Determination of the reference height surfaces in the regions with sparse gravity data

Abstract

The research aims to create a methodology that would lead to a mathematical model of referent surfaces and apply that created model in areas where it is not possible to provide a large number of observations, Global geopotential models, digital models of topographic masses, and available observations were used to model the Earth's potential field parameters to be distributed appropriately and be sufficient in the relevant area. Then, the reference surfaces (geoid and quasi-geoid) are determined from observations and newly modeled parameters of the Earth's gravity potential. The research methods that were used are the method of analysis and synthesis of existing results, mathematical modeling (interpolation, extrapolation, prediction, ...), the process of experiments, the technique of comparing the obtained results, the theory of Earth's gravitational potential, through statistical methods and collocations. The experimental part of the research was performed in two steps using already existing and well-distributed data called Area 01 as the first step, while in the second step, Area 02 was used for sparse data region or the rest area of Egypt territory. The results conclude that it is possible to model the Earth's gravity potential parameters in Area 02, with small numbers and irregular spatial distribution of observation results, in sufficient numbers and with sufficient accuracy. The obtained accuracy for Area 02 geoid was ± 0,479 cm as internal accuracy in terms of Standard deviation compared with 162 GPS/H points. Based on Area 01 results, geoid solutions for Area 01 have been fitted using 80 GPS/leveling stations. In comparison, 100 GPS/leveling stations were used as an external check; the obtained internal accuracy by the LSC technique in terms of the standard deviation was ±0.338 m of the differences, which is considered rather satisfactory. In contrast, external check accuracy was ±0.262 m, considered adequately related to the poor distribution of the available GPS/leveling data in this area. Evidently, from the two obtained Area 01 and Area 02 geoid accuracies, Area 01 geoid has better accuracy, nearly 30%, than Area 02 geoid as an internal check.