and letting the limits of integration be C < x < D and A < y < B, and with 



x =y = h, integration of equation (21) yields 



max ' max 



, ! P. 1 % % " l'n (O m+, -C m+, )(B n+1 -A n+ '). (22) 



C ii " (B-A)(D-Q Ji Q n t (n+l)(m+1) 



The computer program for the bicubic spline algorithm uses this formula to 

 determine estimates of the mean anomaly on a specified grid interval. 



GENERATION OF MODELS FOR TESTING THE ACCURACY OF 

 INTERPOLATION PROCEDURES 



Two essential criteria for determining the accuracy of an interpolation 

 technique are (1) the existence of some reference surface with which the 

 interpolated values can be compared, and (2) all errors due to sources 

 unrelated to the interpolation process be minimal. We are concerned with 

 testing interpolation methods for use with data collected by systematic surveys. 

 For this specific application, the above criteria can be met by properly designed 

 simulated surveys of a mathematically-derived reference surface. Proper design 

 implies that the survey parameters viz., track spacing, track orientation, and 

 down-track sampling interval be chosen so as to define the essential characteristics 

 of the reference surface. In the following material we discuss the theory and 

 application of the fast Fourier transform for the design of surveys. In addition, 

 the method of determining the reference surface for use in obtaining quantitative 

 estimates of interpolation accuracy is given. 



A. The Two-Dimensional Fast Fourier Transform as a Tool for 

 Simulated Survey Design 



Simulated surveys must be designed in such a way as to minimize 

 aliasing o.f the spectral components of the data. At the present time, the 

 sampling theory that we have available is based primarily on the Shannon 



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