Geological uncertainty quantification is critical to subsurface modeling and prediction, such as groundwater, oil or gas, and geothermal resources, and needs to be continuously updated with new data. We provide an automated method for uncertainty quantification and the updating of geological models using borehole data for subsurface developments within a Bayesian framework. Our methodologies are developed with the Bayesian evidential learning protocol for uncertainty quantification. Under such a framework, newly acquired borehole data directly and jointly update geological models (structure, lithology, petrophysics, and fluids), globally and spatially, without time-consuming model rebuilding. To address the above matters, 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 a falsification process, a sequential direct forecasting is designed to perform the joint uncertainty quantification. The direct forecasting is a statistical learning 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, allow for fast-computation posterior geological models. The proposed framework is completely automated in an open-source project. We demonstrate its application by applying it to a generic gas reservoir dataset. 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.

Direct sampling (DS) is a versatile multiple‐point statistics method for generating spatial‐temporal geostatistical models. DS is known for being able to address a variety of training images and hence spatiotemporal stochastic modeling problems. One limitation of DS is the central processing unit (CPU) time, mostly attributed to the use of a random search for patterns in the training image. To improve CPU performance, we propose a tree‐based direct sampling (TDS) method. In our method, training patterns are grouped according to their similarities combined with a clustering tree for fast lookup. Rather than patterns, we store locations in our database. During the simulation, TDS applies a tree‐driven search approach. Two objectives, similarity and diversity, are used to rapidly retrieve patterns and prevent trapping into local optima. We also introduce a way to speed up simulation by means of pasting patterns with adaptive size. The performance of our TDS is investigated using a 2‐D benchmark training image. Moreover, we apply the proposed method to two real cases including gap filling the bedrock topography in Antarctica from radar to better understand subglacial hydrology and creating 3‐D groundwater models in the Danish aquifer system. Based on several quantitative evaluations, we find the proposed TDS is comparable to DS in terms of simulation quality, while significantly saves CPU time.

The interpolation of geospatial phenomena is a common problem in Earth science applications that can be addressed with geostatistics, where spatial correlations are used to constrain interpolations. In certain applications, it can be particularly useful to a perform geostatistical simulation, which is used to generate multiple non-unique realizations that reproduce the variability in measurements and are constrained by observations. Despite the broad utility of this approach, there are few open-access geostatistical simulation software applications. To address this accessibility issue, we present GStatSim, a Python package for performing geostatistical interpolation and simulation. GStatSim is distinct from previous geostatistical tools in that it emphasizes accessibility for non-experts, geostatistical simulation, and applicability to remote sensing data sets. It includes tools for performing non-stationary simulations and interpolations with secondary constraints. This package is accompanied by a Jupyter Book with user tutorials and background information on different interpolation methods. These resources are intended to significantly lower the technological barrier to using geostatistics and encourage the use of geostatistics in a wider range of applications. We demonstrate the different functionalities of this tool for the interpolation of subglacial topography measurements in Greenland.