Kriging-informed graph stochastic neural network for stratigraphic delineation considering spatial variability

Accurate characterization of subsurface stratigraphy with an assessment of associated uncertainties is essential for supporting reliable geotechnical system design and decision-making. In engineering practice, inherent soil variability and sparse site-specific measurements pose a significant challenge for obtaining a comprehensive understanding of subsurface geological conditions. While deep learning-based techniques have sparked a new wave of interest in geological modeling, incorporating soil variability typically described by variogram models into such frameworks is still an open question. This paper proposes a novel kriging-informed graph stochastic neural network (Ki-GSNN) for data-driven stratigraphic delineation and probabilistic mapping that accounts for spatial variability. By explicitly introducing a theoretical autocorrelation function, weighted geological knowledge graphs centered on target locations are constructed with specific spatial constraints. The proposed method can extract stratigraphic patterns by collectively aggregating geological information from constructed graphs. To facilitate efficient stratigraphic simulations, a variational autoencoder is integrated for inferring possible soil events through graph data reconstruction. The model performance is demonstrated using reclamation project data from Hong Kong, while its effectiveness and robustness are further evaluated against the Markov random field approach in a tunnel project in Guangzhou, China. In addition, a synthetic case study is conducted to enable parametric analysis and probabilistic identification of stratigraphic boundaries.