Full-Waveform Inversion With Velocity Model Low-Rank Implicit Neural Representation

Full-waveform inversion (FWI) is pivotal for exploring subsurface structures and physical parameters. However, classical FWI methods often experience challenges like cycle skipping and nonlinearity, necessitating accurate initial velocity models. Pure data-driven approaches based on deep learning are constrained by limited real labeled data and inadequate generalization, hindering practical applications. To address these issues, we propose an unsupervised physics-informed machine learning (PIML) FWI with low-rank implicit neural representation (INR, termed LR-IFWI), which utilizes a low-rank matrix factorization parameterized by coordinate-based neural networks, continuously and compactly representing the velocity model by implicitly encoding low-rank properties and smoothness. Our method has three crucial advantages: 1) LR-IFWI considerably improves inversion accuracy and shows steadier inversion convergence behavior; 2) LR-IFWI can reduce the number of iterations for comparable inversion accuracy, improving efficiency attributed to the compact low-rank representation; and 3) LR-IFWI has better robustness, alleviating the dependence on the initial models and improving noise resistance due to the physical constraints and low-rank neural representation. Numerical tests on the 2-D Marmousi model demonstrate that LR-IFWI achieves efficient and accurate inversion with fewer iterations and greater precision when utilizing smooth, linear, and random initial velocity models. Further experiments with noisy seismic data, missing low-frequency components, and more challenging velocity models, such as 2-D SEG/EAGE salt and overthrust models, highlight its robustness and generalization.