Bayesian Supervised Learning of Site-Specific Geotechnical Spatial Variability from Sparse Measurements

Although the properties of geomaterials vary spatially, geotechnical site investigations often take sparse measurements from a limited number of locations. To estimate geotechnical properties at unsampled locations, interpolation is often needed. This paper presents a Bayesian supervised learning method for interpolation of site-specific geotechnical data from sparse measurements. The interpolation is considered as a supervised learning problem and is solved under a Bayesian framework. Numerical examples are used to evaluate performance of the proposed method and to provide a comparative study with ordinary kriging, a popular interpolation method in geosciences applications. Results show that when the available measurement points are sparse and limited, the Bayesian supervised learning method performs better than kriging. When the number of measurement points is large, results from the proposed method and kriging are almost identical. In addition, the proposed method is data-driven and nonparametric. It does not require a detrending process when dealing with nonstationary data, and it bypasses estimation of a parametric form of autocorrelation structure (e.g., semivariogram in conventional kriging interpolation). A well-known challenge in kriging is the selection of a suitable semivariogram function form or a suitable trend function form for detrending, given sparse geotechnical data. The proposed Bayesian supervised learning method bypasses these challenges and is particularly suitable for nonstationary geotechnical data. Standard preprocessing steps such as outlier removal and noise reduction apply to Bayesian supervised learning.