发表机构
School of Mathematical Sciences, Shanghai Jiao Tong University; CMA-Shanghai, Shanghai Jiao Tong University; School of Mathematics and Statistics, Lanzhou University（上海交通大学数学科学学院; 上海交通大学CMA-上海; 兰州大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对全波形反演中初始化依赖和物理引导不可靠的问题，提出物理状态引导的扩散采样（PSG），通过高斯桥耦合物理速度与扩散先验，在多个数据集上优于基线并支持大模型反演。
AI 中文摘要
全波形反演（FWI）从地震记录中估计地下速度，但其不适定性和非线性使得准确重建强烈依赖于初始化和先验信息。扩散后验采样提供了一种学习到的地质先验，然而将其去噪器直接耦合到非线性波动求解器可能产生不可靠的物理引导。我们提出了物理状态引导的扩散采样（PSG），通过高斯桥将持久的物理速度与扩散先验耦合。物理状态通过由去噪速度正则化的波形拟合进行细化，并反过来引导反向扩散过程。该公式将波动方程和去噪器的梯度分离，同时保留传统FWI的初始化和累积的优化历史。在四个OpenFWI数据集族上，PSG的最终去噪估计在干净和缺失道采集下优于经典和基于扩散的基线，并在测量噪声下保持较强的结构恢复能力。重复的随机运行保留了主要的地质结构，集合变异性集中在地质界面附近，并与局部反演误差正相关。冻结的OpenFWI训练先验进一步支持对更大的Marmousi、Overthrust和BP2004盐模型的反演，无需重新训练即可恢复复杂的地质结构。
英文摘要
Full waveform inversion (FWI) estimates subsurface velocity from seismic recordings, but its ill-posedness and nonlinearity make accurate reconstruction strongly dependent on initialization and prior information. Diffusion posterior sampling provides a learned geological prior, yet directly coupling its denoiser to the nonlinear wave solver can yield unreliable physical guidance. We propose Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity to the diffusion prior through a Gaussian bridge. The physical state is refined by waveform fitting regularized by the denoised velocity, and in turn guides the reverse diffusion process. This formulation separates the wave-equation and denoiser gradients while preserving conventional FWI initialization and accumulated optimization history. On four OpenFWI families, PSG's terminal denoised estimates outperform classical and diffusion-based baselines under clean and missing-trace acquisitions and maintain strong structural recovery under measurement noise. Repeated stochastic runs preserve the dominant geological structures, with ensemble variability concentrated near geological interfaces and positively associated with local inversion error. A frozen OpenFWI-trained prior further supports inversion of the larger Marmousi, Overthrust, and BP2004 Salt models, recovering complex geological structures without retraining.
Comments43 pages, 13 figures
