Investigation of the Molodensky series terms for terrain reduced gravity field data

Masses associated with the local topography are a dominant source of short wavelength gravity field variations. In the modeling of the gravity field it is thus and advantage to eliminate the effect of the terrain in a remove-restore procedure. In this process, terrain reductions are computed for the observation stations at the Earth's surface, considering either the complete topography, the topography and its isostatic compensation, or the residual topography (RTM technique ). Hence, the reduced gravity field observations are referring to the actual ground level. Therefore, Molodensky's theory, considering data on non-level surfaces, should be applied in the traditional gravity field modeling approaches, while in collocation this is handled directly through height dependent covariance functions. In this paper, we provide numerical examples for the computation of the Molodensky series terms associated with the traditionally unreduced observations as well as in connection with various terrain-reduced data. Due to the smoothing, resulting from the terrain reductions, the magnitude of the Molodensky terms is reduced as well and the series convergence is improved. The computations are based on the Fast Fourier Transform (FFT) technique. The numerical tests are done in a mountainous area of the European Alps. The terrain data are on grids with various grid spacings starting at a resolution of 200 m. One of the main goals of this study is to investigate the magnitude of the Molodensky terms with regard to the computation of an improved European quasigeoid model.