A comparison of gravitational effects between a spherical zonal band and a spherical shell discretized using tesseroids

Gravity forward modelling is one of the fundamental topics in geodesy and geophysics. A spherical shell is a commonly used reference model among the mass bodies for the spatial domain of gravity forward modelling. The reason is that it has simple analytical expressions for gravitational effects (e.g. gravitational potential (GP), gravity vector (GV), gravity gradient tensor (GGT), and gravitational or gravity curvatures (GC)). The finer grid size will need more computation time when adopting the numerical strategy of a spherical shell discretized using tesseroids. This contribution presents the simpler analytical expressions for the GV and GGT of a homogeneous zonal band. The new analytical formula of the GC of a homogeneous zonal band is derived. The computation time and relative errors of the GP, GV, GGT, and GC between a spherical zonal band and a spherical shell discretized using tesseroids are quantitatively investigated with different grid sizes. Numerical results reveal that the computation time of a spherical zonal band discretized using tesseroids is about 180/n (i.e. n is the grid size) times less than that of a spherical shell discretized using tesseroids in double and quadruple precision. The relative errors' mean values of the GP, GV, GGT, and GC for a spherical zonal band discretized using tesseroids are smaller than those for a spherical shell discretized using tesseroids. In short, the benefit of a spherical zonal band in comparison with a spherical shell discretized using tesseroids regarding both the computation time and errors is confirmed numerically. The numerical approach of a spherical zonal band discretized using tesseroids can be applied instead of the classical numerical strategy in numerical evaluation of a tesseroid or other spherical mass bodies in gravity field modelling. This study is supported by the project funded by China Postdoctoral Science Foundation (Grant No. 2021M691402).