We present an accurate method for the calculation of gravitational potential (GP), vector (GV), and gradient tensor (GGT) of a tesseroid, considering a density model in the form of a polynomial up to cubic order along the vertical direction. The method solves volume integral equations for the gravitational effects due to a tesseroid by the Gauss–Legendre quadrature rule. A two-dimensional adaptive subdivision technique, which automatically divides the tesseroids near the computation point into smaller elements, is applied to improve the computational accuracy. For those tesseroids having small vertical dimensions, an extension technique is additionally utilized to ensure acceptable accuracy, in particular for the evaluation of GV and GGT. Numerical experiments based on spherical shell models, for which analytical solutions exist, are implemented to test the accuracy of the method. The results demonstrate that the new method is capable of computing the gravitational effects of the tesseroids with various horizontal and vertical dimensions as well as density models, while the evaluation point can be on the surface of, near the surface of, outside the tesseroid, or even inside it (only suited for GP and GV). Thus, the method is attractive for many geodetic and geophysical applications on regional and global scales, including the computation of atmospheric effects for terrestrial and satellite usage. Finally, we apply this method for computing the topographic effects in the Himalaya region based on a given digital terrain model and the global atmospheric effects on the Earth’s surface by using three polynomial density models which are derived from the US Standard Atmosphere 1976.

SUMMARY: The gravity-geological method (GGM) is an approach that utilizes marine gravity anomalies (GAs) and shipborne bathymetric data to invert seafloor topography by resolving short-wavelength GAs through the Bouguer Plate approximation. Such an approximation ignores the non-linear effects caused by surrounding seafloor topographical undulations that actually exist in short-wavelength GAs, and thus leaving the space for further modification of GGM. This study thoroughly derives the relationship between seafloor topography and GA, as well as the formula of GGM. Then, we propose a self-adaptive method to improve the accuracy of the inversion significantly: the enhanced GGM (EGGM). The method uses the equivalent mass line method to approximate the non-linear gravitational effects of the surrounding seafloor topography to correct the short-wavelength GAs. By introducing two optimal density contrast parameters, EGGM has been designed to effectively integrate the combined effects of various non-linear factors to a certain extent. The accuracy of the seafloor topography models, produced with a spatial resolution of 1′ × 1′, was evaluated over the study area (132°E–136°E, 36°N–40°N) located in the Sea of Japan. The results indicate that the accuracy of EGGM has a relative improvement of 13.73 per cent compared to that of GGM in the overall study area, while the accuracy of both models is higher than that of the SIO_unadjusted model. The study further investigated the feasibility and stability of EGGM by examining the accuracy of both GGM and EGGM in various water depth ranges and areas with diverse terrain characteristics.