Bulletin géodésique

, Volume 63, Issue 1, pp 57–67 | Cite as

On the non-linear geodetic boundary value problem for a fixed boundary surface



The fixed gravimetric boundary value problem of Physical Geodesy is a nonlinear, oblique derivative problem. Expanding the non-linear boundary condition into a Taylor series—based upon some reference potential field approximating the geopotential—it is shown that the numerical convergence of this series is very rapid; only the quadratic term may have some practical impact on the solution. The secondorder solution term can be described by a spherical integral formula involving the deflections of the vertical with respect to the reference field. The influence of nonlinear terms on the figure of the level surfaces (e.g. the geoid) is roughly estimated to have an order of magnitude of some few centimetres, based upon a Somigliana-Pizzetti reference field; if on the other hand some high-degree geopotential model is used as reference then the effects by non-linearity are negligible from a practical point of view.


Gravity Field Normal Gravity Spherical Approximation Physical Geodesy Geodetic Boundary 
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Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1989

Authors and Affiliations

  • B. Heck
    • 1
  1. 1.Dept. of Geodetic ScienceUniversity of StuttgartStuttgart 1F.R.G.

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