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    A surface spherical harmonic expansion of gravity anomalies on the ellipsoid

    231911.pdf (1.771Mb)
    Access Status
    Open access
    Authors
    Claessens, Sten
    Hirt, C.
    Date
    2015
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Claessens, S. and Hirt, C. 2015. A surface spherical harmonic expansion of gravity anomalies on the ellipsoid. Journal of Geodesy. 89 (10): pp. 1035-1048.
    Source Title
    Journal of Geodesy
    DOI
    10.1007/s00190-015-0832-2
    ISSN
    0949-7714
    School
    Department of Spatial Sciences
    Remarks

    The final publication is available at Springer via http://doi.org/10.1007/s00190-015-0832-2

    URI
    http://hdl.handle.net/20.500.11937/40788
    Collection
    • Curtin Research Publications
    Abstract

    A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth’s disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellipsoidal approximation with respect to a reference ellipsoid is derived. This transformation cannot rigorously be achieved by the Hotine–Jekeli transformation between spherical and ellipsoidal harmonic coefficients. The method derived here is used to create a surface spherical harmonic model of gravity anomalies with respect to the GRS80 ellipsoid from the EGM2008 global gravity model. Internal validation of the model shows a global RMS precision of <1 nGal. This is significantly more precise than previous solutions based on spherical approximation or approximations to order e2 or e3, which are shown to be insufficient for the generation of surface spherical harmonic coefficients with respect to a geodetic reference ellipsoid. Numerical results of two applications of the new method (the computation of ellipsoidal corrections to gravimetric geoid computation, and area means of gravity anomalies in ellipsoidal approximation) are provided.

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