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Global spherical harmonic computation by two-dimensional Fourier methods

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Abstract

A method is presented for performing global spherical harmonic computation by two-dimensional Fourier transformations. The method goes back to old literature (Schuster 1902) and tackles the problem of non-orthogonality of Legendre-functions, when discretized on an equi-angular grid. Both analysis and synthesis relations are presented, which link the spherical harmonic spectrum to a two-dimensional Fourier spectrum. As an alternative, certain functions of co-latitude are introduced, which are orthogonal to discretized Legendre functions. Several independent Fourier approaches for spherical harmonic computation fit into our general scheme.

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Authors and Affiliations

  1. Institut für Astronomische und Physikalische Geodäsie, Technische Universität München, Arcisstraße 21, D-80290, München, Germany

    Nico Sneeuw

  2. Faculteit der Geodesie, Technische Universiteit Delft, Thijsseweg 11, NL-2629 JA, Delft, The Netherlands

    Richard Bun

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  1. Nico Sneeuw
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  2. Richard Bun
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Sneeuw, N., Bun, R. Global spherical harmonic computation by two-dimensional Fourier methods. Journal of Geodesy 70, 224–232 (1996). https://doi.org/10.1007/BF00873703

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  • DOI: https://doi.org/10.1007/BF00873703

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