Currently, seafloor topography inversion based on satellite altimetry gravity data provides the principal means to predict the global seafloor topography. Researchers often use sea surface geoid height or gravity anomaly to predict sea depth in the space domain. In this paper, a comprehensive discussion on seafloor topography inversion formulas in the space domain is presented using sea surface geoid height, gravity anomaly and introduces an approach that uses vertical gravity gradient. This would be the first study to estimate seafloor topography by vertical gravity gradient in the space domain. Further, a nonlinear iterative least-square inversion process is discussed. Using the search area for the Malaysia Airlines Flight MH370 as study site, we used the DTU17 gravity anomaly model and SIO V29.1 vertical gravity gradient to generate the seafloor topography. The results of the proposed bathymetric models were analyzed and compared with the DTU18 and SIO V20.1 bathymetric models. The experimental results show that the gravity anomaly and vertical gravity gradient in the study area are strongly correlated with the seafloor topography in the 20–200 km wavelength range. The optimal initial iteration values for seafloor topography variance and correlation length are 0.6365 ${\mathrm{km}}^2$ and 10.5′, respectively. Shipborne measurements from SONAR data were used as external checkpoints to evaluate the bathymetric models. The results show that the RMS for BAT_VGG_ILS (inversion model constructed by vertical gravity gradient) is smaller than for BAT_GA_ILS (inversion model constructed by gravity anomaly) and BAT_GA_VGG_ILS (inversion model constructed by gravity anomaly and vertical gravity gradient). The relative accuracy of the DTU18 bathymetry model was 9.27%, while the relative accuracy of the proposed seafloor models was higher than 4%. Within the 200 m difference range, the proportion of checkpoints for BAT_VGG_ILS was close to 95%, about 80% for BAT_GA_ILS and BAT_GA_VGG_ILS, and less than 50% for the DTU18. The results show that the nonlinear iterative least square method in the space domain is feasible.

Marine gravity field recovery relies heavily on satellite altimetry. Thanks to the evolution of altimetry missions and the improvements in altimeter data processing methods, the marine gravity field model has been prominently enhanced in accuracy and resolution. However, high-accuracy and high-resolution gravity field recovery from satellite altimeter data remains particularly challenging. We provide an overview of advances in satellite altimetry for marine gravity field recovery, focusing on the impact factors and available models of altimetric gravity field construction. Firstly, the evolution of altimetry missions and the contribution to gravity field recovery are reviewed, from the existing altimetry missions to the future altimetry missions. Secondly, because the methods of altimeter data processing are of great significance when obtaining high-quality sea surface height observations, these improved methods are summarized and analyzed, especially for coastal altimetry. In addition, the problems to be resolved in altimeter data processing are highlighted. Thirdly, the characteristics of gravity recovery methods are analyzed, including the inverse Stokes formula, the inverse Vening Meinesz formula, Laplace’s equation, and least squares collocation. Furthermore, the latest global marine gravity field models are introduced, including the use of altimeter data and processing methods. The performance of the available global gravity field model is also evaluated by shipboard gravity measurements. The root mean square of difference between the available global marine gravity model and shipboard gravity from the National Centers for Environmental Information is approximately 5.10 mGal in the low-middle latitude regions, which is better than the result in high-latitude regions. In coastal areas, the accuracy of models still needs to be further improved, particularly within 40 km from the coastline. Meanwhile, the SDUST2021GRA model derived from the Shandong University of Science and Technology team also exhibited an exciting performance. Finally, the future challenges for marine gravity field recovery from satellite altimetry are discussed.

Satellite altimetry cannot accurately derive the short-wavelength component of ocean gravity anomaly. Since the short-wavelength seabed topography affects the gravity anomaly, we can forward the short-wavelength gravity anomaly by using seabed topography to make up for the shortcomings of altimetry. Based on the Global Marine Gravity Anomaly version 1 (GMGA1) previously released by our group, and on Parker’s formula, the short-wavelength gravity anomaly is forwarded by using the seabed topographic model SRTM15+V2.4, and a new product, Global Marine Gravity Anomaly Version 2 (GMGA2), is obtained. Compared with internationally recognized gravity field products such as SIO V32.1 and DTU17, the accuracy of GMGA2 is 2.5mGal, which is 0.7 mGal higher than GMGA1, and the absolute differences smaller than 5mGal account for more than 96%. An evaluation using ship-borne gravity data showed the accuracy of GMGA2 is 4.8 mGal, which is 0.3 mGal higher than GMGA1. It is concluded from the above results that using the forward method with water depth data significantly improves the short-wavelength gravity anomaly of the altimetry-derived gravity field model, and the accuracy of GMGA2 is close to that of the advanced international level.

Geodetic applications of altimetry have largely been inversions of gravity anomaly. Previous studies of Earth's gravity gradient tensor mostly presented only the vertical gravity gradient (VGG). However, there are six unique signals that constitute the gravity gradient tensor. Gravity gradients are signals suitable for detecting short-wavelength topographic and tectonic features. They are derived from double differentiation of the disturbing potential and hence are susceptible to noise amplification which was exacerbated by low across-track resolution of altimetry data in the past. However, current generation of altimetry observations have improved spatial resolutions, with some better than 5 km. Therefore, this study takes advantage of current high-resolution altimetry datasets to present CUGB2023GRAD, a global (latitudinal limits of ±80°) 1 arcmin model of Earth's gravity gradient tensor over the oceans using deflections of the vertical as inputs in the wavenumber domain. The results are first assessed via Laplace's equation, whereby the resultant residual gradient is virtually zero everywhere. Further analysis at local regions in the Arctic and south Indian oceans showed that T_xy, T_xz and T_yz are the most dominant gravity gradients for bathymetric studies. This proves that bathymetric signatures in the non-diagonal tensor components are worth exploiting. Bathymetric coherence analysis of T_zz over the Tonga Trench showed strong correlation with multibeam shipboard depths. This study proves that current generation of altimetry geodetic missions can effectively resolve Earth's gravity gradient tensor. The CUGB2023GRAD model data can be freely accessed at https://doi.org/10.5281/zenodo.10511125 (Annan et al., 2024).