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A comparison of the least squares collocation and the fast Fourier transform methods for gravimetric geoid determination
The objective of the research was to study the performance of the least squares collocation (LSC) and the fast Fourier transform (FFT) techniques for gravimetric geoid computation. The Land Levelling Datum (LLD) is the South African vertical datum based on more than 100 years old tide gauge measurem...
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| Format: | Thesis |
| Language: | English |
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School of Architecture, Planning and Geomatics
2017
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| Summary: | The objective of the research was to study the performance of the least squares collocation (LSC) and the fast Fourier transform (FFT) techniques for gravimetric geoid computation. The Land Levelling Datum (LLD) is the South African vertical datum based on more than 100 years old tide gauge measurements of mean sea level (MSL). The LLD is poorly defined so an alternative is required. The SAGEOID10 (Merry, 2009) hybrid geoid model was computed for the purpose of replacing the existing vertical datum. Two gravimetric geoid models were computed using different techniques for evaluation of the Stokes' integral, such as, LSC and one dimensional fast Fourier transform (1D-FFT) technique. The long wavelength component of the geoid models were computed using the EGM2008 geopotential model truncated at degree 720. The use of fast spectral techniques is required due to an increase of both quality and type of data available for geoid determination. The FFT method is most reliable than the LSC method, since it requires less computational time on large data set than the LSC. A system of linear equations of order equal to the number of data points is generated on the LSC method. The geoid model was computed over the province of Gauteng. It was then compared to the SAGEOID10 hybrid geoid model. The computed geoid models, SiPLSC and SiPFFT geoid model compared to the SAGEOID10 model with standard deviation of 5.6cm. The long wavelength component of the computed geoid model compared to the EGM2008 geopotential geoid model with a standard deviation of 4.2cm. |
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