Modeling of vertical gravity gradient by normal gravity field and digital terrain models

Vertical gravity gradient, as a change of gravity with the change in height, is a significant physical quantity used in many geodetic and geophysical modeling applications. In this research, we used a normal gravity field and digital terrain models to model the vertical gravity gradient without using other sources of information such as global geopotential models, results of gravity measurements, or digital density models of topographic masses. We measured vertical gravity gradients by relative gravimeters at 120 points, which we used as validation values for a typical forward modeling problem. In all calculations, we assumed a constant density of topographic masses above the ellipsoid and accounted for the effects of the Earth's curvature. In the territory of Slovenia, where a digital terrain model with a resolution of 1 x 1 m is available, the differences between the measured and modeled values of the vertical gravity gradients are on average - 9.3 mu Gal/m with a standard deviation of 12.3 mu Gal/m. For the territory of Serbia, using a digital terrain model with a resolution of 25 x 25 m, the same differences were obtained with an average of - 7.8 mu Gal/m and a standard deviation of 21.4 mu Gal/m. It can be said that the quality of the modeled values of vertical gravity gradients is directly related to the resolution of the digital terrain model.