Local coupled Markov chain model for simulating varied stratigraphy

Abstract

The coupled Markov chain (CMC) model is widely employed to simulate geological uncertainty based on sparse borehole data, owing to its simplicity, parameter efficiency, and computational effectiveness. However, the existing CMC methods exhibit limitations in accurately predicting the orientation and significant dip angle changes of soil stratigraphy. These limitations stem from their reliance on a globally constant Walther constant, resulting in generated layer boundaries converging to a fixed angle. To address these issues, this study develops a local CMC model to enhance the accuracy of predicting layer sequences and describe the geological uncertainty of complex geological structures using limited borehole and surface data. In the proposed local CMC method, the global geological profile is decomposed into interconnected fragments, guided by reference boreholes. For each CMC fragment, the likelihood of observational scenarios is determined to identify the layer orientation and optimal Walther’s constant corresponding to the local geological profile. By combining the most likely realizations from all CMC fragments, the final geological profile and stratigraphic uncertainty are obtained. Illustrative case studies demonstrate that the proposed approach effectively addresses the limitations of conventional CMC models in accurately simulating significant changes in layer orientation and dip angle variations, given the same conditions of sparse borehole data. The employed localization strategy enables the prediction of geological profiles that encompass special layers such as soil interlayers, anticlines, and synclines, which cannot be well achieved by conventional CMC models. The local CMC model significantly improves the matching accuracy of geological model in situations with limited boreholes. Therefore, it plays a crucial role in the analysis of geological structures under data-scarce conditions.