Bayesian Full-waveform Monitoring of CO2 Storage with Fluid-flow Priors via Generative Modeling

TL;DR

This work addresses the uncertainty in time-lapse seismic monitoring of CO$_2$ storage by developing a Bayesian full-waveform monitoring framework that couples physics-based priors with a generative latent-space model. A 64-dimensional VAE latent space compresses high-dimensional saturation fields learned from 4{,}000 geomodel realizations and flow simulations, enabling efficient Hamiltonian Monte Carlo sampling conditioned on time-lapse data and rock-physics forward modeling. The approach yields posterior ensembles that recover plume geometry with quantified uncertainties, even under sparse acquisition and realistic noise, and identifies where additional measurements would most reduce ambiguity. By integrating geostatistics, multiphase flow physics, rock physics, and Bayesian inference, the framework provides robust uncertainty quantification and practical guidance for survey design and bias mitigation in CO$_2$ storage monitoring and other subsurface processes.

Abstract

Quantitative monitoring of subsurface changes is essential for ensuring the safety of geological CO2 sequestration. Full-waveform monitoring (FWM) can resolve these changes at high spatial resolution, but conventional deterministic inversion lacks uncertainty quantification and incorporates only limited prior information. Deterministic approaches can also yield unreliable results with sparse and noisy seismic data. To address these limitations, we develop a Bayesian FWM framework that combines reservoir flow physics with generative prior modeling. Prior CO2 saturation realizations are constructed by performing multiphase flow simulations on prior geological realizations. Seismic velocity is related to saturation through rock physics modeling. A variational autoencoder (VAE) trained on the priors maps high-dimensional CO2 saturation fields onto a low-dimensional, approximately Gaussian latent space, enabling efficient Bayesian inference while retaining the key geometrical structure of the CO2 plume. Hamiltonian Monte Carlo (HMC) is used to infer CO2 saturation changes from time-lapse seismic data and to quantify associated uncertainties. Numerical results show that this approach improves inversion stability and accuracy under extremely sparse and noisy acquisition, whereas deterministic methods become unreliable. Statistical seismic monitoring provides posterior uncertainty estimates that identify where additional measurements would most reduce ambiguity and mitigate errors arising from biased rock physics parameters. The framework combines reservoir physics, generative priors, and Bayesian inference to provide uncertainty quantification for time-lapse monitoring of CO2 storage and other subsurface processes.

Figures (13)

• Figure 1: Workflow of the proposed Bayesian FWM framework. Reservoir realizations are generated using geostatistical models and fluid-flow simulations to produce CO$_2$ saturation fields. A VAE learns a low-dimensional manifold of these fields to construct a generative prior, which is mapped to seismic velocities through rock physics modeling. HMC sampling in the latent space infers posterior distributions conditioned on time-lapse seismic data.
• Figure 2: (a) Baseline P-wave velocity model for the geological CO$_2$ injection. The dashed box marks the target reservoir, spanning lateral positions of 550-1,440 m and depths of 1,300-1,370 m. The purple dashed line indicates the injection well, and the black solid line denotes the observational geophone well. Red stars indicate the five surface seismic sources. The selected monitoring geomodel realization and its associated porosity field (b), CO$_2$ saturation distribution at the 10th month of injection (c), and the resulting P-wave velocity change (d) are also shown. Note the zero depth value in (b), (c) and (d) corresponds to a depth of 1,300 m in (a).
• Figure 3: Comparison between the original CO$_2$ saturation fields modeled with GEOS and their VAE reconstructions on the validation dataset. The spatial domain corresponds to the target reservoir interval outlined in Figure \ref{['fig:model']}a, spanning depths of 1,300-1,370 m and lateral distance of 550-1,440 m. Column 2 represents VAE reconstructions of the GEOS results in column 1, column 4 shows reconstructions of the results in column 3, and column 6 provides reconstructions of the results in column 5.
• Figure 4: Latent-space interpolation tests. (a-c) Saturation realizations generated at interpolation steps $\delta = 0.0$ to $1.0$ for three random latent vector pairs. (d) Sky-blue curves show similarity as measured by SSIM between consecutive interpolants, and orange curves show similarity between each interpolant and the end-member at $\delta = 0$.
• Figure 5: Sampling diagnostics of the HMC results after the burn-in phase. (a,c,e) Trace plots for latent variables of dimensions 10, 30, and 50, respectively. (b,d,f) Corresponding autocorrelation functions (ACF) truncated at lag 1,000, where the dashed lines denote the $\pm 0.1$ bounds. (g) Negative log-probability across samples. (h) Distribution of bulk and tail effective sample sizes (ESS) across all 64 latent variables.