Enhanced Markov-type Categorical Prediction with geophysical soft constraints for hydrostratigraphic modeling

Abstract. Accurately characterizing hydrostratigraphic structures is essential for reliable groundwater flow and transport modeling. Due to limited borehole coverage and geological complexity, uncertainty analysis plays a vital role in supporting robust hydrogeological modeling. Traditional geostatistical approaches such as Multiple-Point Statistics (MPS), offer flexibility in reproducing complex geological patterns and uncertainties, but they are computationally demanding, may struggle to maintain stratigraphic consistency, and can be difficult to apply in practice. Alternatively, the Markov-type Categorical Prediction (MCP) framework has a better computational efficiency and enforces stratigraphic ordering. However, its effectiveness is challenged in areas with sparse borehole data. To address this limitation, this study presents an enhanced MCP approach that incorporates airborne electromagnetic (AEM) geophysical data as soft probabilistic constraints on lithology occurrence. A tunable parameter controls the relative contribution of geophysical and geological information, allowing for flexible data integration within the simulation process. The approach is tested on both synthetic and real-world cases. Synthetic experiments of different scenarios demonstrate that incorporating geophysical constraints improves lithological prediction accuracy, particularly when combined with borehole data. In the field application from Egebjerg, Denmark, we demonstrate how a statistical relationship between lithology and resistivity can be derived by integrating SkyTEM data with borehole lithological logs and depth information. That relation is then combined with conditional probabilities from training images extracted from a 3D interpreted model, using the MCP framework. The results show that the integrated approach enhances the generations of complex geological features, such as buried valleys, especially in areas with limited direct observations. By embedding geophysical information into the MCP framework, the method combines the spatial consistency and stratigraphic ordering of MCP with the extensive coverage and subsurface sensitivity of geophysical data. This integration overcomes a key limitation of MCP and enables more reliable simulations in regions where direct subsurface observations are limited, providing a practical and adaptable tool for improving geological modeling in groundwater studies.