With the help of the analytical expression of the vertical gravity gradient (VGG) generated by a rectangular prism, an analytical algorithm for predicting seafloor topography using the VGG data has been studied. Nevertheless, ship sounding data are an essential constraint in solving the seafloor topography. This paper combines ship sounding data with VGG anomaly to predict the seafloor topography. The main research contents include the following: Using the ship soundings and VGG data in the study area, the observation equations about sea depth are established, and the stability of the equations are studied; furthermore, considering the influence of seafloor topography outside the study area on the observation equations, these effects are divided into boundary effects and far‐field effects, and different processing methods are proposed. Finally, the method is tested on the East Pacific Rise, only using VGG anomaly and adding the mean value to fix the boundary region, the RMS error of the results is 108.8 m; SIO's model is added to the boundary region and the seven maximum absolute errors are replaced by ship sounding data, the RMS error of the results can reach 94.2 m and the accuracy improvement is 13.42%.

In the present methods to estimate seafloor topography from gravimetric data, some parameters need be computed in advance from the known bathymetric data, which leads some uncertainties in applying the methods. To overcome such uncertainties, an analytical method to estimate the seafloor topography from the vertical gravity gradient (VGG) is introduced in the paper. Based on the expression of VGG generated by a cubic prism, the observation equations for the seabed depth are established firstly. Then, the simulation results show that the observation equations established are solvable. Especially, the piecewise bilinear interpolation is introduced to separate the influence of the far-field anomalous bodies on VGG. In addition, some imitation arithmetic examples are given in order to examine the solvability of the observation equations and estimate the accuracies of their solutions. Finally, an actual seafloor topography located in South China Sea (117.6-118.25°E, 17-17.65°N), is estimated by the method proposed in the paper, and compared with ship depth sounding, the root mean square (RMS) error of bathymetry prediction is 77 m.

When using the dynamic approach to recover the time-variable gravity field, the reference orbit generated by the perturbation model and the non-conservative force observed from the accelerometer should be introduced at first, and then the observation equations of the residual orbit and the residual range rate are established. This introduces a perturbation model error and instrument noise. Thus, there are low-frequency errors in the residual orbit and the residual range rate. Currently, most studies only focus on the low-frequency error of the residual range rate, neglecting the influence of the low-frequency error in the residual orbit. Therefore, under the condition of the perturbation model error and instrument noise including the constant term and 1CPR term, the low-frequency error formulas of the residual orbit and residual range rate are derived according to the characteristics of the solution of the Hill equation. Then, the influence of the low-frequency error on the residuals is analyzed by using the simulation and the real data processing respectively. In the simulation and real data processing, the accuracy of the recovered gravity field can maintain a good consistency for different arc lengths by removing the low-frequency error in the residual orbit. Finally, the time-variable gravity field model UCAS-IGG (University of Chinese Academy of Sciences-Institute of Geodesy and Geophysics) was solved from January 2005 to February 2010 by removing the low-frequency error of the residual orbit and residual range rate. Compared with the official institutions, the UCAS-IGG presents a good consistency in the estimating time-variable gravity field signal. This study demonstrates how the effect of the low-frequency error of the residual orbit should be taken into consideration when the longer arc length is used to recover a time-variable gravity field. Using a long arc length can reduce the variables of the initial state and recover the influence of the small force.

As high-resolution global coverage cannot easily be achieved by direct bathymetry, the use of gravity data is an alternative method to predict seafloor topography. Currently, the commonly used algorithms for predicting seafloor topography are mainly based on the approximate linear relationship between topography and gravity anomaly. In actual application, it is also necessary to process the corresponding data according to some empirical methods, which can cause uncertainty in predicting topography. In this paper, we established analytical observation equations between the gravity anomaly and topography, and obtained the corresponding iterative solving method based on the least square method after linearizing the equations. Furthermore, the regularization method and piecewise bilinear interpolation function are introduced into the observation equations to effectively suppress the high-frequency effect of the boundary sea region and the low-frequency effect of the far sea region. Finally, the seafloor topography beneath a sea region (117.25°-118.25° E, 13.85°-14.85° N) in the South China Sea is predicted as an actual application, where gravity anomaly data of the study area with a resolution of 1′×1′ is from the DTU17 model. Comparing the prediction results with the data of ship soundings from the National Geophysical Data Center (NGDC), the root-mean-square (RMS) error and relative error can be up to 127.4 m and approximately 3.4%, respectively.