Currently, research on seafloor topographic inversion primarily focuses on various gravity data and inversion methods, while little attention has been given to the seafloor sediment effects. Additionally, there is ongoing controversy regarding the extent to which sediment effects influence the seafloor topographic inversion. To address these, we first apply Parker’s method to estimate the sediment gravity anomalies (GAs) using sediment thickness data, thereby resolving the difficulty of directly inputting sediment thickness into the inversion. In previous regression methods, the coefficient factors, when treated as outputs, significantly deviated from theoretical value. Therefore, we then propose the coefficient-constrained multivariate regression (MR-CC) method. By constraining the output range of the coefficient factors, we investigates the contribution of incorporating sediment effects to improving the accuracy of the coefficient factors and enhancing the effectiveness of seafloor topographic inversion. The accuracy of the seafloor topography models was evaluated over the study area located in the Sea of Japan. The results show that, compared to the linear regression (LR) model, the MR-CC series models, which consider the sediment contributions, improves RMS by 19.54% and MAPE by 26.27%, effectively enhancing the regression and inversion accuracy. Furthermore, we evaluated the impact of various sediment thickness ranges on the inversion accuracy and concluded that the sediment thickness data within the range of 0-4000 m offer higher accuracy, making them more suitable for seafloor topographic inversion. Finally, we employ the Convolutional Neural Network (CNN) to fuse sediment thickness and sediment GAs separately, demonstrating the effectiveness of data preprocessing in mitigating feature dependency in artificial intelligence (AI) applications, which further clarifies the previous controversies on sediment effects in seafloor topographic inversion.

The ICESat-2 (Ice, Cloud, and land Elevation Satellite-2) provides abundant ocean satellite altimetry data. Photon point clouds data denoised by the official ATL03 algorithm exhibit insufficient continuity, and classical gravity anomaly inversion algorithms suffer from high computational complexity. To address these issues, we propose a two-step denoising method for ATL03 data to obtain instantaneous sea surface heights (SSHs): photon point clouds data are denoised using the adaptive OPTICS algorithm, followed by secondary denoising using the Linear-Interquartile algorithm. The resulting SSHs demonstrate superior continuity and larger data volume than those of ATL12 data. This paper proposes the Attention-GraphSAGE algorithm—a graph neural network approach based on neighbor node sampling and self-attention-weighted feature aggregation. An Adam optimizer with L2 regularization is employed for iterative training to achieve nonlinear fitting. The architecture incorporates two-layer neighbor node sampling and aggregation, with residual connections between layers to prevent gradient explosion and preserve original data features. During model training, each input contains 81×81×4 feature values. Nodes consist of shipborne measurement points and surrounding grid points; edges represent connection relationships between shipborne points and first-layer neighbor nodes (grid points), as well as connections between grid points and second-layer nodes (grid points). Edge weights are determined by calculating the correlation coefficient of geoid height between each neighbor node and the shipborne measurement point (using self-attention mechanism). The output corresponds to the difference between shipborne gravity anomaly data and SIO V32.1 gravity anomaly data. The gravity anomaly model inverted utilizing denoised photon with the Attention-GraphSAGE algorithm (AGP-GRA model) demonstrated a correlation coefficient of 0.99 and a standard deviation of 3.36 mGal with shipborne gravity anomaly data. Compared to the model inverted directly utilizing ATL12 data with the same algorithm (AGA-GRA model), this represents a standard deviation reduction of 0.09 mGal. Experiments confirm the algorithm’s effectiveness for gravity anomaly inversion demonstrating with favorable model performance.

High-resolution sea surface heights (SSHs) can be obtained from the wide-swath data of the Surface Water and Ocean Topography (SWOT) project. The distance between two points used to calculate geoid gradients from SSH data significantly influences the accuracy of these gradients. The moving method is proposed to obtain high-precision and high-resolution geoid gradients for gravity recovery, wherein gradients are calculated using SSH data from two points that are separated by a defined distance rather than relying on adjacent points. Marine gravity models around the South China Sea are derived from SWOT-measured SSHs and CryoSat-2-measured SSHs, respectively. The global marine gravity models with high international recognition are also used for comparison. Assessed by shipborne gravity data, the accuracy of SWOT-derived gravity from three-direction geoid gradients is significantly higher than that from one-direction geoid gradients along-track, but slightly higher than that from two-direction geoid gradients. The moving method enhances the precision of the SWOT-derived gravity model by approximately 4% and improves its resolution by about 10%. Compared to CryoSat-2-derived and recognized gravity models, SWOT-derived gravity models using the moving method demonstrate accuracy improvements exceeding 12% and resolution enhancements of over 20%. All these verifications show that SWOT data has advantages over traditional altimeter data in the accuracy and resolution of SSH-derived gravity. For gravity recovery from wide-swath data, it is essential to utilize both along-track and cross-track gradients together, while the inclusion of diagonal-track gradients is optional. The proposed moving method significantly enhances the accuracy and resolution of SWOT-derived gravity, showcasing its effectiveness in marine gravity recovery.

The deep learning method based on multi-channel convolutional neural network(MCCNN) can be used for gravity recovery from altimetry and bathymetry data. Compared with the traditional inverse Vening Meinesz (IVM) method, the MCCNN method enhances gravity accuracy but introduces long-wavelength gravity errors in training data-scarce areas. The Enhanced MCCNN method (EMCCNN) is proposed, which treats geo-locations in the input layer as nodes rather than channels. Evaluated by independent ship-borne data, the EMCCNN method demonstrates a gravity accuracy improvement of 0.05-0.24 mGal compared to the IVM method, maintaining consistent gravity accuracy compared to the MCCNN method. Additionally, assessed by a recognized global marine gravity model, the EMCCNN method achieves the highest accuracy. Particularly in regions with limited training data, the EMCCNN method outperforms the MCCNN method in minimizing gravity differences relative to assessment data. In the wavelengths larger than 100 km, the gravity noise for EMCCNN method can be reduced by up to about 50% compared to MCCNN method. These findings highlight EMCCNN’s effectiveness in improving gravity recovery in training data-scarce areas.

The ATL03 data provided by the ICESat-2 satellite contain a significant amount of noise photons. This noise profoundly impacts the extraction and application of signal photons. Presently, the most widely used density-based clustering method faces two main challenges: one relates to parameter configuration, and the other pertains to the algorithm’s elevated complexity. To address the previously mentioned challenges, this study proposes adaptive ordering points to identify the clustering structure (adaptive OPTICS) algorithm that comprises two denoising stages: rough denoising and fine denoising. In the rough denoising stage, a histogram thresholding technique is used to eliminate a large number of noise photons, thereby reserving computational resources and time for further denoising steps. In the fine denoising stage, the K-nearest neighbors (KNN) algorithm is used to calculate the average distance and establish an dataset, named as D. Following this, the density-based spatial clustering of applications with noise (DBSCAN) algorithm is applied to the dataset D to perform clustering operations, dynamically determining the minimum sample size for the OPTICS algorithm. A section of Zhengzhou is selected as the experimental area for this research. The experimental results show that the accuracy of the denoising process using the adaptive OPTICS algorithm reaches 93.7%, outperforming both the conventional OPTICS algorithm and the ATL03 algorithm.

The Gravity Recovery and Climate Experiment (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). First, the multisatellite altimeter data from 1993 to 2019 are grouped, preprocessed, and utilized to establish mean sea-level models; then, the long-term altimetry sea-level change rate (SLCR) is estimated. Second, the altimetry SLCR subtracts the effects of Steric and Glacial Isostatic Adjustment (GIA) 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$5^{\prime } \times 5^{\prime }$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~\mu $Gal/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.

Temporal variations of hydrological mass causes changes in geoid height and surface deformation, resulting in time-variation of orthometric height. The daily Gravity Recovery and Climate Experiment (GRACE) gravity field model and global hydrological models consistent with the temporal resolution of daily Global Position System (GPS) data were employed in this study to estimate the orthometric height variations in mainland China. Based on the spherical harmonic function and Green’s function, the orthometric height variations of 10 major river basins in mainland China showed obvious sub-monthly and annual fluctuations. The annual amplitude of orthometric height variations was distributed according to latitude, and decrease gradually with an increase in latitude. Among the 249 selected GPS stations, >96.8% positively correlated with both daily GRACE and hydrological models derived orthometric height variations, with the GPS stations in the Southwest River Basin having the best correlation. To compare with the daily GPS vertical displacement, it is necessary to consider the surface loading derived from satellite gravity data or hydrological models in relation to their temporal resolution. By removing the surface loading effect from the GPS height, it was observed that the hydrological load was best corrected using the hydrological model instead of GRACE solutions. Finally, we analyzed the vertical tectonic motion of the main tectonic blocks in mainland China by removing the loading derived from the hydrological model and discussed the main influencing factors of tectonic motion.

The topography of the seafloor is highly correlated with the local gravity through intrinsically nonlinear relationships across a particular wavelength band. The purpose of this study is to compare a fully connected deep neural network (FC-DNN) and a convolutional neural network (CNN) with the gravity-geologic method (GGM) to determine whether deep learning can provide superior predictions of bathymetry. We include the short-wavelength gravity and geological models as training parameters, and assess the performance of different models and parameter combinations using various inputs. Compared with the CNN method, the FC-DNN with the short-wavelength gravity as an input reduces the standard deviation of bathymetry differences from 118.6 m to about 73.5 m. The FC-DNN with short-wavelength gravity reduces the standard deviation of bathymetry differences by up to 13.3% compared with the conventional GGM. Furthermore, we demonstrate that the addition of geological information alongside the short-wavelength gravity does not significantly enhance the accuracy. Power spectral density analysis suggests that the FC-DNN is superior for predicting wavelengths shorter than 6 km.

Based on the nonlinear relationship between multi-source marine geodetic data and seafloor topography, the multilayer perceptron (MLP) neural network is introduced into bathymetry prediction to improve the accuracy of bathymetry model. This method not only integrates multi-source marine geodetic data, but also takes into consideration the nonlinear relationships between these data and seafloor topography. Firstly, we utilize terrain information and the multi-source marine geodetic data (vertical deflection, gravity anomaly, vertical gravity gradient, mean dynamic topography) around the shipborne sounding control points within a 6’×6’ grid as input data, while using the actual bathymetry at control points as output data to train the MLP neural network model. Subsequently, inputting the input data from the central point of a 1’×1’ grid within the study area into the MLP model to predict the bathymetry at the grid’s center. Then, based on the predicted bathymetry, a bathymetry model is established of this research area. Utilizing this methodology, this paper establishes the Gulf of Mexico Bathymetric Chart of the Oceans (MBCO1) model. Due to the influence of complex seafloor topography and the distribution of shipborne bathymetry points, there are differences in training and prediction among different regions. To address this, this study divides the research area into five sub-regions (A, B, C, D, and E) and establishes bathymetry model (MBCO2 models) through each sub-region. Finally, we evaluated the accuracy and effectiveness of this method by comparing it with existing bathymetry models, as well as shipboard depths.

The satellite altimetry missions could measure high-accuracy sea surface heights (SSHs) that can be used to recover the marine gravity field. Traditional methods for estimating the marine gravity field from SSHs all rely on approximate physical correlations between SSHs and gravity, which may neglect nature’s complex nonlinearity. This work presents a new deep network-based method to recover the gravity anomaly. This new method uses a multi-channel convolutional neural network (MCCNN) architecture to capture the nolinear features between ship-borne gravity and a group of input parameters including deflections of the vertical (DOVs), submarine topography and the geo-locations. To validate the gravity, ship-borne gravity anomalies on the two independent cruises were not used in the deep learning process. For comparison, we also estimated the gravity using the traditional inverse Vening Meinesz (IVM) method. Our results indicate that the MCCNN method can derive high-quality marine gravity anomalies. The assessments using 1 mGal-accuracy ship-borne gravity anomalies show that the average accuracy for gravity from MCCNN method is higher than 3 mGal and this method achieves 0.05-0.50 mGal improvement over benchmark methods IVM. Assessed by marine gravity anomaly models with the accuracy of 1-2 mGal, the MCCNN method has shown to improve the accuracy of gravity by at least 4%. Comparisons with the IVM results show that improvements of the MCCNN method were mainly in wavelengths between 8 km and 100 km due to the using of bathymetry. The results show that our deep learning method maintains good performance and is promising for gravity recovering.

The conventional gravity-geologic method (GGM), as a widely used method for bathymetric prediction, is a single-point calculation method between the gravity anomaly and unknown bathymetry. To enhance the accuracy of bathymetric prediction, the improved GGM (IGGM) reliably removing the long-wavelength gravity effect of regional seafloor topography was proposed. The modeling of the long-wavelength gravity field was refined by calculating the short-wavelength gravity correction at the control points based on the weight parameters introduced into the Bouguer slab formulation. The IGGM bathymetric model for the experimental area (113°E-119°E, 12°N-19°N) in the South China Sea was constructed by combining shipborne bathymetry data from the National Centers for Environmental Information (NCEI) and the V31.1 gravity anomaly model from the Scripps Institution of Oceanography (SIO). The standard deviation of the difference between the IGGM model and shipborne bathymetry was approximately 103.46 m at iteration points, which was better than the DTU18, GEBCO_2021 and topo_23.1 bathymetric models. Compared with the accuracy of the model derived from the GGM, the accuracy of the model from IGGM was improved by about 27%. At checkpoints, the accuracy of IGGM was improved by approximately 17 m, and the improvement was larger in areas with complex terrain.