Abdalla, A and Green, CM (2016) Utilisation of Fast Fourier Transform and Least-squares Modification of Stokes formula to compile approximate geoid heights over Khartoum State: Sudan. Arabian Journal of Geosciences, 9 (3). 236. ISSN 1866-7511
Abstract
We use Fast Fourier Transform (FFT) and Least-squares modification (LSM) of Stokes formula to compute the approximate geoid over Khartoum State in Sudan. The two methods (FFT and LSM) have been utilised to test their efficiency with respect to EGM08 and the local GPS-levelling data. The FFT method has many advantages, it is fast and it reduces the computational complexity. The modification of Stokes formula is widely used in geoid modelling, however, its implementation based on point-wise summation requires a considerable amount of time. In FFT we combine the terrestrial gravity data and the global geopotential model (GGM) by means of a remove-compute-restore procedure and we successfully apply the modification of the Stokes formula in the least-squares sense. FFT and LSM approximate geoid solutions are evaluated against EGM2008 and the GPS-levelling data. The analysis of the undulation differences shows that the LSM solution is more compatible with EGM08 and GPS-levelling data. The discrepancies of the differences are removed using a 4-parameter model, the standard deviation (STD) of the undulation differences of LSM decreased from 0.41 m to 0.37 m and from 0.48 m to 0.39 m for FFT solution. There is no significant impact to the LSM geoid when adding the additive corrections, while the FFT geoid solution is slightly improved when terrain correction is applied.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Saudi Society for Geosciences. This is an author produced version of a paper published in Arabian Journal of Geosciences. The final publication is available at Springer via http://dx.doi.org/10.1007/s12517-015-2117-8 |
Keywords: | EGM08, FFT, GPS-levelling, geoid, least-squares modification, remove-compute-restore, Stokes formula, terrestrial gravity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) > Inst of Geophysics and Tectonics (IGT) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Sep 2015 15:33 |
Last Modified: | 01 Jul 2017 17:53 |
Published Version: | http://dx.doi.org/10.1007/s12517-015-2117-8 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s12517-015-2117-8 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90170 |