The Influence Analysis Of The Observed Data On Regional Geoid Determination

The regional geoid determination involves different kinds of data and complex computations. Now its precision is mostly analyzed through the actual test method by GPS leveling, in which the regional gravimetric geoid model is first fitted and converted to GPS leveling system, and then compared with GPS leveling data. Because the correlated errors are canceled out dramatically, there might be remarkable distortion inevitably in the test results. On the other hand, observation optimization design is still a virgin land because of the lack of analytical methods. In this dissertation, the influence of observed data on precision of regional geoid determination was studied by analytical method in frequency domains. The causal associations between observation data and geoid model precision were analyzed in specific topographical region. The rigorous simulated algorithm was constructed to estimate model precision from specific technology indicators of observational data.Firstly, this dissertation studied the errors influence of regional terrestrial gravity measurements and global geopotential model on regional gravimetric geoid model. Based on the Stokes formula and the spatial domain truncation approximation method, the analytic relationship was deduced between free-air gravity anomalies grid on geoid used in the inner area, global geopotential model in the outer area and precision of regional gravimetric geoid. Based on the correlation analysis between topographic conditions and free-air gravity anomalies on the ground, a new Stokes integral formula, calculated by ground free-air gravity anomalies, and the effect of topography above geoid being considered as well, was proposed and deduced. A strict algorithm of the representation error of ground free-air gravity anomalies grid, calculated by topographic elevation values, was also proposed. Consequently, the influence of topographic conditions on geoid precision was analyzed. Numerical simulation calculation indicated the corresponding relationships between terrestrial gravity measurements precision, resolution, integral radius, topographic conditions, geopotential model precision and resolution, and regional gravimetric geoid precision. Secondly, this dissertation studied the errors influence of topographic elevation values and crust density values on regional gravimetric geoid model. The analysis method of topographic values' influence on geoid determination through spherical harmonics of total topographic effects, i.e. the combination of both direct and indirect effect, was proposed in advance. Based on the spatial domain truncation approximation method of topographic effects computation, the analytic relationship between measuring point data, inner topographic data, outer topographic spherical harmonics model and computational precision of total topographic effects was deduced. For resolution difference between elevation data and density data, a decomposition algorithm was proposed, through which error influence of each set of data was calculated respectively by its own resolution. A comparative analysis was also carried out to the classical Stokes-Helmert method, and its analysis formulas of topographic values'influence were deduced. Numerical simulation calculation indicated the corresponding relationships between inner terrestrial data's precision, resolution, integral radius, outer topographic spherical harmonics model's precision and resolution, and computational precision of total topographic effects.Thirdly, this dissertation studied the errors analysis of the combination of GPS leveling and regional gravimetric geoid model. The errors analysis of GPS leveling geoid model in frequency domain was first conducted. Homogeneous GPS leveling network was treated as regular grid and analyzed with Spherical Harmonics. The analytic relationship was deduced between measuring errors of GPS leveling, measuring point density and precision of GPS geoid model. The error influence of crust density values on orthometric height was also deduced by spherical harmonics. The combination of GPS leveling and regional gravimetric geoid model was treated as the combination of their respective spectral component. The spectral weights of spectral component were determined according to the combination method, i.e. the combined adjustment or the GPS height collocation. And then the hybrid geoid model's precision was determined in frequency domain. Numerical simulation calculation indicated the corresponding relationships between match combination of GPS leveling and gravimetric geoid model, and hybrid geoid model's precision in different topographic conditions.Finally, a computation program was made based on the mathematical model proposed in this dissertation. Shenzhen geoid model (SZGEOID2001) and Hong Kong geoid model (HKGEOID2000) were used for numerical calculation and analysis. The causal relationships between the observational data and final geoid model precision were shown in detail through the data. Strict precision estimation and simulative optimization design were realized from the technical indicators of the observational data to model precision.