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    The Meissl scheme for the geodetic ellipsoid

    115115_9023_20071116 Author-made.pdf (387.4Kb)
    Access Status
    Open access
    Authors
    Claessens, Sten
    Featherstone, Will
    Date
    2008
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Claessens, Sten and Featherstone, Will. 2008. The Meissl scheme for the geodetic ellipsoid. Journal of Geodesy 82 (8): 513-522.
    Source Title
    Journal of Geodesy
    DOI
    10.1007/s00190-007-0200-y
    ISSN
    09497714
    Faculty
    Department of Spatial Sciences
    Faculty of Science & Engineering
    Remarks

    The original publication is available at http://www.springerlink.com

    http://dx.doi.org/10.1007/s00190-007-0200-y

    URI
    http://hdl.handle.net/20.500.11937/17068
    Collection
    • Curtin Research Publications
    Abstract

    We present a variant of the Meissl scheme to relate surface spherical harmonic coefficients of the disturbing potential of the Earth's gravity field on the surface of the geodetic ellipsoid to surface spherical harmonic coefficients of its first- and second-order normal derivatives on the same or any other ellipsoid. It extends the original (spherical) Meissl scheme, which only holds for harmonic coefficients computed from geodetic data on a sphere. In our scheme, a vector of solid spherical harmonic coefficients of one quantity is transformed into spherical harmonic coefficients of another quantity by pre-multiplication with a transformation matrix. This matrix is diagonal for transformations between spheres, but block-diagonal for transformations involving the ellipsoid. The computation of the transformation matrix involves an inversion if the original coefficients are defined on the ellipsoid. This inversion can be performed accurately and efficiently (i.e., without regularisation) for transformation among different gravity field quantities on the same ellipsoid, due to diagonal dominance of the matrices. However, transformations from the ellipsoid to another surface can only be performed accurately and efficiently for coefficients up to degree and order 520 due to numerical instabilities in the inversion.

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