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Solving Molodensky’s series by fast Fourier transform techniques

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Abstract

The use of the fast Fourier transform algorithm in the evaluation of the Molodensky series terms is demonstrated in this paper. The solution by analytical continuation to point level has been reformulated to obtain convolution integrals in planar approximation which can be efficiently evaluated in the frequency domain. Preliminary results show that the solution by Faye anomalies is not sufficient for highly accurate deflections of the vertical and height anomalies. The Molodensky solution up to at least the second-order term must be carried out. Part of the unrecovered deflection and height anomaly signal appears to be due to density variations, verifying the essential role of density modelling. A remove-restore technique for the terrain effects can improve the convergence of the series and minimize the interpolation errors.

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  1. Division of Surveying Engineering, The University of Calgary, 2500 University Dr. N.W., T2N 1N4, Calgary, Alberta, Canada

    M. G. Sideris & K. P. Schwarz

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  1. M. G. Sideris
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  2. K. P. Schwarz
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Sideris, M.G., Schwarz, K.P. Solving Molodensky’s series by fast Fourier transform techniques. Bull. Géodésique 60, 51–63 (1986). https://doi.org/10.1007/BF02519354

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  • DOI: https://doi.org/10.1007/BF02519354

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