Monte Carlo Simulations for Uncertainty Estimation in 3D Geological Modeling, A Guide for Disturbance Distribution Selection and Parameterization

Three-dimensional (3D) geological modeling aims to determine geological information in a 3D space using structural data (foliations and interfaces) and topological rules as inputs. They are necessary in any project where the properties of the subsurface matters, they express our understanding of geometries in depth. For that reason, 3D geological models have a wide range of practical applications including but not restrained to civil engineering, oil and gas industry, mining industry and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator’s parameterization) combined with input uncertainty (observational-, conceptual- and technical errors). Because 3D geological models are often used for impactful decision making it is critical that all 3D geological models provide accurate estimates of uncertainty. This paper’s focus is set on the effect of structural input data uncertainty propagation in implicit 3D geological modeling using GeoModeller API. This aim is achieved using Monte Carlo simulation uncertainty estimation (MCUE), a heuristic stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed. The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of inappropriate disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e. scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminishes the occurrence of artefacts.