The free versus fixed geodetic boundary value problem for different combinations of geodetic observables |
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| Authors: | E W Grafarend B Heck and E H Knickmeyer |
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| Institution: | (1) Department of Geodetic Science, Stuttgart University, Keplerstr. 11, D-7000 Stuttgart 1, (Federal Republic of Germany);(2) Department of Geodetic Science, Karlsruhe University, Englerstr. 7, D-7500 Karlsruhe 1, (Federal Republic of Germany);(3) Lortzingstr. 10, D-8000 München 60, (Federal Republic of Germany) |
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| Abstract: | Various formulations of the geodetic fixed and free boundary value problem are presented, depending upon the type of boundary
data. For the free problem, boundary data of type astronomical latitude, astronomical longitude and a pair of the triplet
potential, zero and first-order vertical gradient of gravity are presupposed. For the fixed problem, either the potential
or gravity or the vertical gradient of gravity is assumed to be given on the boundary.
The potential and its derivatives on the boundary surface are linearized with respect to a reference potential and a reference
surface by Taylor expansion. The Eulerian and Lagrangean concepts of a perturbation theory of the nonlinear geodetic boundary
value problem are reviewed. Finally the boundary value problems are solved by Hilbert space techniques leading to new generalized
Stokes and Hotine functions. Reduced Stokes and Hotine functions are recommended for numerical reasons. For the case of a
boundary surface representing the topography a base representation of the solution is achieved by solving an infinite dimensional
system of equations. This system of equations is obtained by means of the product-sum-formula for scalar surface spherical
harmonics with Wigner 3j-coefficients. |
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