Gravity field convolutions without windowing and edge effects

Abstract

A new set of formulas has been developed for the computation of geoid undulations and terrain corrections by FFT when the input gravity anomalies and heights are mean gridded values. The effects of the analytical and the discrete spectra of kernel functions and that of zero-padding on the computation of geoid undulations and terrain corrections are studied in detail. Numerical examples show that the discrete spectrum is superior to the analytically-defined one. By using the discrete spectrum and 100% zero-padding, the RMS differences are 0.000 m for the FFT geoid undulations and 0.200 to 0.000 mGal for the FFT terrain corrections compared with results obtained by numerical integration. This paper presents a set of new formulas for computing geoid undulations and terrain corrections by using FFT when the input is mean data, gives a brief description of numerical results obtained to test the effect of the analytical and the discrete spectra, as well as that of zero-padding on the computation of geoid undulations and terrain corrections. All results computed by FFT are compared with those from integral formulas. It is shown that, with proper application of convolutions, no edge effects occur and no window is required. In fact, the FFT results agree exactly with those of numerical integration. The geoid undulations, N, were computed in an area covered by a 48 x 48 grid of point gravity anomalies, Ag, with spacing 5.28 km × 9.27 km. The terrain corrections were computed in another area covered by 36 x 56 gridded 1 krn x 1 km height data. Table 1 gives the statistics of the gravity anomalies and the heights; RMS is the root-mean- square value and 6 is the standard deviation.