Topographic effects up to gravitational curvatures of tesseroids: A case study in China

Topographic effects on gravity field modeling are important for geodesy, geophysics and related geosciences. In this study we evaluate the gravitational effects of tesseroids in spherical coordinates, including the gravitational potential (GP), gravity vector (GV), gravity gradient tensor (GGT) and especially the gravitational curvatures (GC). With the adaptive discretization stack-based algorithm by Gauss-Legendre quadrature approach, the optimized distance-size ratio values (D) of the GC components are analyzed. Numerical experiments demonstrate that the difference percentage values of the GC components (e.g., V_xxz, V_yyz and V_zzz) are larger at the range of D ∈ [0; 10] compared to those of the GP, GV and GGT components (i.e., V, V_z, V_zz). Different distance-size ratio values D = 6, 7, 14, 30, 35, 41 and 50 for the GC component V_zzz are recommended to reach the 0.1% threshold error at corresponding computational heights 260, 150, 50, 10, 8, 6 and 4 km. Moreover, the forward modeling for the gravitational effects up to GC of tesseroids based on the ETOPO1 model in China is investigated. The GC functionals could help to extend the knowledges of interior structures of the Earth and other planetary objects.