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    Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the Earth's surface using the gradient approach.

    173467_Hirt2012_efficientSHS_JGeod_av[1].pdf (794.4Kb)
    Access Status
    Open access
    Authors
    Hirt, Christian
    Date
    2012
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Hirt, Christian. 2012. Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the Earth's surface using the gradient approach. Journal of Geodesy. 86 (9): p.p. 729-744.
    Source Title
    Journal of Geodesy
    DOI
    10.1007/s00190-012-0550-y
    ISSN
    09497714
    School
    Department of Spatial Sciences
    Remarks

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

    URI
    http://hdl.handle.net/20.500.11937/25692
    Collection
    • Curtin Research Publications
    Abstract

    Spherical harmonic synthesis (SHS) of gravity field functionals at the Earth’s surface requires the use of heights. The present study investigates the gradient approach as an efficient yet accurate strategy to incorporate height information in SHS at densely spaced multiple points. Taylor series expansions of commonly used functionals quasigeoid heights, gravity disturbances and vertical deflections are formulated, and expressions of their radial derivatives are presented to arbitrary order. Numerical tests show that first-order gradients, as introduced by Rapp (J Geod 71(5):282–289, 1997) for degree 360 models, produce cm- to dm-level RMS approximation errors over rugged terrain when applied with EGM2008 to degree 2190. Instead, higher-order Taylor expansions are recommended that are capable of reducing approximation errors to insignificance for practical applications. Because the height information is separated from the actual synthesis, the gradient approach can be applied along with existing highly efficient SHS routines to compute surface functionals at arbitrarily dense grid points. This confers considerable computational savings (above or well above one order of magnitude) over conventional point-by-point SHS. As an application example, an ultra-high resolution model of surface gravity functionals (EurAlpGM2011) is constructed over the entire European Alps that incorporates height information in the SHS at 12,000,000 surface points.Based on EGM2008 and residual topography data, quasigeoid heights, gravity disturbances and vertical deflections are estimated at ~200m resolution. As a conclusion, the gradient approach is efficient and accurate for high-degree SHS at multiple points at the Earth’s surface.

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