Abstract
In this paper, some features of the local disturbing potential model developed by the GGI method (based on Geophysical Gravity Inversion) were analyzed. The model was developed for the area of the Western Carpathians covering the Polish–Slovak border. A detailed assessment of the model’s property was made regarding the accuracy of the disturbing potential values (height anomalies), gravity values, complete Bouguer anomalies (CBA), and differences between geoid undulations and height anomalies (N−ζ). Obtained accuracies of the GGI quasigeoid model (in terms of standard deviation of the residuals to the reference quasigeoid models) were at the level of ±2.2 cm for Poland and ±0.9 cm for the Slovak area. In terms of gravity, there was shown dependence of the accuracy of the GGI model on the digital elevation model (DEM) resolution, the point height, the density of gravity data used, and used reference density of topography model. The best obtained results of gravity prediction were characterized by an error of approximately 1 mGal. The GGI approach were compared with classical gravity prediction methods (using CBA and topographic-isostatic anomalies supported by Kriging prediction), getting very similar results. On the basis of the GGI model, CBA and differences (N−ζ) were also determined. The strong dependence of resolution of the CBA model obtained by GGI approach, on the size of the constant density zones, has been demonstrated. This significantly reduces the quality of such a model. The crucial importance of the topographic masses density model for both determined values (CBA and (N−ζ)) was also indicated. Therefore, for determining these quantities, all available information on topographic mass densities should be used in modelling.
Highlights
Gravity measurements in geodesy are used in many ways
Differences ∆ζ = ζ − ζGGI and ∆g = g − gGGI were determined for test points, where ζ is the height anomaly determined from the adopted quasigeoid model, g is the measured gravity, ζGGI and gGGI are height anomaly and gravity calculated from the GGI model according to Equations (7) and (9) respectively, wherein the disturbing potential is calculated by Equations ((4), (5), (6) and (21)), and the gravity disturbance value is determined by Equation (8)
With the developed GGI model using density of the gravity points 2.4 1km point, the UNB_TopoDens model as a reference density of topography model, digital elevation model (DEM) with resolution of 0.1 × 0.1 km, and assuming zones of constant density equal 4 × 4 km, the complete Bouguer anomalies were determined according to Equation (17) while the differences between the geoid undulations and the height anomalies were determined according to Equation (18)
Summary
Gravity measurements in geodesy are used in many ways. One of the basics is their use in defining and determining the height of geoid and quasigeoid as a reference surface, as well as determining the height of points in a given height system in classical spirit levelling. Models that have the ability to determine from the same model the values of different characteristics high, but in mountainous areas, they are still much lower than the aforementioned of the gravity field are global geopotential models. Their accuracy is currently very high, but classical solutions and requires introduction of the appropriate corrections. We can formulate an inversion problem: Find the density distribution functions ρ and δ in defined volumes Ω and κ and find the coefficients of the polynomials modelling the potential TE to satisfy Equation (1) for given data. It should be mentioned that calculations can be performed with or without (version use in the article) a global geopotential model
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