3D nonstationary lithofacies characterization via manifold embedding and transition probabilities for hydrogeological applications

• 3D method uses manifold embedding & TPs for nonstationary lithofacies estimation. • Novel TP matrix generation improves lithological modeling with sparse data • Demonstrated via hypothetical scenarios & flow simulations, validating the method. Subsurface characterization remains a pivotal challenge in geology, largely due to the inherent complexity and nonstationarity of geological processes. Conventional geostatistical methods—often relying on two-point statistics and stationarity assumptions—struggle to accurately capture the spatial heterogeneity and transitional dynamics of subsurface materials. In hydrogeology, such simplifications can lead to significant misrepresentations of groundwater flow and solute transport pathways. This study introduces a novel three-dimensional lithofacies characterization approach that integrates manifold embedding with a transition probability-based spatial estimation technique. By incorporating structural and lithological information such as pole-to-plane orientations and lithological proportions, the proposed method effectively addresses nonstationarity and overcomes the limitations of traditional geostatistical models. Through a series of hypothetical scenarios and simulations, we demonstrate the method’s capability to reconstruct complex geological formations and reliably estimate subsurface characteristics without requiring predefined training images, making it especially suitable for data-scarce site investigations. These results highlight the importance of accounting for nonstationarity in geological modeling and emphasize the method’s potential impact on hydrogeological applications. Accurate lithological distribution estimation, facilitated by our approach, is essential for improving groundwater flow and solute transport simulations and thus guiding effective water resource management. This study thus enriches the geostatistical toolkit, paving the way for empirical validation in real-world hydrogeological settings and guiding its adoption in early-stage site investigations where data scarcity and uncertainties remain critical challenges.