基于扩散正则化斯坦变分梯度下降的结构感知贝叶斯全波形反演
Structure-aware Bayesian full waveform inversion via diffusion-regularized Stein variational gradient descent
AI总结：
该研究针对传统ASVGD-FWI的先验不足问题，将学习型扩散模型作为隐式正则化引入框架，结合FWI数据一致性、ASVGD后验多样性，提升了反演稳定性与不确定性可解释性。
摘要：
全波形反演（FWI）是用于高分辨率地下模型重建的强大工具，但它仍具有高度非线性和不适定性，尤其是当初始模型不准确或采集的数据存在噪声且不完整时。退火斯坦变分梯度下降（ASVGD）为FWI提供了基于粒子的贝叶斯框架，通过速度模型集合近似后验分布，从而实现超越单一确定性解的不确定性量化。然而，传统ASVGD-FWI通常依赖简单的手工先验，如高斯或平滑假设，这些先验往往不足以表征复杂的地质结构。为解决这一局限，我们在ASVGD-FWI框架内引入学习型扩散模型（DM）作为隐式正则化机制。训练后的扩散模型无需显式计算扩散先验密度，而是作为学习型地质投影算子，引导更新后的粒子向合理速度模型的分布靠拢。通过这种方式，所提方法结合了FWI的数据一致性、ASVGD的后验多样性以及扩散先验的结构真实性。数值实验表明，扩散正则化ASVGD-FWI能生成更符合地质规律的均值模型，抑制非物理伪影，并在结构复杂、约束不足的区域得到更集中的不确定性估计。这些结果表明，学习型扩散先验可通过提升反演稳定性和后验不确定性的可解释性，有效增强贝叶斯FWI的性能。
英文摘要：
Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed, especially when the initial model is inaccurate or the acquired data are noisy and incomplete. Annealed Stein variational gradient descent (ASVGD) provides a particle-based Bayesian framework for FWI by approximating the posterior distribution with an ensemble of velocity models, thereby enabling uncertainty quantification beyond a single deterministic solution. However, conventional ASVGD-FWI commonly relies on simple handcrafted priors, such as Gaussian or smoothing assumptions, which are often insufficient to represent complex geological structures. To address this limitation, we introduce a learned diffusion model (DM) as an implicit regularization mechanism within the ASVGD-FWI framework. Instead of explicitly evaluating the diffusion prior density, the trained diffusion model acts as a learned geological projection operator that guides updated particles toward the distribution of plausible velocity models. In this way, the proposed method combines data consistency from FWI, posterior diversity from ASVGD, and structural realism from the diffusion prior. Numerical experiments demonstrate that the diffusion-regularized ASVGD-FWI produces more geologically consistent mean models, suppresses nonphysical artifacts, and yields uncertainty estimates that are more concentrated around structurally complex and poorly constrained regions. These results suggest that learned diffusion priors can effectively enhance Bayesian FWI by improving both inversion stability and the interpretability of posterior uncertainty.
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