Delta-PINN: Decoupling Macroscopic Kinematics and High-Frequency Perturbations in Physics-Informed Full Waveform Inversion

Full Waveform Inversion (FWI) is a high-resolution seismic imaging technique that formulates subsurface velocity estimation as a highly non-linear, PDE-constrained optimization problem. However, classical grid-based FWI suffers from cycle-skipping and gradient starvation under sparse acquisition geometries. While Physics-Informed Neural Networks (PINNs) have recently emerged as continuous functional regularizers to mitigate these ill-posed dynamics, standard coordinate-based multilayer perceptrons (MLPs) exhibit severe spatial spectral bias and succumb to catastrophic forgetting, whereby the optimization of high-frequency structural details obliterates the low-frequency background kinematic model. In this paper, we introduce the Delta-PINN, a hybrid data-driven architecture that rigorously decouples these regimes. By freezing a structure-oriented Migration Velocity Model (MVM) as a non-differentiable prior, the neural network is strictly bounded to learning residual velocity perturbations (ΔV). Furthermore, we integrate Latent-Fourier feature mapping and Anisotropic Total Variation (TV) annealing to enforce topological continuity. We benchmark the architecture across escalating tiers of geological complexity. Spatial cross-validation on the Marmousi-II model demonstrates that the Delta-PINN successfully resolves extreme tectonic regimes, including steep unconformities, deep anticlines, and complex overthrusts, achieving highly stable, sub-0.001 Mean Squared Error reconstructions while overcoming the local minima traps of classical FWI.