Evaluation of deflections of the vertical on the sphere and the plane: a comparison of FFT techniques |
| |
| Authors: | Q. W. Liu Y. Cai Li Michael G. Sideris |
| |
| Affiliation: | (1) Institute of Geodesy and Cartography, Department of Surveying, Helsinki University of Technology, Otakaari 1 FIN-02150, Espoo Finland, FI;(2) Department of Geomatics Engineering, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4 Canada Phone: (403) 220 5834; fax: (403) 284 1980; e-mail: yli@acs.ucalgary.ca (http://www.ucalgary.ca/∼yli), CA |
| |
| Abstract: | This paper presents a set of efficient formulas to evaluate the deflections of the vertical on the sphere using gridded data. The Vening-Meinesz formula, the topographic indirect effect on the deflections of the vertical as well as the terrain corrections are expressed as both 2D and 1D convolutions on the sphere, and consequently can be evaluated by the 2D and the 1D fast Fourier transform (FFT). When compared with the results obtained from pointwise integration, the use of the 1D FFT gives identical results, and therefore these results were used as control values in this paper. The use of the spherical 2D FFT improves significantly the computational efficiency with little sacrifice of accuracy (0.6″ rms difference from the 1D FFT results). The planar 2D FFT, which is as efficient as the spherical 2D FFT, gives worse results (1.2″ rms difference from the 1D FFT results) because of the extra approximations. Received: 27 February 1996; Accepted: 24 January 1997 |
| |
| Keywords: | . Fast Fourier transform Vertical deflections Terrain corrections |
| 本文献已被 SpringerLink 等数据库收录！ |
|
