Vertical gravity anomaly gradient effect of innermost zone on geoid-quasigeoid separation and an optimal integration radius in planar approximation

Abstract

This study mainly focuses on the solution of the vertical gravity anomaly gradient and determination of its effect on the total geoid-quasigeoid separation. Due to its small effect on geoid-quasigeoid separation, the planar approximation of vertical gravity anomaly in the innermost zone has been implemented. The computation of a strongly singular integral expressing the vertical gravity anomaly gradient was used for this purpose for even order (up to n=6) of the Simpson and Newton-Cotes integration technique. The derivation of the relationships for different integration radii has been made to obtain these solutions using gridded data of free air anomaly. The comparison of relationships for the different integration radii was made in order to select an optimum radius of the integration in planar approximation for the vertical gravity anomaly gradient dependent geoidquasigeoid separation term. The integration radii of 3.1, 6.2 and 9.3 km show an increasing behaviour towards saturation. The effect of vertical gravity anomaly gradient has similar pattern on the geoid-quasigeoid separation term towards saturation. The saturation trend for vertical gravity anomaly gradient is comparatively faster than its corresponding geoidquasigeoid separation dependent term. The results also show that 2nd order Newton-Cotes integration is found to be comparable with the approximate linear solution for the vertical gravity anomaly gradient given by Heiskanen and Moritz. The vertical gravity anomaly dependant term has a rather small effect on geoid-quasigeoid separation in the mid elevation range and ranges from -6.18 to 2.7 mm for n=6. The findings of the study leads to the inferences that the order of integration should be selected either n=4 or n=6 for better estimates of vertical gravity anomaly gradient solution. This criterion is also valid for their effect on geoidquasigeoid separation with planar approximation in the innermost zone for the low- to mid-range elevation areas. © The Author(s) 2010.