A conversion of the geoid to the quasigeoid at the Hong Kong territories

Abstract

A levelling network was readjusted and a new geoid model compiled within the framework of geodetic vertical datum modernization at the Hong Kong territories. To accomplish all project objectives, the quasigeoid model has to be determined too. A quasigeoid model can be obtained from existing geoid model by applying the geoid-to-quasigeoid separation. The geoid-to-quasigeoid separation was traditionally computed as a function of the simple planar Bouguer gravity anomaly, while disregarding terrain geometry, topographic density variations, and vertical gravity changes due to mass density heterogeneities below the geoid surface. We applied this approximate method because orthometric heights of levelling benchmarks in Hong Kong were determined only approximately according to Helmert’s theory of orthometric heights. Considering a further improvement of the accuracy of orthometric heights by applying advanced numerical procedures, we determined the geoid-to-quasigeoid separation by applying an accurate method. The comparison of the accurately and approximately computed values of the geoid-to-quasigeoid separation revealed significant differences between them. The approximate values are all negative and reach -2.8 cm, whereas values from the accurate method vary between -4.1 and + 0.2 cm. In addition, we assessed the effect of anomalous topographic density on the geoid-to-quasigeoid separation by employing a newly developed digital rock density model. According to our estimates the effect of anomalous topographic density reaches a maximum value of 1.6 cm, reflecting a predominant presence of light volcanic rocks and sedimentary deposits at the Hong Kong territories. Our numerical findings indicate that the conversion between geoid and quasigeoid models should be done accurately, even in regions with a moderately elevated topography.