A quasi-manifold-based probabilistic method for real-time interpretation of interbedded strata from sparse boreholes

Interbedded strata commonly exist in nearshore marine environments and play a crucial role in determining the resilience of coastal infrastructure. However, delineating the spatial distribution of these strata from sparse and incomplete site-specific boreholes is challenging due to their complex spatial features and significant variability. This study proposes a quasi-manifold learning approach to address these challenges in a stochastic and non-parametric manner. Sparse and incomplete borehole measurements are first transformed from a low-dimensional categorical feature space into a high-dimensional continuous feature space, providing a richer representation of inclusion characteristics. A quasi-manifold-based spatial interpolator is then developed to stochastically interpret high-dimensional features by traversing an embedded manifold, which concisely preserves the essential and meaningful stratigraphic patterns. Subsequently, inverse transformations convert the spatially predicted continuous variables back to categorical feature spaces for constructing two-dimensional geological cross-sections and three-dimensional domains with quantified stratigraphic uncertainty. Applications to a Hong Kong reclamation site and the Singapore Tuas port site demonstrate that the proposed approach effectively interprets the spatial distribution of interbedded strata without abrupt stratigraphic transitions or noisy patterns. The data-driven strategy is also robust, bypassing the need for extensive computational resources, parametric calibrations and customised prior geological settings.