Potential field determination due to the given masses of a Digital Terrain Model for a system of target points

For the computation of the gravitational field of a given mass distribution, as defined through the sampled heights of a Digital Terrain Model (DTM), several analytical as well as numerical methods exist. The computation may take place at individual points/gravity stations, or over a system of target points, which can either coincide with the DTM-points or may lay on the horizontal plane at a certain flight height above the terrain. The possibility of evaluating the gravitational terrain effect simultaneously for all points of a regular grid, made numerical methods, in particular those based on the fast Fourier Transform (FFT), a very popular tool in geodesy. The present paper offers an up-to-date survey on different analytical and numerical methods for the evaluation of terrain effects using the information of a densely sampled DTM of a test area situated in the Bavarian Alps. It is demonstrated, that the choice of the modeling technique for the surface relief can be made only with analytical methods. The choice between an analytical or a numerical method in the practical application should be made keeping in mind the respective accuracy of the final results, were the analytical methods are shown to be clearly superior.