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    Spherical harmonic analysis of a harmonic function given on a spheroid

    241252_241252.pdf (1.507Mb)
    Access Status
    Open access
    Authors
    Claessens, Sten
    Date
    2016
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Claessens, S. 2016. Spherical harmonic analysis of a harmonic function given on a spheroid. Geophysical Journal International. 206 (1): pp. 142-151.
    Source Title
    Geophysical Journal International
    DOI
    10.1093/gji/ggw126
    ISSN
    0956-540X
    School
    Department of Spatial Sciences
    Remarks

    This article has been accepted for publication in Geophysical Journal International©2016. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

    URI
    http://hdl.handle.net/20.500.11937/30661
    Collection
    • Curtin Research Publications
    Abstract

    A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.

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