Springer Online Journal Archives 1860-2000
Architecture, Civil Engineering, Surveying
Abstract Least-squares collocation and Stokes integral formula, as implemented using the Fast Fourier Technique, handle the harmonic downward continuation problem quite differently. FFT furthermore requires gridded data, amplifying the difference of methods. We have in this paper studied numerically the effects of downward continuation and gridding in a mountainous area in central Norway. Topographically smoothed data were used in order to reduce these effects. Despite the smoothing, it was found that the vertical gravity gradient had values up to -11 mgal/km. The corresponding differences between geoid heights and the height anomalies at altitude reached 12 cm. The differences between geoid heights obtained using collocation or FFT with gravity data at terrain level or sea level showed differences between the values of up to 10 cm r.m.s. A part of this difference was a consequence of different data areas used in the FFT and collocation solution, though. Major discrepancies between the solutions were found in areas where the topographic smoothing could not be applied (deep fjords with no depth information in the used DTM) or where there seemed to be gross errors in the data. We conclude that proper handling of harmonic continuation is important, even when we as here have used a 1 km resolution DTM for the calculation of topographic effects. The effect of data gridding, required for the FFT method, seems not to be as serious as the need to limit the data distribution area, required when least squares collocation is used with randomly distributed data.
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