Precise determination of local geoid and its geophysical interpretation

Abstract

The geoid, which is defined as the equipotential surface of the gravity field at the mean sea level, gives a consistent height system of the topography on land as well as on sea. The precise determination of local geoid is of considerable importance not only for surveying and mapping but also for oceanographic and geophysical applications. Geometric leveling has been traditionally used to determine the heights of the earth surface. Because it is labour-intensive and time-consuming many efforts were made in the last decades to develop alternative methods and technologies. Nowadays the relative positioning accuracy of Global Positioning System (GPS) is found to be a few millimeters plus 1-2 ppm. Thus the GPS derived height can be transferred to elevation (orthometric height) if the geoid is accurate enough. This makes GPS heighting an alternative to geometric leveling. The precise determination of local geoid will allow the surveyor to use GPS to its full capacity. Methods for the precise determination of local geoid have been studied and put forward in this research, which include the geometric (GPS/leveling) method, the gravimetric method and the combined method. These methods were employed in the precise determination of the Hong Kong geoid. The research has shown that the geometric (GPS/leveling) method can provide precise local geoid with accuracy of 3 centimeters, and the relative error of geoid height differences is smaller than 1 ppm when the base line is longer than 30 km. Many aspects in the determination of gravimetric geoid has been tested in this research. The Hong Kong gravimetric geoid has been computed using the remove-restore technique via the FFT and was compared with GPS/leveling derived geoid. The results show that the accuracy of 25 mm is achievable. The relative accuracy of geoid height differences is less than 1 ppm when the base line is longer than 40 km. Three methods are discussed for the combined determination of local geoid using GPS/leveling data and the gravimetric geoid heights. They are the weighted average method, the least squares collocation method and the multiquadric function method. The weighted average method gives the better results from the Hong Kong example. The accuracy of such derived geoid is about 2 cm. The gravity field changes in time. Its variation can be measured by using gravity meters on land and satellite altimetry at sea. Measurement of the variation of gravity field is a hot topic. The NASA has planned to launch Gravity Recovery And Climate Experiment (GRACE) mission in 2001. The main objectives of this mission are to investigate temporal changes in gravity field and their causes. Because temporal changes in gravity field measure mass flux in the atmosphere, oceans, cryosphere, solid earth and its core, geophysical investigation of the causes of temporal gravity changes is of considerable importance. The existing interpretation methods are not suitable because they are time independent. Therefore, two time dependent interpretation methods have been derived and were tested with a simple mass body - infinite slab. In the formula two kinds of independent observations are required, which are time variation of gravity field and vertical deformation of the crust. These two kinds of observations may be obtained by using gravimeter and leveling on land as well as satellite altimetry, GRACE and GPS at sea. Therefore, the interpretation models can be used to investigate the causes of time variation of gravity field especially when GRACE mission launched in 2001.