A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth's gravitational field measured from the gravity field and steady-state ocean circulation explorer (GOCE), up to 250 degrees, influenced by the radial gravity gradient V_zz and three-dimensional gravity gradient V_ij from the satellite gravity gradiometry (SGG) are contrastively demonstrated based on the analytical error model and numerical simulation, respectively. Firstly, the new analytical error model of the cumulative geoid height, influenced by the radial gravity gradient V_zz and three-dimensional gravity gradient V_ij are established, respectively. In 250 degrees, the GOCE cumulative geoid height error measured by the radial gravity gradient V_zz is about 2^1/2 times higher than that measured by the three-dimensional gravity gradient V_ij. Secondly, the Earth's gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V_zz and three-dimensional gravity gradient V_ij by numerical simulation, respectively. The study results show that when the measurement error of the gravity gradient is 3×10^-12/s², the cumulative geoid height errors using the radial gravity gradient V_zz and three-dimensional gravity gradient V_ij are 12.319 cm and 9.295 cm at 250 degrees, respectively. The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V_ij is improved by 30%-40% on average compared with that using the radial gravity gradient V_zz in 250 degrees. Finally, by mutual verification of the analytical error model and numerical simulation, the orders of magnitude from the accuracies of the Earth's gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients, respectively. Therefore, it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10^-13/s²-10^-15/s² for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.