Quasi-site-specific multivariate probability distribution model for sparse, incomplete, and three-dimensional spatially varying soil data

In a previous work, the first two authors proposed a data-driven method that can construct a site-specific multivariate probability density function model for soil properties using sparse, incomplete, and spatially variable site investigation data. The spatial variability was limited to the depth direction (horizontal variability was not considered). This data-driven method is referred to as GPR-MUSIC-X. In the current paper, two improvements with respect to GPR-MUSIC-X are made. First, the one-dimensional spatial variability considered by GPR-MUSIC-X is extended to three-dimensional spatial variability (denoted by GPR-MUSIC-3X). Second, a hierarchical Bayesian model (HBM) is adopted to learn the cross-correlation (correlation among different soil parameters) behaviour of generic sites in a soil database accounting for site differences (or uniqueness), and the learning outcome is incorporated into GPR-MUSIC-3X. The resulting model is a quasi-site-specific model (denoted by HBM-MUSIC-3X) because it not only is based on site-specific data but also is informed by the soil database in a manner sensitive to site uniqueness. A case history is used to illustrate the effectiveness of the proposed HBM-MUSIC-3X.