Perturbation-Based Implicit Full-Waveform Inversion with Improved Optimization Conditioning

Summary Implicit full-waveform inversion (IFWI) has shown strong potential for seismic velocity reconstruction due to the implicit regularization of neural networks. However, conventional IFWI based on direct modeling represents multi-scale structures within a unified parameter space, where gradients associated with different wavenumber components may interfere, leading to slow convergence and limited recovery of deep structures. To address this issue, we propose a perturbation-based IFWI framework that decomposes the velocity model into a fixed background and a learnable perturbation. This parameterization reduces multi-scale gradient interference and improves optimization efficiency by restricting updates to the perturbation subspace. In addition, a coordinate normalization strategy is introduced to decouple spatial scale from the network frequency response, enabling stable optimization across different model sizes. Numerical experiments demonstrate that the proposed method achieves more stable convergence, improved structural resolution, and more reliable deep recovery compared to direct modeling IFWI. The approach also shows strong robustness under challenging conditions, including inaccurate initial models, varying spatial scales, and missing low-frequency data.