Triangulated irregular network-based probabilistic 3D geological modelling using Markov Chain and Monte Carlo simulation

Three-dimensional geological modelling based on triangulated irregular networks (TINs) often results in deterministic models that do not capture the uncertainty of stratigraphic attributes. This study presents a method for building a 3D TIN geological model that incorporates probability analysis and random simulation to account for this uncertainty. First, we generated the Markov chain sequence of the stratum and combined it with the correlation of boreholes to obtain the transition probability matrix of the virtual borehole. This matrix was then used to describe the probability of changes in the stratum. Second, we constructed a probabilistic model of stratum thickness and generated the stratum state of virtual boreholes through Monte Carlo simulation. Using the TIN algorithm, we built an overall probabilistic model and added validation boreholes to adjust the virtual boreholes and obtain the maximum probabilistic model of the study area. Finally, we performed a case analysis in South China to verify the modelling method, including visualisation, probability analysis and comparative analysis. Our results demonstrate that the proposed modelling method effectively visualises the stratigraphic configuration and quantifies the stratigraphic uncertainty, providing a reference for 3D geological modelling.