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Abstract
Gravity field modeling has a vital role in geodetic applications. Therefore, the objective of current thesis was to model the local gravity field in Egypt, based on the recent available global and local gravity field data, in order to obtain the maximum attainable geoid accuracy and precision. This aim was split into two main objectives. The first objective was the preliminary investigation of the local performance of the recent available global geopotential models in Egypt. The second objective of this thesis was to fit the high-degree model EGM96 to the Egyptian heterogeneous data, and so the low-degree GRIM5-C1 and UCPH2002 models, for the sake of comparison. Firstly, a high-resolution 30”x30” digital terrain model was developed for Egypt by collocation, based on the recent available terrain elevation data and using the remove-restore technique. Having a spatial external accuracy of 8 meters, the developed DTM is recommended for future detailed geoid solutions in Egypt.
Regarding the first objective, a detailed preliminary study was carried out in order to investigate the behaviors of a set of recent global geopotential models, with respect to the local heterogeneous data in Egypt. The results of this study showed that the local behaviors of the available high-degree global geopotential models are nearly similar to the low-degree models. Therefore, none of such high-degree models have optimally recovered the long-medium gravity field features in Egypt, due to the their lack in the local gravity field data.
Concerning the second objective, both the least-squares collocation and integral methods for spherical harmonic analysis were applied in a local scheme, in order to tailor the EGM96 global harmonic model to Egypt. The EGM96 was tailored up to degree and order 599 and 650, by the LSC and integral technique, respectively, based on the local heterogeneous data. The relevant fitted models were denoted as EGM96EGCT and EGM96EGIT. These two models showed nearly the same low-medium frequency behavior, regarding Egypt, which implies that the local data features have been efficiently launched into them. The EGM96EGCT and EGM96EGIT models have decreased the residual anomaly variance, by about 70% and 73%, respectively, compared with the EGM96. Regarding the residual discrete geoidal height data, these two models have decreased the standard deviation and RMS by about 50% and 52%, respectively. As such, these tailored models are highly recommended as reference fields in local geoid determination in Egypt.
Globally, it was found that tailoring the EGM96 model to Egypt did not deform the degree variances’ trend of the EGM96. On the other hand, the standard errors of the EGM96EGCT terms, and hence its error degree variances, were slightly better than those of the original model. Moreover, it was found that the incorporation of the local terrestrial data into a global geopotential model, such as EGM96, did not affect its behavior over geographically remote regions.
The GRIM5-C1 and UCPH2002 low-degree models were fitted to Egypt, using the integral technique, up to degree and order 650. The local behaviors of the resulting solutions were found to be almost identical to that of the EGM96EGIT model. On the other hand, Helmert’s 2nd condensation direct and indirect effects of the local long wavelength topography on the geopotential models in Egypt were investigated, regarding the EGM96EGIT model. Such local topographic effects on geopotential models in Egypt are significant in mountainous areas and should be taken into account.
The EGM96EGIT, reduced for the terrain signal, was used to develop a 2’x2’ detailed geoid for Egypt by collocation, and based on this geoid solution, a quasi-geoid model was estimated. It was found that the precision and accuracy of the predicted detailed geoid solution were greatly improved. Namely, the mean precision has been improved by about 52%, due to the tailoring of the EGM96 model to Egypt. Regarding the external accuracy, an improvement of about 30% has been achieved in the RMS of single difference, compared to the EGM96-based detailed geoid solution. The external accuracy, as computed from the random geoidal residuals, was found to be 27cm. Being the most precise detailed geoid model for Egypt, this geoid solution is recommended for future geodetic work in Egypt.