AI summaryⓘ
The authors studied ways to update 3D underground geological models using observed data from wells, focusing on keeping the models realistic. They compared traditional methods that update directly in model space with newer methods that update in a simpler latent space created by latent diffusion models (LDMs). They found that updating in model space reduces uncertainty more but often produces unrealistic geology, while updating in latent space keeps geology realistic but reduces uncertainty less. To improve this, the authors tested advanced sampling methods (MCMC and SMC) in the latent space, supported by a fast flow model. These methods gave better data fits and reduced uncertainty more reliably than simpler ensemble methods, showing that rigorous sampling can be more effective when using complex latent models.
Data assimilationSubsurface flowLatent diffusion modelsEnsemble smoother with multiple data assimilation (ESMDA)Markov chain Monte Carlo (MCMC)Sequential Monte Carlo (SMC)Geological realismUncertainty quantificationSurrogate flow modelsInverse problems
Authors
Guido Di Federico, Wenchao Teng, Louis J. Durlofsky
Abstract
Data assimilation (DA) in subsurface flow entails calibrating model parameters to match observed data, typically at wells, while preserving geological realism. Latent diffusion models (LDMs) provide efficient mappings from high-dimensional geological model space to a low-dimensional latent variable, reducing the dimensionality of the inverse problem while maintaining plausibility in posterior geomodels. However, the high nonlinearity in the LDM mapping may degrade the performance of Kalman-gain-based ensemble updates. We present a systematic comparison of DA algorithms applied to large-scale 3D channelized geomodels with hierarchical geological uncertainty. We compare model-space and latent-space DA using the ensemble smoother with multiple data assimilation (ESMDA), and demonstrate a key trade-off: model-space updates achieve significant uncertainty reduction but produce geologically unrealistic posterior models, while latent-space updates preserve realism but exhibit limited uncertainty reduction. Motivated by this, we explore rigorous Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) algorithms in the 3D-LDM latent space. To accommodate their high computational demands, we develop a fast surrogate flow model that approximates well-rate responses. MCMC and SMC are evaluated against ESMDA across three synthetic test cases, with DA performed in the LDM latent space. All models maintain geological realism due to the LDM parameterization. MCMC and SMC are consistent with one another and achieve lower data mismatch and more uncertainty reduction than latent-space ESMDA. Our overall results demonstrate that ensemble Kalman methods may provide overestimated posterior uncertainty with highly nonlinear parameterizations, while rigorous Monte Carlo sampling, enabled by fast surrogate models, can provide a more reliable alternative.