procedure to the survey data 

 from model 3. Figure 22 is a contour chart showing the differences between the 

 true one-minute means and those generated by application of the Lagrange 

 procedure to the model -3 data. The contour interval is the same in these two 

 figures. The errors produced by the lack of control of the derivatives in the 

 Lagrange interpolation method is apparent in Figure 22. It is probable that 

 these errors could be reduced somewhat by using a third-degree Lagrange 

 polynomial instead of the fourth-degree but, in light of the obvious advantages 

 of the spline formulation, no additional testing of this approach was undertaken. 



41 



