High-resolution marine geomagnetic anomaly maps are a prerequisite for accurate geomagnetic matching navigation. However, existing compilations are sparse and of low resolution, and conventional interpolation techniques fail to capture fine-scale anomalies. Although deep learning models have achieved remarkable success in natural-image super-resolution, they have rarely been tailored to geomagnetic grid data; their lack of physically motivated constraints frequently introduces geologically implausible structures. To address these limitations, we propose a physics-constrained generative adversarial network (PC-GAN) for the super-resolution reconstruction of marine geomagnetic anomaly maps. Building upon the Super-Resolution Generative Adversarial Network (SRGAN) backbone, we incorporate physics-informed loss terms for spatial continuity and edge preservation into the training objective, thereby endowing the data-driven architecture with geological consistency while maintaining numerical accuracy. Experiments were conducted on the NOAA EMAG2_V3 dataset across four representative marine regions. Over the Philippine Sea Plate, PC-GAN reduces the root-mean-square error (RMSE) by 28.0% and increases the peak signal-to-noise ratio (PSNR) by 2.85 dB relative to bicubic interpolation, and lowers RMSE by 27.5% while raising PSNR by 2.79 dB compared with PSO-Kriging. Ablation studies corroborate that the physics-based modules make a statistically significant contribution to reconstruction quality. PC-GAN furnishes a robust tool for generating high-fidelity geomagnetic reference maps and holds promise for high-precision geomagnetic matching navigation and related applications.

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.

Traditional fusion methods for integrating multi-source gravity data rely on predefined mathematical models that inadequately capture complex nonlinear relationships, particularly at wavelengths shorter than 10 km. We developed a convolutional neural network incorporating differential marine geodetic data (DMGD-CNN) to enhance marine gravity anomaly recovery from HY-2A satellite altimetry. The DMGD-CNN framework encodes spatial gradient information by computing differences between target points and their surrounding neighborhoods, enabling the model to explicitly capture local gravity field variations. This approach transforms absolute parameter values into spatial gradient representations, functioning as a spatial high-pass filter that enhances local gradient information critical for short-wavelength gravity signal recovery while reducing the influence of long-wavelength components. Through systematic ablation studies with eight parameter configurations, we demonstrate that incorporating first- and second-order seabed topography derivatives significantly enhances model performance, reducing the root mean square error (RMSE) from 2.26 mGal to 0.93 mGal, with further reduction to 0.85 mGal achieved by the differential learning strategy. Comprehensive benchmarking against international gravity models (SIO V32.1, DTU17, and SDUST2022) demonstrates that DMGD-CNN achieves 2–10% accuracy improvement over direct CNN predictions in complex topographic regions. Power spectral density analysis reveals enhanced predictive capabilities at wavelengths below 10 km for the direct CNN approach, with DMGD-CNN achieving further precision enhancement at wavelengths below 5 km. Cross-validation with independent shipborne surveys confirms the method’s robustness, showing 47–63% RMSE reduction in shallow water regions (<2000 m depth) compared to HY-2A altimeter-derived results. These findings demonstrate that deep learning with differential marine geodetic features substantially improves marine gravity field modeling accuracy, particularly for capturing fine-scale gravitational features in challenging environments.