A prior regularized 3D full waveform inversion using 2D generative diffusion models

Full waveform inversion (FWI) has great potential in reconstructing high-resolution subsurface models. However, due to limitations in observation, this inverse problem is highly ill-posed, especially for recovering a 3D velocity model. To solve this problem, regularization is often used, like those given by a fixed form (total variation) or learned by a machine. However, those regulations often have an adverse effect on the data fitting. On the other hand, diffusion models can sufficiently and efficiently introduce prior information about our expectations within FWI. When dealing with 3D, extending the 2D diffusion model to 3D is extremely expensive, due to its high dimension and requirement for training data. Therefore, we propose using a 2D diffusion model to guide the 3D inversion. For a 3D subsurface model, we implement 2D diffusion reverse progress for inline profiles slice by slice independently, and add a 1D total variation (TV) regularization along the crossline direction to effectively suppress the inconsistency between inline profiles. The numerical experiments on the Overthrust model demonstrate the effectiveness of our method, especially compared to using 3D TV penalty.