Accession Number : AD0755486

Title :   Mathematical Methods Applied to Ocean-Surface Topography and Satellite Geodesy.

Descriptive Note : Semiannual progress rept. no. 1, 1 Jun-30 Nov 72,

Corporate Author : SMITHSONIAN ASTROPHYSICAL OBSERVATORY CAMBRIDGE MASS

Personal Author(s) : Lundquist,Charles A.

Report Date : DEC 1972

Pagination or Media Count : 28

Abstract : Two specific studies are mentioned. In the first study, the transformation matrices between spherical harmonics and spherical sampling functions have been tabulated for linear spaces truncated after degrees 22 and 36. The matrix elements were calculated by evaluating analytical expressions for the transformations and their inverses. The matrices are 529 by 529 and 1369 by 1369 arrays, respectively. These matrices allow facile transformation between equivalent earth gravity models expanded in spherical harmonics or sampling functions. In the second study, spherical sampling functions can be used instead of spherical harmonic functions in a truncated series representation for the geoid or the geopotential. The spherical sampling-function representation of the geopotential has a simple relationship to the mass-layer models or mass-concentration models suggested by other investigators. The spherical reference surface on which the sampling points are arrayed can be transformed into a nearby surface such as an ellipsoid. Sampling functions defined for a set of concentric reference surfaces might provide a convenient representation for the mass distribution of the earth. (Author)

Descriptors :   (*GRAVITY, NUMERICAL METHODS AND PROCEDURES), POTENTIAL THEORY, SAMPLING, HARMONIC ANALYSIS, SPECIAL FUNCTIONS(MATHEMATICAL), SERIES(MATHEMATICS), SCIENTIFIC SATELLITES

Subject Categories : Geodesy

Distribution Statement : APPROVED FOR PUBLIC RELEASE