Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

Abstract

Abstract. Three-dimensional (3-D) geological structural modeling aims to determine geological information in a 3-D space using structural data (foliations and interfaces) and topological rules as inputs. This is necessary in any project in which the properties of the subsurface matters; they express our understanding of geometries in depth. For that reason, 3-D geological models have a wide range of practical applications including but not restricted to civil engineering, the oil and gas industry, the 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) and the inherent lack of knowledge in areas where there are no observations combined with input uncertainty (observational, conceptual and technical errors). Because 3-D geological models are often used for impactful decision-making it is critical that all 3-D geological models provide accurate estimates of uncertainty. This paper's focus is set on the effect of structural input data measurement uncertainty propagation in implicit 3-D geological modeling. This aim is achieved using Monte Carlo simulation for uncertainty estimation (MCUE), a 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 3-D 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 incorrect 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 diminish the occurrence of artifacts.

Uncertainty assessment for 3D geologic modeling of fault zones based on geologic inputs and prior knowledge

“…The same flexibility that allows MCUP to be effectively formulated for nearly any geologic modeling problem is also a potential susceptibility of MCUP -that the model formulation and input uncertainties must be predefined by the user. This can lead to potential over-or under-estimation and biases in the uncertainty assessment performed with MCUP due to inappropriate selection of modeling inputs or incorrect parameterization of input probability distributions (de la Varga and Wellmann, 2016;Wellmann and Caumon, 2018;Pakyuz-Charrier et al, 2018b). Following the school of thought reviewed by Nearing et al (2016), the modeler must ask questions along the lines of:…”

Topological Analysis in Monte Carlo Simulation for Uncertainty Estimation

“…In the case of a heterogeneous population or a mixture of populations, this procedure will fail to represent accurately the behavior of the variable in the same way a bimodal distribution cannot be fully described by its mean and variance ( Figure 2). In the case of MCUE, perturbation is usually performed using unimodal gaussian disturbance distributions (Pakyuz-Charrier et al, 2018; and at first sight it may seem that model building should result in a homogenous population of plausible models. However, it has been demonstrated on simple synthetic cases that plausible models with strikingly different structural geological features may arise from perturbing the same original dataset (Thiele et al, 2016a;Thiele et al, 2016b) using unimodal disturbance distributions (Figure 3).…”

“…How reliable a 3D geological model is and how this reliability varies in space are indispensable data to seek improvement of said model. Monte Carlo based 5 uncertainty estimation (MCUE) algorithms have recently been proposed to tackle this issue (de la Varga and Wellmann, 2016;Pakyuz-Charrier et al, 2018). MCUE methods ( Figure 1) aim to propagate the measurement uncertainty of structural input data (interface points, foliations, fold axes) through implicit 3D geological modeling engines to produce probabilistic geological models (PGM) and uncertainty index models (UIM).…”

Towards geologically reasonable lithological classification from integrated geophysical inverse modelling: methodology and application case

“…where represents the measurements and is the model; is the forward operator calculating the data produces; is the prior model. In this contribution, is a diagonal matrix where each element is equal to the The matrix is calculated following (Giraud et al, 2019a), who use the probabilistic geological modelling approach described in Pakyuz-Charrier et al (2018c, 2018b, 2019. In the case of gravity inversion as presented 20 here, the complete Bouguer anomaly of density contrast model is calculated as the product of the Jacobian matrix with model , i.e., we have ( ) = .…”

“…Geological uncertainty is estimated from probabilistic geological modelling. During this process, a series of geological models is generated using the Monte-Carlo Uncertainty Estimator (MCUE) of Pakyuz-Charrier et al 25 (2018a, 2018b, 2018c, 2019. MCUE relies on the perturbation of orientation measurements (interfaces and foliations) defining structures of a reference geological model accordingly with their uncertainty.…”