Nyamangunda, Patrick; (1997) Towards a 10cm local gravimetric geoid for Zimbabwe using FFT. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The thesis describes a new methodology and refinement of the determination of a local geoid in an area with large gravity data gaps or scarce data using geological and topographical information in terms of topographical density anomalies. Such was the case in Zimbabwe. The work was prompted by the importance of GPS Levelling and potential applications of geoid information in engineering projects in Zimbabwe. The determination of the geoid requires complete gravimetric data coverage for the area under consideration and some way beyond. In Zimbabwe, however, in common with other similar parts of the Earth, substantial data gaps are found. The rugged terrain and high relief present another hurdle in trying to create a uniform grid of data. The method that has been adopted is to smooth the gravity field prior to the geoid predictions using the "remove-restore method". The proposed method is the combination of gravimetry, geopotential model expansion, a Digital Elevation Model (DEM) and a Digital Density Model (DDM) using Stokes' numerical integration by the Fast Fourier Transform method, with final validation by GPS. Initial investigations looked at preliminary gravity data analysis, terrain corrections, gridding effects and their implications for a 10cm geoid. Gravity data analysis shows the observed gravity (i.e. the free-air anomalies) to have a small mean value of 4.73 ±35.55mgals in the area. The OSU91A geopotential model was shown to represent the gravity field in the area better than the OSU89B model. Residual mean and standard deviations of 4.27mgals ±19.70mgals and 5.29mgals ±19.90 mgals were obtained respectively for the OSU91A and OSU89B reference models. The terrain correction analysis was done to find relationship, if any, between DEM resolution, terrain roughness/smoothness and effect on both gravity anomalies and geoid height and their implications for the Zimbabwean geoid. Terrain correction analysis results show that the terrain effect is quite significant, and there was therefore a need for a DEM in the area. Use was made of ERS-1 altimetry data and heights associated with gravity data points to create a DEM. Problems in gridding the data and obtaining uniform geoid predictions are encountered due to substantial data gaps in some areas. This led to the adoption of geophysical gravity data smoothing techniques. Tests were done where the geophysical gravitational contribution of density anomalies in the data gaps was computed and used in data smoothing. Typical signal sizes of 0 to 37.57mgals (-2.19m to 5.33m geoid effects) and -1.35 to 2.79mgals (0.93m to 2.65m geoid effects) were obtained for terrain corrections and density anomalies corrections respectively. The GRAVSOFT software package and new software GEOTOPODENC were used. Final geoid computation using FFT followed on the basis of these results with final validation using GPS geoid determination. The final geoid has a north-east to south-west rise with typical values of -11.95m to 22.70m above the GRS80 reference ellipsoid. Improvements of 0.03±0.56m and 0.01±0.10m were obtained by using the DEM and DDM respectively in the geoid determination. The geophysical gravity smoothing goes some way to tackling the problem of data gaps which still occur in many land areas around the world.

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