Abstract

Subsurface characterization remains a pivotal challenge in geology, hindered by the inherent complexity and nonstationarity of geological processes. Conventional geostatistical methods, relying on two-point statistics and kriging, often fall short in capturing the spatial heterogeneity and transitional dynamics of subsurface materials. This study introduces a novel three-dimensional lithofacies characterization method that incorporates manifold embedding and a transition probability-based spatial estimation technique, significantly deviating from conventional approaches. The proposed method addresses existing limitations by providing a robust framework for capturing the nonstationary nature of geological processes, utilizing data such as pole-to-plane orientations and lithological transitions for structural and juxtapositional information. Through hypothetical scenarios and simulations, the performance of the proposed method is demonstrated, showcasing its capability to model complex geological formations and accurately estimate subsurface characteristics. The study underscores the importance of considering nonstationarity in geological estimations and highlights the potential impact on hydrogeological modeling. Accurate lithological distribution estimation is crucial for reliable groundwater flow and solute transport modeling. This study advances the methodological toolkit for subsurface characterization and paves the way for future research, including empirical validation with real-world data and exploration of the method's applicability in early-stage site characterization, where data scarcity and quality are pressing concerns.