This paper proposes a method for constructing a seafloor topography model based on a Transformer-enhanced U-Net network (Trans-UNet) to improve the accuracy of bathymetry predictions. The method incorporates gravity data (gravity anomalies, vertical deflections, and vertical gravity gradients) and geological data (the sea surface to Moho, sediment thickness, mean dynamic topography, and seafloor age). The proposed method is tested in the South China Sea (112°E-119°E, 11°N-20°N), and a seafloor topography model (Trans-UNet model) with a resolution of 1′×1′ is constructed for the region. By comparison, a seafloor topography model (U-Net model) for this region was constructed using U-Net. Compared to the inspect points, the standard deviation of the difference between the Trans-UNet model and the measured bathymetry at those points is 124.11 m. Compared to the U-Net model, topo_25.1, DTU18BAT and GEBCO_2024 models, the accuracy of Trans-UNet model shows improvements of 7.64 m, 21.49 m, 76.91 m, and 4.94 m, respectively. These results effectively demonstrate the validity of the proposed method and verify the accuracy of the Trans-UNet model's performance. By comparing the accuracy of various seafloor topography models across different depth ranges, the Trans-UNet model shows superior performance in deeper water regions, with improvements of 7.37m and 7.28m compared to the GEBCO_2024 model in the depth ranges of 2000-4000m and greater than 4000m, respectively.

Determining the detailed Moho topography is crucial for understanding geodynamic processes. Inversion of the Moho depth in the frequency domain from gravity observations is an effective tool for this purpose. However, existing inversion methods such as the Parker-Oldenburg (P-O) and Bott-Parker (B-P) methods face challenges including nonconvergence and noise amplification. We develop a modified B-P (mB-P) method to estimate the Moho depth with variable density contrast from gravity data. Our method casts exponential density-based Parker’s formula into the iterative continuation theoretical framework, allowing the use of an adaptive filter that has been proven effective in iterative continuation studies. This modification retains the efficiency of the B-P method while offering improved control over solution stability. Gauss-fast Fourier transform is adopted to improve the precision of the forward and inverse Fourier transforms in the inversion process. Furthermore, the mathematical connection between the P-O and B-P methods is established. Specifically, the B-P method acts as a low-pass filter to reduce the downward continuation effect in the P-O method and recovers the nonlinear topography through the nonlinearity of the fitting function. Synthetic inversion tests demonstrate that our method achieves superior inversion accuracy compared with the P-O and B-P methods under 3% gravity observation noise and significantly outperforms the P-O method in terms of computational efficiency. We apply the mB-P method to estimate the Moho depth beneath the Tibetan Plateau using satellite gravity data and seismic data, achieving reasonable agreement between the gravimetric model and seismic data.

The seafloor topography (ST) is essential for oceanographic research and geophysical applications, and its modeling relies on satellite altimetry-derived gravity data. The ST inversion commonly applies linear regression method that account primarily for shipborne bathymetry errors, while often neglecting the potential uncertainties in altimetry-derived gravity data. To address this question, we draw on the idea of total least squares, which has been widely applied in numerical analysis. In this study, we propose an improved linear regression framework for ST inversion: we use high-precision multibeam shipborne bathymetry data (MSB1) as a constraint to iteratively determine the optimal weight ratio between bathymetry and gravity data, and subsequently construct initial weight matrices; then the Robust Weighted Total Least Squares (RWTLS) method is applied to estimate regression parameters, and the corresponding ST model is constructed. A case study is conducted in a region of the South China Sea (113°∼118°E, 13°∼19°N). Comparisons with the check data (MSB2) and existing models (topo_27.1, ETOPO2022, and SDUST2023BCO) indicate that the overall accuracy of the constructed ST model is approximately 150 m. And compared with traditional method, the application of RWTLS improves ST inversion accuracy, with power spectral density analysis further revealing a significant enhancement in topographic energy within the 12∼30 km wavelengths. Moreover, we find that the improvement in ST accuracy is mainly concentrated in offshore waters; in these areas, altimetry-derived gravity data tend to have greater uncertainty, nevertheless, the improved method effectively enhances the reliability of ST modeling by jointly accounting for the errors in both bathymetry and gravity data. This study proposes a robust inversion framework that considers multi-source data uncertainties, offering a novel strategy for robust linear ST modeling.

The GRACE gravity satellites can only detect low-resolution marine gravity change. This study proposes to use satellite altimetry data to construct high-resolution marine gravity change rate (MGCR) model. The marine gravity field change is mainly caused by the seawater mass migration. Based on the spherical harmonic function (SHF) method and mass loading theory, a spherical harmonic synthesis formula is constructed to calculate MGCR. This idea is utilized to establish MGCR model in Arabian Sea (AS). Firstly, the multi-satellite altimeter data from 1993 to 2019 is grouped, preprocessed and utilized to establish mean sea level models, then the long-term altimetry SLCR is estimated. Secondly, the altimetry SLCR subtracts effects of Steric and Glacial Isostatic Adjustment to obtain the SLCR model caused by mass migration (AS_MM_SLCR). Finally, we perform spherical harmonic analysis on AS_MM_SLCR, and apply the spherical harmonic synthesis formula to estimate MGCR model on 5’×5’ grids (AS_SHF_MGCR). AS_SHF_MGCR has higher resolution than GRACE_MGCR, compensating for inability of GRACE to detect small-scale marine gravity changes; the MGCR mean of AS_SHF_MGCR is 0.13 μGal/year, which indicates the long-term rising trend of marine gravity in AS. This letter proposes a method for calculating the MGCR using satellite altimetry, which offers a novel approach for marine time-varying gravity research.

A satellite altimetry mission can measure high-precision sea surface height (SSH) to recover a marine gravity field. The reference gravity field model plays an important role in this recovery. In this paper, reference gravity field models with different degrees are used to analyze their effects on the accuracy of recovering gravity anomalies using the inverse Vening Meinesz (IVM) method. We evaluate the specific performance of different reference gravity field models using CryoSat-2 and HY-2A under different marine bathymetry conditions. For the assessments using 1-mGal-accuracy shipborne gravity anomalies and the DTU17 model based on the inverse Stokes principle, the results show that CryoSat-2 and HY-2A using XGM2019e_2159 obtains the highest inversion accuracy when marine bathymetry is less than 2000 m. Compared with the EGM2008 model, the accuracy of CryoSat-2 and HY-2A is improved by 0.6747 mGal and 0.6165 mGal, respectively. A weighted fusion method that incorporates multiple reference models is proposed to improve the accuracy of recovering gravity anomalies using altimetry satellites in shallow water. The experiments show that the weighted fusion method using different reference models can improve the accuracy of recovering gravity anomalies in shallow water.