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    Determination of the Boundary Values for the Stokes-Helmert Problem

    Access Status
    Fulltext not available
    Authors
    Huang, J.
    Novak, P.
    Martinec, Z.
    Featherstone, Will
    Vanicek, P.
    Pagiatakis, S.
    Veronneau, M.
    Date
    1999
    Type
    Journal Article
    
    Metadata
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    Citation
    Vanicek, P. and Huang, J. and Novak, P. and Pagiatakis, S. and Veronneau, M. and Martinec, Z and Featherstone, W.E. 1999. Determination of the boundary values for the Stokes-Helmert problem. Journal of Geodesy 73 (4): pp. 180-192.
    Source Title
    Journal of Geodesy
    DOI
    10.1007/s001900050235
    ISSN
    09497714
    Faculty
    Department of Exploration Geophysics
    Faculty of Science and Engineering
    WA School of Mines
    School
    Department of Spatial Sciences
    URI
    http://hdl.handle.net/20.500.11937/29922
    Collection
    • Curtin Research Publications
    Abstract

    The definition of the mean Helmert anomaly is reviewed and the theoretically correct procedure for computing this quantity on the Earth's surface and on the Helmert co-geoid is suggested. This includes a discussion of the role of the direct topographical and atmospherical effects, primary and secondary indirect topographical and atmospherical effects, ellipsoidal corrections to the gravity anomaly, its downward continuation and other effects. For the rigorous derivations it was found necessary to treat the gravity anomaly systematically as a point function, defined by means of the fundamental gravimetric equation. It is this treatment that allows one to formulate the corrections necessary for computing the `one-centimetre geoid'. Compared to the standard treatment, it is shown thata `correction for the quasigeoid-to-geoid separation', amounting to about 3 cm for our area of interest, has to be considered. It is also shown that the `secondary indirect effect' has to be evaluated at the topography rather than at the geoid level. This results in another difference of the order of several centimetres in the area of interest. An approach is then proposed for determining the mean Helmert anomalies from gravity data observed on the Earth's surface. This approach is based on the widely-held belief that complete Bouguer anomalies are generally fairly smooth and thus particularly useful for interpolation, approximation and averaging. Numerical results from the Canadian Rocky Mountains for all the corrections as well as the downward continuation are shown.

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