Automated Monte Carlo-based Quantification and Updating of Geological Uncertainty with Borehole Data (AutoBEL v1.0)

Abstract

Abstract. We provide an automated method for uncertainty quantification and updating of geological models using borehole data for subsurface developments (groundwater, geothermal, oil & gas, and CO2 sequestration, etc.) within a Bayesian framework. Our methodologies are developed with the Bayesian Evidential Learning protocol for uncertainty quantification. Under such framework, newly acquired borehole data directly and jointly update geological models (structure, lithology, petrophysics and fluids), globally and spatially, without time-consuming model re-buildings. To address the above, an ensemble of prior geological models is first constructed by Monte Carlo simulation from prior distribution. Once the prior model is tested by means of falsification process, a sequential direct forecasting is designed to perform the joint uncertainty quantification. The direct forecasting is a data-scientific method that learns from a series of bijective operations to establish “Bayes-linear-Gauss” statistical relationships between model and data variables. Such statistical relationships, once conditioned to actual borehole measurements, allows for fast computation posterior geological models. The proposed framework is completely automated in an opensource project. We demonstrate its application by applying to a generalized synthetic dataset motivated by a gas reservoir from Australia. The posterior results show significant uncertainty reduction in both spatial geological model and gas volume prediction, and cannot be falsified by new borehole observations. Furthermore, our automated framework completes the entire uncertainty quantification process efficiently for such large models.

Advancing measurements and representations of subsurface heterogeneity and dynamic processes: towards 4D hydrogeology

“…In such a case, classical inversion might still be needed (Scheidt et al, 2018). Recent advances have shown that BEL can also estimate the model parameter distributions and be used as a more traditional inversion technique (Yin et al, 2020;Michel et al, 2020a). However, such more advanced applications require further development of appropriate tools to identify highly non-linear relationships (Park and Caers, 2020) which will inevitably come at a larger computational cost (Michel et al, 2020b).…”

Machine Learning for Bayesian Experimental Design in the Subsurface

“…Because the prediction is much simpler than the underlying model, such a small training size is sufficient. Previous BEL applications have shown that this order of magnitude is adequate for making accurate predictions (Athens and Caers, 2019;Hermans et al, 2019Hermans et al, , 2018Hermans et al, , 2016Michel et al, 2020a,b;Park and Caers, 2020;Yin et al, 2020). The influence of the size of the training set is discussed in Section §3.3.2.…”

“…The previously considered hydraulic conductivity fields have two degrees of uncertainty: the mean of hydraulic conductivity and the spatial distribution of the stochastically generated fields. The goal of this chapter is not to demonstrate BEL's capabilities for more complex prior distributions, as this has already been established in previous works such as Hermans et al (2016); Satija and Caers (2015); Yin et al (2020). However, it is important to demonstrate that the experimental design approach remains feasible when the uncertainty is greater.…”

“…It is a Python program that uses geophysical data to perform stochastic 1D imaging of the subsurface, and has been used to estimate the uncertainty of model parameters in a variety of geophysical problems, including surface nuclear magnetic resonance (Michel et al, 2020b) and interpretation of surface waves dispersion curves (Michel et al, 2022a). Yin et al (2020) shared AutoBEL, a Python implementation of the BEL framework that provides an automated method for quantifying uncertainty and updating geological models using borehole data for subsurface developments.…”

“…To apply dimension reduction to the target, a suitable operator must be chosen to convert this Boolean matrix to a real-valued one, with smoothness being a desirable property. Yin et al (2020) demonstrated how to successfully apply PCA to a two-dimensional discrete lithology model using the signed distance function (SDF) before dimension reduction. This approach is also adopted in this work.…”