Utilisation of Fast Fourier Transform and Least-squares Modification of Stokes formula to compile a gravimetric geoid model over Khartoum State: Sudan

Abstract

We use Fast Fourier Transform (FFT) and least-squares modification (LSM) of Stokes formula to compute the 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 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 to 0.37 m and from 0.48 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.