Spherical and planar approach in determination of local geoid: case study in Trabzon, Turkey
Yurt, Kemal and Ertan Gokalp
Geoid determination is the process of calculation of the length of the ellipsoidal normal (geoid undulation) between the geoid surface and the reference ellipsoid. Various methods are used in determination of the geoid undulations. The solution, that considers a global geopotential model (GM), gravity anomalies (Δg), and topographic effects, is used to determine the gravimetric geoid undulation. The remove-restore technique is a combination of the spherical harmonic and Stokees formulation. The long wavelength effects from a geopotential model and short wavelength effects from the topography are mathematically removed from the observed gravity anomalies in this technique. The Stokees formulation of the residual parts of the gravity anomalies yields the medium wavelength of the geoid height. The geoidal height of a point is determined by restoring the long and short wavelength components. If the area for determining local geoid is chosen small and is considered as planar, it can be divided into M by N grids while distances Δx and Δy are the grid intervals. The geoid undulations can be calculated from Fast Fourier Transform (FFT) solutions of the Kernel functions of the gridded gravity anomalies and distances.
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