Self-Flow-Matching assisted Full Waveform Inversion

Abstract

Full-waveform inversion (FWI) is a high-resolution seismic imaging method that estimates subsurface velocity by matching simulated and recorded waveforms. However, FWI is highly nonlinear, prone to cycle skipping, and sensitive to noise, particularly when low frequencies are missing or the initial model is poor, leading to failures under imperfect acquisition. Diffusion-regularized FWI introduces generative priors to encourage geologically realistic models, but these priors typically require costly offline pretraining and can deteriorate under distribution shift. Moreover, they assume Gaussian initialization and a fixed noise schedule, in which it is unclear how to map a deterministic FWI iterate and its starting model to a well-defined diffusion time or noise level. To address these limitations, we introduce Self-Flow-Matching assisted Full-Waveform Inversion (SFM-FWI), a physics-driven framework that eliminates the need for large-scale offline pretraining while avoiding the noise-level alignment ambiguity. SFM-FWI leverages flow matching to learn a transport field without assuming Gaussian initialization or a predefined noise schedule, so the initial model can be used directly as the starting point of the dynamics. Our approach trains a single flow network online using the governing physics and observed data. At each outer iteration, we build an interpolated model and update the flow by backpropagating the FWI data misfit, providing self-supervision without external training pairs. Experiments on challenging synthetic benchmarks show that SFM-FWI delivers more accurate reconstructions, greater noise robustness, and more stable convergence than standard FWI and pretraining-free regularization methods.

Figures (16)

• Figure 1: SFM-FWI schematic. The method alternates between outer sampling and inner misfit-driven online training of a flow network to update $\hat{\mathbf{m}}_1$. This produces a stable coarse-to-fine inversion without pretrained priors.
• Figure 2: Convergence curves on the Marmousi sub-region benchmark. Left: data-misfit versus iteration. Middle: relative L2 error of the inverted velocity model with respect to the ground truth. Right: SSIM versus iteration.
• Figure 3: Marmousi sub-region inversion results (clean data). Top row: true velocity model, Gaussian-smoothed initial model, and conventional FWI result. Bottom row: TV-regularized FWI, DIP-FWI, and the proposed SFM-FWI.
• Figure 4: Marmousi inversion results (clean data). Top row: true velocity model, Gaussian-smoothed initial model, and conventional FWI result. Bottom row: TV-regularized FWI, DIP-assisted FWI, and the proposed SFM-FWI.
• Figure 5: Overthrust inversion results (clean data). Top row: true velocity model, Gaussian-smoothed initial model, and conventional FWI result. Bottom row: TV-regularized FWI, DIP-assisted FWI, and the proposed SFM-FWI.