Improved coupled Markov chain method for simulating geological uncertainty

Geological uncertainty is common in nature due to complex depositional processes as one layer appears to be randomly embedded in neighbouring layers. However, the geo-structures could be significantly affected by the geological uncertainty, often simulated using the coupled Markov chain (CMC) model. The objective of this study is to develop an improved CMC method by enhancing the rationality of determining the horizontal transition probability matrix (HTPM) in the CMC model to simulate complex multi-layer strata based on limited borehole data. This difficulty of determining HTPM is solved by combining the vertical transition count matrix and intermediate horizontal matrix with Walther's law. The effectiveness of this method is evaluated by the artificial HTPM and virtual boreholes. Boreholes collected from Norway are adopted to illustrate the proposed method for HTPM estimation. Estimating the HTPM has been dramatically enhanced for the improved CMC model and is not sensitive to the borehole layout schemes. The error of HTPM between estimated and actual strata is less than 3% for different borehole schemes. A matching rate indicator is defined to evaluate the accuracy of the simulated results. The results show that the proposed method has good performance and robustness. An optimizing design approach for the borehole location and number is presented to minimize the uncertainty of the stratum simulation based on the information entropy.