Spherical Bouguer effect of topography on gravity with constant and laterally varying density

: Gravitational attraction of the Earth’s visible topography above the mean sea level is generally regarded as an unwanted signal in various geoscience applications. It should be removed from the observations to reveal the remaining signals of subsurface anomalous density distribution or to satisfy the boundary condition in solving the geodetic boundary value problems. However, the task of determining the gravimetric terrain effects involves tedious numerical computations when high‐resolution elevation data is used. While the traditional computational approach relies on flat-Earth approximation and neglects the topographic masses beyond some fixed integration radius, e.g., planar complete Bouguer correction, the modern methods apply spherical-Earth approximation and consider the far zone contribution, e.g., spherical complete Bouguer correction. This study compares the planar and spherical complete Bouguer corrections with constant topo-density at two test areas in Turkey, then assesses the performance of the recently released ultra-high resolution SRTM2gravity model in the same regions. Moreover, the first lateral global topographical density model (UNB_ TopoDens) has been employed to quantify the effect of topographic mass-density anomalies on gravity across the study areas. The numerical investigations have shown that simple planar complete Bouguer corrections exhibit similar spatial structure to those of the spherical counterparts, but with different magnitudes. There exists an average bias of around 30 mGal between the planar and spherical Bouguer correction because the latter takes the gravitational attraction of global topography into account. The SRTM2gravity model performs exceptionally well in the test regions and can directly be used to derive spherical Bouguer corrections over land areas with little computational effort. The topo-density anomalies may induce gravity effects up to 60 mGal, particularly over the mountainous parts of the study regions. This considerable amount of contribution should be treated carefully and cautiously especially in geodetic applications since the solution of geodetic boundary problems requires rigorous compensation of topographical gravity effects with actual density distribution. The results of the study are also hoped to give insights into the reproduction of the forthcoming regional Bouguer anomaly map of Turkey.