Assessing geometrical uncertainties in geological interface models using Markov chain Monte Carlo sampling via abstract graph

Uncertainty assessment is a common requirement in 3D modeling applications. The Markov chain Monte-Carlo (MCMC) method is a practical way to generate multiple realizations of 3D models to evaluate model uncertainty. However, when probing high-dimensional target distributions related to the detailed geometry of 3D geological interfaces, the generating 3D models by existing MCMC methods always suffer from the presence of artifacts in large geometrical deformation that modeling deformed geometries in stochastic perturbation, which limits their effectiveness and efficiency. This paper presents an abstract graph-based MCMC method for the uncertainty assessment of 3D geological interfaces. An abstract graph is used to represent the reasonable shape of the geological interface. In proposing new candidate 3D models via the MCMC iterations, the 3D models are perturbed such that the energy function measuring the distortion of the abstract graph is minimized in a least-squares sense. This can preserve the plausible geometry of the 3D models against high perturbations and provide artifact-free 3D models as candidates for MCMC sampling. The resulting MCMC iterations enable the drawing of probable realizations of 3D models while maintaining a high acceptance rate in probing the complicated target distributions of 3D geological interface models. The proposed method was applied to the assessment of uncertainties in three regional faults in the Jiaodong Peninsula, eastern China. The uncertainty assessment was carried out based on a complex probability distribution with consideration of geological-geophysical observations and prior knowledge of fault geometry. The results show that the proposed MCMC method could reasonably locate the uncertainties in free-form fault models defined by thousands of constraints. And the abstract graph-based MCMC method can sample highly-perturbed and geometrically plausible 3D models in high-resolution, which is crucial to the effectiveness and efficiency of the geometrical uncertainty assessment. •An MCMC method for assessing detailed geometrical uncertainty in 3D models.•An MCMC method that can propose highly perturbed but artifact-free 3D models.•Effectively assessing uncertainty in detailed 3D models from posterior distribution.•Integrating observations and knowledge for uncertainty assessment of 3D models.