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    The rigorous determination of orthometric heights

    117363_117363.pdf (766.9Kb)
    Access Status
    Open access
    Authors
    Tenzer, R.
    Vanicek, P.
    Santos, M.
    Featherstone, Will
    Kuhn, Michael
    Date
    2005
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Tenzer, R. and Vanicek, P. and Santos, M. and Featherstone, W. and Kuhn, M. 2005. The rigorous determination of orthometric heights. Journal of Geodesy. 79 (1-3): pp. 82-92.
    Source Title
    Journal of Geodesy
    DOI
    10.1007/s00190-005-0445-2
    ISSN
    09497714
    Faculty
    Department of Spatial Sciences
    Faculty of Science and Engineering
    WA School of Mines
    Remarks

    The final publication is available at Springer via http://doi.org/10.1007/s00190-005-0445-2

    URI
    http://hdl.handle.net/20.500.11937/9386
    Collection
    • Curtin Research Publications
    Abstract

    The main problem of the rigorous definition of the orthometric height is the evaluation of the mean value of the Earth’s gravity acceleration along the plumbline within the topography. To find the exact relation between rigorous orthometric and Molodensky’s normal heights, the mean gravity is decomposed into: the mean normal gravity, the mean values of gravity generated by topographical and atmospheric masses, and the mean gravity disturbance generated by the masses contained within geoid. The mean normal gravity is evaluated according to Somigliana–Pizzetti’s theory of the normal gravity field generated by the ellipsoid of revolution. Using the Bruns formula, the mean values of gravity along the plumbline generated by topographical and atmospheric masses can be computed as the integral mean between the Earth’s surface and geoid. Since the disturbing gravity potential generated by masses inside the geoid is harmonic above the geoid, the mean value of the gravity disturbance generated by the geoid is defined by applying the Poisson integral equation to the integral mean. Numerical results for a test area in the Canadian Rocky Mountains show that the difference between the rigorously defined orthometric height and the Molodensky normal height reaches 0.5 m.

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