Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to obtain the desired high-resolution model with FWI. To address this challenge, we propose a new paradigm for FWI regularized by generative diffusion models. Specifically, we pre-train a diffusion model in a fully unsupervised manner on a prior velocity model distribution that represents our expectations of the subsurface and then adapt it to the seismic observations by incorporating the FWI into the sampling process of the generative diffusion models. What makes diffusion models uniquely appropriate for such an implementation is that the generative process retains the form and dimensions of the velocity model. Numerical examples demonstrate that our method can outperform the conventional FWI with only negligible additional computational cost. Even in cases of very sparse observations or observations with strong noise, the proposed method could still reconstruct a high-quality subsurface model. Thus, we can incorporate our prior expectations of the solutions in an efficient manner. We further test this approach on field data, which demonstrates the effectiveness of the proposed method.

翻译：全波形反演（FWI）具有提供高分辨率地下模型估计的潜力。然而，由于观测条件的限制（例如区域噪声、有限的炮点或接收器以及带限数据），FWI难以获得期望的高分辨率模型。为解决这一挑战，我们提出了一种由生成扩散模型正则化的FWI新范式。具体而言，我们以完全无监督的方式在表示地下先验期望的模型速度分布上预训练扩散模型，随后通过将FWI融入生成扩散模型的采样过程，使其适应地震观测数据。扩散模型在此类实现中具备独特优势，其生成过程保留了速度模型的形式和维度。数值实验表明，本方法在仅增加可忽略额外计算成本的情况下即可超越传统FWI。即使在观测数据极为稀疏或存在强噪声的情况下，所提方法仍能重建高质量的地下模型。因此，我们能够以高效方式融入对解的先验期望。我们进一步将这一方法应用于现场数据，验证了所提方法的有效性。