A Geopotential Representation with Sampling Functions

  1. Soren W. Henriksen,
  2. Armando Mancini and
  3. Bernard H. Chovitz
  1. C. A. Lundquist1 and
  2. G. E. O. Giacaglia2

Published Online: 15 MAR 2013

DOI: 10.1029/GM015p0125

The Use of Artificial Satellites for Geodesy

The Use of Artificial Satellites for Geodesy

How to Cite

Lundquist, C. A. and Giacaglia, G. E. O. (1972) A Geopotential Representation with Sampling Functions, in The Use of Artificial Satellites for Geodesy (eds S. W. Henriksen, A. Mancini and B. H. Chovitz), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM015p0125

Author Information

  1. 1

    Smithsonian Astrophysical Observatory, Cambridge, Massachusetts 02138

  2. 2

    University of Texas, Austin, Texas 78712

Publication History

  1. Published Online: 15 MAR 2013
  2. Published Print: 1 JAN 1972

ISBN Information

Print ISBN: 9780875900155

Online ISBN: 9781118663646

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Keywords:

  • Geoid;
  • Latitude;
  • Sampling functions;
  • Satellite orbit theory;
  • Satellite-to-ocean altitudes

Summary

Satellite-to-ocean altitudes measured to meter accuracy eventually can yield a geoid representation with significant short-wavelength structure over ocean areas. To cope conveniently with this expected detail, one suggested analytical technique would represent the geopotential or the geoid as an expansion in sampling functions that are linear combinations of spherical harmonics. Each of the sampling functions makes its principal contribution to the geopotential in a single geographical region. For a representation truncated after degree N, there are (N + 1)2 such functions associated with a like number of points distributed nearly regularly on the globe. The features of this geopotential representation can be illustrated by considering the case N = 22, for which an expansion in sampling functions can be produced that is equivalent to the geopotential of the 1969 Smithsonian standard earth.