UNCLASSIFIED 



Security Classification 



DOCUMENT CONTROL DATA -R&D 



(Security classification of title, body of abstract and indexii 



sd when the 



rlassified) 



ORIGINATING ACTIVITY (Corporate author) 



U.S. NAVAL OCEANOGRAPHIC OFFICE 



2a. REPORT SECURI TY C L A SSI F I C A Tl Or> 



UNCLASSIFIED 



3- REPORT TITLE 



SPLINE INTERPOLATION ALGORITHMS FOR TRACK-TYPE SURVEY DATA WITH APPLICATION 

 TO THE COMPUTATION OF MEAN GRAVITY ANOMALIES 



DESCRIPTIVE NOTES (Type of report and inclusive dates) 



Technical Report 



I THOR(S) (First i 



iddle initial, last I 



Thomas M. Davis 



Angelo L. Kontis 



6. REPORT DATE 



December 1970 



rOTAL NO. OF PAGES 



82 



?b. NO. OF RE FS 



14 



8a. CONTRACT OR GRANT NO. 

 b. PROJEC T NO. 



709-EJ-GLG 

 HF 05 552 320 



9a. ORIGINATOR'S REPORT NUMBER(S) 



TR-226 



10. DISTRIBUTION STATEMENT 



This document has been approved for public release and sale; its distribution is unlimited. 



SUPPLEMENTARY NOTES 



12. SPONSORING MILI 



U.S. Naval Oceanographic Office 

 Washington, D. C. 20390 



13. ABSTRACT 



Cubic spline interpolation is a mathematical procedure which is an analog of the 

 draftsman's plastic spline. The advantage of this interpolation procedure over the more 

 commonly used methods such as Lagrange lies in its ability to not only fit each given data 

 value exactly but to maintain continuity of the first and second derivatives. 



The relative accuracy of the cubic spline interpolation procedure for generating 

 gridded data values and estimates of mean gravity anomalies from track -type geophysical 

 surveys is shown to be excellent when applied to properly designed surveys. Techniques 

 for interpreting the two-dimensional Fourier transform in terms of track spacing, track 

 orientation, and down-track sampling rate are presented to demonstrate the effect of 

 these parameters on interpolation accuracy. A procedure for utilizing closed form 

 integration of the bicubic spline surface to produce mean gravity anomalies is shown to 

 yield accuracies comparable to the method of averaging cubic spline grid values. 



DD, f n°o r v m 65 1473 



S/N 0101-807-6801 



(PAGE 1 



UNCLASSIFIED 



Security Classification 



