3D Stratigraphic-based geo-property random field using Markov random fields and the concept of fractional Brownian motion

Stratigraphic and geo-property models play a crucial role in geotechnical engineering, geological hazard assessment, and risk evaluation. However, few random field models can capture these spatial dependencies. This paper presents a new approach to modelling stratigraphic and geo-properties, known as MRF-fBm, which integrates stochastic Markov random fields (SMRF), hidden Markov random fields (HMRF), and the concept of fractional Brownian motion (fBm). MRF-fBm allows for complex three-dimensional modelling of stratigraphy and geo-properties while effectively capturing their spatial correlations. To improve the accuracy of MRF-fBm, we utilise Bayesian analysis, which enables continuous refinement of statistical parameters through Markov-Chain Monte Carlo simulations. We also construct a synthetic stratigraphic model (SSM) to validate the effectiveness of MRF-fBm in simulating strata geometry and geo-property distribution. Our findings demonstrate that MRF-fBm can model these components in alignment with expected geological patterns. We also present a case study demonstrating the use of MRF-fBm for correlated stratigraphy and geo-property modelling on a regional scale, considering the heterogeneity of random field parameters, to evaluate liquefaction potential. The proposed method shows great promise for three-dimensional geological and geo-property modelling, as well as various engineering applications.