Geo-spatial Information Science

, Volume 3, Issue 2, pp 53–57 | Cite as

Discussion on some FFT problems to determine the geoid

  • Essam Ghanem
  • Li Jiancheng


The aim of this investigation is to study some FFT problems related to the application of FFT to gravity field convolution integrals. And the others, such as the effect of spectral leakage, edge effects, cyclic convolution and effect of padding, are also discussed. A numerical test for these problems is made. A large area of Western China selected for the test is located between 30°N∼36°N and 96°E∼102°E and includes 1 858 gravity observations on land. The results show that the removal of the bias in the residual gravity anomalies is important to avoid spectral leakage. One hundred percent zero padding is highly recommended for further research of the geoid to remove cyclic convolution errors and edge effects. 1-D FFT is recommended for precise local geoid determination because it does not use kernel approximation.

Key Words

fast Fourier transformation (FFT) geoid determination 


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  1. 1.
    Forsberg R, Sideris M G. Geoid computations by the multi-band spherical FFT approach.Manuscripta Geodaetica, 1993, 18:82–90Google Scholar
  2. 2.
    Haagmans R, Min De E, Gelderen M Van. Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes'.Manuscripta Geodaetica, 1993, 18:227–241Google Scholar
  3. 3.
    Heiskanen W A, Moritz H.Physical Geodesy. San Francisco-London: Freeman & Company, 1967Google Scholar
  4. 4.
    Liu J N, Ning J S, Chao D B. Comments on two dimensional convolutions of the geodetic problems in planar and spherical coordinates. IAG Scientific Assembly, Brazil, 1997Google Scholar
  5. 5.
    Li Y C. Optimized spectral geoid determination: [Master Thesis]. Calgary: Department of Geomatics Engineering, The university of Calgary, 1993Google Scholar
  6. 6.
    Schwarz K P, Sideris M G, Forsberg R. The use of FFT techniques in physical geodesy.Geophys. Int., 1990, 100:485–514.CrossRefGoogle Scholar
  7. 7.
    Sideris M G. Spectral methods for the numerical solution of Molodensky Problem. UCSE Report #20050. Department of Surveying Eng., The University of Calgary, Calgary, Alberta, 1987Google Scholar
  8. 8.
    Sideris, M G, Li Y C. Gravity field convolutions without windowing and edge effects.Bulletin Geodesique, 1993, 67:107–118CrossRefGoogle Scholar
  9. 9.
    Strang Van Hees G. Stokes' formulae using fast Fourier techniques.Manuscripta Geodaetica, 1990, 15:235–239Google Scholar
  10. 10.
    Vermer M, Li J, Guo C. Geoid Determination by FFT Techniques and MGM in the Western China Test Area. Finnish Geodetic Institute, 1997Google Scholar
  11. 11.
    Wang Y M. Comments on proper use of the terrain correction for the computation of height anomalies.Manuscripta Geodaetica, 1993, 18:53–57Google Scholar

Copyright information

© Wuhan University of Technology & Springer 2000

Authors and Affiliations

  • Essam Ghanem
    • 1
  • Li Jiancheng
  1. 1.GPS CenterWuhan Technical University of Surveying and MappingWuhanChina

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