Residual terrain correction on the sphere by an FFT algorithm

Abstract

The computation of the vertical attraction due to masses above the mean topogra phy (Residual Terrain Correction, RTC) is still a matter of study in the high precision geoid estimation by remove-restore technique. This topographical effect can be evaluated from the knowledge of a Digital Terrain Model (DTM) in two different ways: numerical integration by prisms or Fast Fourier Transform (FFT) technique. Both these methods can't be used when wide areas are considered, the ¯rst approach, more rigorous, requires an excessive computation time, while the second one, faster, implies restrictive hypotheses like planar approximation of the topographical surface. For these reasons a new algorithm, based on a convenient transformation of the starting DTM, has been studied and implemented. This new method enables the use of planar formulas also with the spherical approximation of the area. The new algorithm is presented both from a theoretical and practical point of view, particular attention is paid to neglected terms that are of the order of about $10^{-5}Gal$. The method has been studied in order to compute the RTC in a large area like that implied by the new European geoid project. Some tests have been performed for proving the goodness of the model.