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Methods to Reduce Aliasing in Spherical Harmonic Analysis

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Global Gravity Field and Its Temporal Variations

Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 116))

Abstract

The effect of aliasing is rigorously formulated for various currently practiced methods of harmonic analysis of gravity anomalies on the sphere. This shows clearly not only the suboptimality, in terms of aliasing error, of some methods, but also the inappropriateness of uniformly weighted averaging of gravity anomalies in latitude/longitude grid cells. The following results are obtained: 1) The simple quadratures method and related methods of analysis are biased even with band-limited functions. 2) A modification of Colombo’s method of least squares, requiring only a slight increase in number of computations, further reduces the aliasing error. 3) The essential elimination of aliasing can only be effected with weighted, spherical cap averages, not with the often used, unweighted, constant angular block averages.

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References

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Authors and Affiliations

  1. Department of Geodetic Science and Surveying, The Ohio State University, Columbus, OH, 43210, USA

    Christopher Jekeli

Authors
  1. Christopher Jekeli
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Editors and Affiliations

  1. Dept. of Geodetic Science and Surveying, The Ohio State University, 1958 Neil Ave., 43210, Columbus, OH, USA

    Richard H. Rapp

  2. GRGS- CNES, 18 Avenue Edouard Belin, F-31400, Toulouse, France

    Anny A. Cazenave

  3. Dept. of Aerospace Engineering and Engineering Mechanics, CO 600, Center for Space Research, CO 605, The University of Texas at Austin, 78712, Austin, TX, USA

    R. Steven Nerem

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© 1996 Springer-Verlag Berlin Heidelberg

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Jekeli, C. (1996). Methods to Reduce Aliasing in Spherical Harmonic Analysis. In: Rapp, R.H., Cazenave, A.A., Nerem, R.S. (eds) Global Gravity Field and Its Temporal Variations. International Association of Geodesy Symposia, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61140-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-61140-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60882-0

  • Online ISBN: 978-3-642-61140-7

  • eBook Packages: Springer Book Archive

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