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.

Direct bathymetry is a primary data source for creating high-precision seafloor topography but cannot easily achieve high-resolution global coverage. Therefore, using gravity data for seafloor topography prediction is an alternative method. Current algorithms, reliant on the measurement of ship soundings and geophysical parameters, still have room for improvement in accuracy and coverage. In this study, we establish observation equations based on vertical gravity anomalies (VG, also called gravity anomalies) and vertical gravity gradient (VGG) anomalies generated by a rectangular prism and develop a new analytical algorithm for predicting topography. We validate its effectiveness through numerical simulations and actual applications. We determine the source of the errors, the mid–high frequency error caused by the boundary area is reduced by regularization, whereas the low-frequency error caused by the far area is reduced by the error equation algorithm. In the shallow areas with a maximum depth of 2 kilometers and deep-sea areas with a maximum depth of 5 kilometers, the root mean square errors (RMS) for VGG anomalies prediction are 93.8 m and 233.8 m, respectively, while for VG anomalies prediction they are 101.2 m and 239.4 m. We also find that VGG anomalies are more sensitive to topography fluctuations, but VG anomalies have a stronger linear correlation with topography. Additionally, we propose a cubic spline interpolation algorithm to effectively fuse the prediction results and ship soundings, improving topographic prediction accuracy in shallow and deep-sea areas by up to 53.2% and 39.67%, respectively.