Geodetic Institute, University of Karlsruhe (TH), Englerstr. 7, D-76128 Karlsruhe
Topographic reductions in Physical Geodesy
Theory from Stokes (Stokes’ formula)
Objective: Geoid determination Boundary value problem (BVP) by Stokes: |
Theory from Molodensky
Approximation of the (residual) topography using a homogeneous vertical prism
- Coordinate system defined as the cuboid’s system of the edges
- Transformation of the effect of the vertical prism on dg and M in the topocentric horizon system of the calculation point P
- Distance between the calculation point Pand the variable integration point Q:
Effect on the potential in P |
Effect on the gravity in P |
Effect on the second radial derivative in P |
For the vertical prism with constant density, analytical solutions exist in terms of their potential and first derivatives, and the elements of the Marussi Tensor
Approximation of the (residual) topography using Tesseroids
There are no elementary solutions: Elliptical integrals!
? Easy to use, strong reduction of the required computation time
Approximation error of potentials, their first and second radial derivativeTesseroid dimensions: 5’ x 5’ x 2 km r = R + h; h(V) = h(g^{*}_{z}) = 2 km; h(M_{rr}) = 260 km
? The computation time is reduced by ten-fold when Tesseroids are used instead of prisms |