Nonparametric and data-driven interpolation of subsurface soil stratigraphy from limited data using multiple point statistics

An essential task in many geotechnical projects is delineation of subsurface soil stratigraphy from scatter measurements. Geotechnical engineers often use their knowledge on local geology and interpret soil strata boundaries by linear interpolation of measured data. This usual practice may encounter difficulties when interpreting complex deposits, particularly when measurements are limited. In this study, a novel nonparametric, data-driven method based on multiple point statistics (MPS) is proposed to interpolate subsurface soil stratigraphy from sparse measurements. MPS may be formulated as Bayesian supervised machine learning, which adaptively learns high-order spatial information (e.g., curvilinear features of soil layers) using sparse measurements obtained in a specific site and training image that reflects pre-existing engineering knowledge on similar geological settings. The proposed method is the first ever purely data-driven method (i.e., without using any pre-specified parametric functions) for geotechnical site characterization. The proposed method is illustrated by a simulated example and real data from a reclamation site in Hong Kong. The proposed method not only accurately interpolates the subsurface soil stratigraphy from sparse measurements, but also quantifies uncertainty associated with the interpolation. Effects of governing parameters in the proposed method are explicitly investigated, and parameters appropriate for subsurface soil stratigraphy are identified.