[论文解读] Self-Flow-Matching assisted Full Waveform Inversion

Xinquan Huang, Paris Perdikaris|arXiv (Cornell University)|Mar 13, 2026

Seismic Imaging and Inversion Techniques被引用 0

一句话总结

SFM-FWI 使用在线流匹配作为确定性、自监督先验来引导全波形反演，无离线预训练，在合成基准测试中实现更准确且更鲁棒的重建。

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.

研究动机与目标

• Motivate improving FWI robustness to nonlinearity, noise, and poor initialization without relying on offline pretrained priors.
• Introduce a flow-matching based, physics-driven regularization that works online during inversion.
• Couple short physics-driven refinements with a self-supervised flow model to guide the inversion along a stable coarse-to-fine path.
• Demonstrate improved reconstruction accuracy and convergence stability on challenging synthetic benchmarks compared to standard FWI and pretraining-free baselines.

提出的方法

• Formulate standard time-domain acoustic FWI with data misfit and optional regularization.
• Introduce flow matching to learn a transport field that maps states via an ODE, avoiding Gaussian initialization and predefined noise schedules.
• Develop Self-Flow-Matching assisted FWI (SFM-FWI) that alternates between interpolating a current model and online training of a single flow network using FWI data misfit.
• Use a time-dependent flow field v_theta(m_t,t) to propose updated target models via m_hat1,k = m_t + (1−t) v_theta(m_t,t), trained by minimizing the FWI data misfit through backpropagation.
• Parameterize the flow with a U-Net and train online with gradients from the waveform misfit, employing automatic differentiation through the forward solver.
• Provide a warm-start procedure and an outer/inner loop scheme to progressively refine the model from coarse to fine scales.

实验结果

研究问题

• RQ1 Does SFM-FWI improve reconstruction accuracy over conventional FWI and pretraining-free regularization across synthetic benchmarks?
• RQ2 How does online, self-supervised flow matching affect robustness to noise, limited illumination, and poor initial models in FWI?
• RQ3 Can a deterministic transport field learned online provide stable coarse-to-fine evolution without Offline pretrained priors?
• RQ4 What is the impact of the flow-guided updates on convergence behavior and high-wavenumber content recovery?

主要发现

Approaches	Relative L2 error	SSIM
Conventional FWI	0.0213	0.853
Conventional FWI with TV	0.0217	0.862
DIP-FWI	0.0177	0.866
SFM-FWI	0.0130	0.907
Conventional FWI	0.0933	0.762
Conventional FWI with TV	0.0934	0.786
DIP-FWI	0.0765	0.779
SFM-FWI	0.0682	0.791
Conventional FWI	0.0962	0.664
Conventional FWI with TV	0.0959	0.742
DIP-FWI	0.0443	0.851
SFM-FWI	0.0390	0.869

• SFM-FWI achieves lower relative L2 error and higher structural similarity (SSIM) than conventional FWI, TV-regularized FWI, and DIP-FWI in Marmousi sub-region, Marmousi larger, and Overthrust benchmarks.
• The method demonstrates improved robustness to noise and imperfect data conditions, with more stable convergence than baselines.
• Online flow learning guided by FWI misfit provides a coherent, coarse-to-fine transport that preserves geological plausibility while enhancing resolution where illumination is weaker.
• By avoiding offline pretraining and diffusion-time alignment issues, SFM-FWI yields more accurate and artifact-reduced velocity models across challenging nonlinear inversion scenarios.
• The approach leverages differentiable wave equation solvers to backpropagate through the forward model, enabling end-to-end training of the flow network without paired velocity datasets.