Physically consistent interpolation of sparse marine magnetic anomaly data using physics-informed neural networks

Summary High-resolution and spatially continuous magnetic anomaly datasets are crucial for accurate geological interpretation and resource exploration. However, real-world marine shipborne surveys often suffer from sparse sampling, irregular track lines, and significant data gaps, making accurate field reconstruction a fundamental challenge. While conventional gridding techniques and recent purely data-driven deep learning methods excel at numerical fitting, they fundamentally lack physical constraints, often generating statistically plausible but geophysically invalid artifacts in unobserved regions. Conversely, traditional physics-based ES methods enforce harmonicity but remain highly sensitive to discrete source-layer parameterization. To address the inherent conflict between data fidelity and physical consistency, we propose a mesh-free interpolation framework based on physics-informed neural network (PINN). By explicitly embedding the Laplace equation into the learning process as a continuous physical constraint, our framework restricts the solution space to valid harmonic fields. An adaptive sampling strategy and a gradient-based dynamic weighting scheme are introduced to ensure training stability and optimal convergence. Extensive validation using synthetic models under varying noise conditions and real-world EMAG2_V3 survey data demonstrates that the PINN framework exhibits strong robustness against noise and achieves superior numerical accuracy, yielding a relative root-mean-square error (RRMSE) of approximately 1.0%, significantly outperforming conventional approaches and the ES method. More importantly, quantitative evaluation using Laplacian residuals proves that the proposed method effectively suppresses high-frequency spurious artifacts and strictly preserves the physical integrity of the reconstructed anomalies. These findings indicate that physics-informed learning offers a robust, flexible, and physically consistent paradigm for marine magnetic field reconstruction, providing a valuable advancement over established potential-field interpolation techniques.