WISE: full-Waveform variational Inference via Subsurface Extensions

TL;DR

The paper tackles uncertainty quantification in full-waveform inversion (FWI) by casting it as a Bayesian problem and employing amortized variational inference with conditional normalizing flows (CNFs) to approximate the posterior $p(\mathbf{x}|\mathbf{y})$. It introduces physics-informed summary statistics, notably common-image gathers (CIGs) derived from subsurface-offset modeling, as information-preserving conditioning for CNFs to overcome difficulties with nonlinear FWI. Empirical results on Open FWI CurveFault-A and Compass 2D slices show that CIG-based conditioning yields more informative posterior samples and improved downstream imaging, including higher SSIM scores and better reflector delineation, while enabling explicit propagation of inverse and forward uncertainties to amplitude and positioning. Overall, WISE presents a scalable, uncertainty-aware inversion framework that integrates physics with generative AI to produce data-conditioned distributions of migration-velocity fields and their imaging consequences.

Abstract

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.

Figures (4)

• Figure 1: Applying WISE for two unseen test samples in Open FWI CurveFault-A dataset.
• Figure 2: (a) an unseen ground-truth velocity model; (b) 1D initial FWI-velocity model; (c) conditional mean estimate for RTM as summary statistics ($\mathrm{SSIM}=0.48$); (d) conditional mean estimate from WISE ($\mathrm{SSIM}=0.56$).
• Figure 3: CIGs calculated by the initial FWI-velocity model given by (a) the 1D background model (shown in Figure \ref{['fig-true-migration']}(b)) or by (b) the conditional mean estimate (shown in Figure \ref{['fig-true-migration']}(d)).
• Figure 4: Using WISE in the downstream imaging task: (a) imaged reflectors using the conditional mean estimate (shown in Figure \ref{['fig-true-migration']}(d)) as the migration velocity; (b) point-wise standard deviation of the posterior velocity samples; (c) point-wise deviation of the imaged reflectivities; (d) point-wise maximum depth shift. Note: (a) and (c) are normalized by the same constant. The images are all grided for visualization purpose.