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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris


CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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1862-9024
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Volume 8, Issue 1

Issues

Comparison Among Three Harmonic Analysis Techniques on the Sphere and the Ellipsoid

Hussein Abd-Elmotaal / Mostafa Abd-Elbaky / Kurt Seitz
  • Geodetic Institute, Karlsruhe Institute of Technology, Englerstr. 7, D-76128 Karlsruhe, Germany
  • Other articles by this author:
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/ Bernhard Heck
  • Geodetic Institute, Karlsruhe Institute of Technology, Englerstr. 7, D-76128 Karlsruhe, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-04-08 | DOI: https://doi.org/10.1515/jag-2013-0008

Abstract

The paper presents a comparison among three different techniques for harmonic analysis on the sphere and the ellipsoid. The EGM2008 global geopotential model has been used up to degree and order 360 in order to create gravity anomaly fields on both the sphere and the ellipsoid as the function fields of the current investigation. Harmonic analysis has then been carried out to compute the dimensionless potential coeficients using the created function fields. Three different harmonic analysis techniques have been applied: the least-squares technique, the Fast Fourier Transform (FFT) technique and the Gauss-Legendre numerical integration technique. The computed coeficients in spherical harmonics have then been compared with EGM2008 (in the frequency domain) and the computed fields on the sphere and the ellipsoid have been compared with fields created by EGM2008 up to degree and order 360 (in the space domain) in order to estimate the accuracy of the three different harmonic analysis techniques used within the current investigation. The results proved that the least-squares technique gives the best accuracy both in frequency and space domain. The FFT technique provides quite good results in a very short cpu time. The Gauss-Legendre technique gives the worst results among the presented techniques, but still the residuals in the space domain are negligibly small.

Keywords : Harmonic analysis; least-squares technique; Fast Fourier Transform FFT; numerical integration; harmonic synthesis

About the article

Published Online: 2014-04-08

Published in Print: 2014-04-01


Citation Information: Journal of Applied Geodesy, Volume 8, Issue 1, Pages 1–20, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2013-0008.

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