An experimental investigation on the discrete Poisson’s upward continuation of anomalous gravity field data

The Poisson upward continuation of gravity field functionals, typically given on the Earth’s irregular topography with limited spatial extent, necessitates some proper treatments due to the theoretical requirements. This study reviews the Poisson theory and investigates a more rigorous methodology for the numerical solution of the spherical integral equation by addressing many issues such as spherical-Earth model implementation, far-zone effect, Poisson kernel modification, and suitable ground data reduction scheme. We first explore the far-zone effect and search for an optimal near-zone spherical cap radius above which the truncation error is negligible. We then compare different variants of remove-restore technique with a modified Poisson kernel to upwardly continue the ground gravity field data to predefined height levels close to the Earth’s surface. Different combinations of long-and short-wavelength contributions are studied extensively. Numerical experiments have been performed using simulated ground gravity anomaly and gravity disturbance data synthesized from ultrahigh-degree global geopotential model (GGM). Numerical results show that the far-zone contribution may reach up to several milligal levels and should be taken into consideration when the cap size radius is less than 1° for the upward continuation height levels between 3000 m and 5000 m above the sea level. Among the various solutions, the best agreement between the Poisson upward-continued ground data and its synthetic counterpart has been obtained when the gravity field data input directly into the Poisson integral is reduced both for GGM and residual terrain model (RTM).