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.

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.

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.

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 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.