Accurately characterizing migration velocity models is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional velocity model building methods such as Full-Waveform Inversion (FWI) are powerful but often struggle with the inherent complexities of the inverse problem, including noise, limited bandwidth, receiver aperture and computational constraints. To address these challenges, we propose a scalable methodology that integrates generative modeling, in the form of Diffusion networks, with physics-informed summary statistics, making it suitable for complicated imaging problems including field datasets. By defining these summary statistics in terms of subsurface-offset image volumes for poor initial velocity models, our approach allows for computationally efficient generation of Bayesian posterior samples for migration velocity models that offer a useful assessment of uncertainty. To validate our approach, we introduce a battery of tests that measure the quality of the inferred velocity models, as well as the quality of the inferred uncertainties. With modern synthetic datasets, we reconfirm gains from using subsurface-image gathers as the conditioning observable. For complex velocity model building involving salt, we propose a new iterative workflow that refines amortized posterior approximations with salt flooding and demonstrate how the uncertainty in the velocity model can be propagated to the final product reverse time migrated images. Finally, we present a proof of concept on field datasets to show that our method can scale to industry-sized problems.

We introduce a probabilistic technique for full-waveform inversion, employing variational inference and conditional normalizing flows to quantify uncertainty in migration-velocity models and its impact on imaging. Our approach integrates generative artificial intelligence with physics-informed common-image gathers, reducing reliance on accurate initial velocity models. Considered case studies demonstrate its efficacy producing realizations of migration-velocity models conditioned by the data. These models are used to quantify amplitude and positioning effects during subsequent imaging.