Sammendrag
Over the last decade, there has been an increased interest in the determination of the geoid. This is mainly due to the demands for height transformation from users of GPS (Global Positioning System) (GPS-levelling). GPS-levelling replaces costly conventional levelling operations with quicker and cheaper GPS surveys, as long as the geoidal height has been computed to a high accuracy. Therefore, there is a common goal among geodesists to determine “the 1-cm geoid model”. This study focuses on the impact of different modification of Stokes’s formula and Global Geopotential Models (GGM). Five different implementations of Stokes's formula are theoretically studied: Vincent-Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong-Gore (1969), Molodensky et al. (1962) and Vaníček-Kleusberg (1987) models, which use a high-degree reference gravity field and modification of Stokes's kernel; and a Least-squares spectral weighting proposed by Sjöberg (1991). The results of the use of these different solutions (except Vincent-Marsh model) are shown over Iran. The geoid model computed by the Vaníček-Kleusberg (1987) solution provides the best residuals relative to the GPS-levelling data, used for an independent evaluation of computed geoid models. However it should be mentioned that the two models of Molodensky and the Least-squares also provide good results. The use of EGM96 global geopotential model and the GGM02s model from Gravity Recovery and Climate Experiment (GRACE) twin-satellites is studied and some differences between two global models are observed. The final geoid of Iran in this study employs the GGM02s Model. Classical topographic correction formulas are improved in this study. The effect of a Bouguer shell is also included in the formulas, which is neglected in classical formulas due to planar approximation. The gravimetric geoid is compared with GPS-levelling derived geoid heights at 200 GPS-levelling stations distributed over Iran. The Vaníček-Kleusberg (1987) method agrees the best with a -117.3 cm mean and ±67.2 cm standard deviation in the differences between gravimetric and GPS-levelling geoid heights. The gravimetric geoid was also fit to the GPS-levelling derived geoid using Least-squares collocation model. The results after fitting also show the best consistency of the Vaníček-Kleusberg (1987) model, with the standard deviation of differences reduced to ±36.3 cm. For comparison, the official geoid of Iran (Hamesh and Zomorrodian 1992) yields a -25.9 cm mean and ±114 cm standard deviation of agreement with the same GPS stations. After fitting to the GPS stations, the standard deviation reduces to ±55.7 cm for the Hamesh and Zomorrodian geoid. We conclude that the new corrections and modification procedures as well as the new global geopotential model are the reasons for the improvement of the accuracy of the new gravimetric geoid. The new geoid model of Iran ranges from -42.62 to 26.27 m with a mean value of -9.18 m and a standard deviation of ±13.3 m for the selected geographical area.
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