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- W118415314 abstract "Almost all integral formulae in geodetic problems can be expressed in a convolution form, which makes it possible to perform a convolution evaluation by the fast Fourier transform or the fast Hartley one. The 2D convolution forms are usually in planar or spherical coordinates. Unfortunately, the accuracy of results from the evaluation of the 2D convolution in planar coordinates is lower than that in spherical coordinates and the numerical integration in the past. This conflict is caused by inadequately ignoring terms of the kernel function which follow the principal term. To satisfy the convolution theorem, it is necessary for the 2D convolutions in spherical coordinates to take the latitude approximation in their kernel function. Consequently, it leads to larger errors in results. The proposed new idea is that all terms of Stokes kernel functions can be taken into account by transforming all variables sin(ψ/2) of the functions to the l, a straight line length corresponding to the spherical distance ψ, and the functions could strictly be expressed in planar coordinates. In this case, any approximation will be avoided. Therefore, the results from the 2D convolution in planar coordinates can be obtained with much better accuracy than that in spherical coordinates, and they are very close to that from the 1D convolution or the numerical integration. Based on the above discussion, the evaluations of the Stokes formula are carried out using the 1D convolution and the 2D convolution in planar coordinates, and also that in spherical coordinates for the comparisons between them.KeywordsGeoidal HeightPhysical GeodesyTerrain CorrectionResidual Gravity AnomalyStokes FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W118415314 date "1998-01-01" @default.
- W118415314 modified "2023-10-14" @default.
- W118415314 title "Comments on Two Dimensional Convolutions of the Geodetic Problems in Planar and Spherical Coordinates" @default.
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- W118415314 doi "https://doi.org/10.1007/978-3-642-72245-5_31" @default.
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