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′ are 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.

Owing to the dependence of algorithms on the measurement of ship soundings and geophysical parameters, the accuracy and coverage of topography still need to be improved. Previous studies have mostly predicted topography using gravity or gravity gradient, However, there is a relative lack of integrated research combining or comparing gravity and gravity gradient. In this study, we develop observation equations to predict topography based on vertical gravity anomalies (VG; also called gravity anomalies) and vertical gravity gradient (VGG) anomalies generated by a rectangular prism. The sources of interference are divided into medium- to high-frequency errors and low-frequency errors, and these new methods reduce these errors through regularization and error equations. We also use numerical simulations to test the efficiency of the algorithm and error-reduction method. Statistics show that VGG anomalies are more sensitive to topographic fluctuations; however, the linear correlation between VG anomalies and topography is stronger. Additionally, we use the EIGEN-6C4 model of VG and VGG anomalies to predict topography in shallow and deep-sea areas, with maximum depths of 2 km and 5 km, respectively. In the shallow and deep-sea areas, the root mean square (RMS) errors of VGG anomalies prediction are 93.8 m and 233.8 m, and the corresponding accuracies improved by 7.3% and 2.3% compared with those of VG anomaly prediction, respectively. Furthermore, we use cubic spline interpolation to fuse ship soundings and improve the accuracy of the final topography results. We develop a novel analytical algorithm by constructing an observation equation system applicable to VG and VGG anomalies. This will provide new insights and directions to refine topography prediction based on VG and VGG anomalies.

Seafloor topography prediction can fill in sea areas without ship sounding data. However, the dependence of various topographic prediction algorithms on ship soundings varies significantly. Hence, this study explores the impact of the number and distributions of ship soundings on topographic prediction using the gravity–geologic method (GGM) and an analytical algorithm. Firstly, this study investigates the influence of ship sounding coverage on the two algorithms. The simulation results demonstrate that increasing coverage from 5.40% to 31.80%, coupled with more uniform distributions across the study area, substantially reduces the RMS error of the GGM. Specifically, the RMS error decreases from 238.68 m to 42.90 m, an improvement of 82.03%. The analytical algorithm maintains a consistent RMS error of 40.39 m because it does not depend on ship soundings. Furthermore, we select a 1° × 1° sea area (134.8°–135.8°E, 30.0°–31.0°N), and the ship soundings are divided into two control groups, Part I and Part II, with coverages of 8.19% and 33.19%, respectively. When Part II is used for calculation, the RMS error of the GGM decreases from 204.17 m to 126.95 m compared to when Part I is used, while the analytical algorithm exhibits an RMS error of 167.94 m. The findings indicate that the prediction accuracy of the GGM is significantly affected by ship soundings, whereas the analytical algorithm is more stable and independent of ship soundings. Based on simulation experiments and realistic examples, when the effective ship soundings coverage exceeds 30%, the GGM may have more advantages. Conversely, the analytical algorithm may be better. This suggests that effectively combining and utilizing different algorithms based on the ship sounding coverage can improve the accuracy of topographic prediction. This will provide a basis for integrating multiple algorithms to construct a global seafloor topography model.