Trend estimation and layer boundary detection in depth-dependent soil data using sparse Bayesian lasso

This paper proposes a method for estimating trends and detecting layer boundaries in depth-dependent soil data based on a least absolute shrinkage statistical operator (lasso). Although the lasso appears to be promising for subsurface modeling because no predetermined basis functions or stratification models are required, it does not provide information on the uncertainty of its estimated solution, i.e., a point estimate. In subsurface modeling, however, characterization of uncertainty is pivotal because soil data can be (spatially) sparse and noisy. A lasso-based method that can quantify its estimation accuracy while preserving its attractive sparsity feature is proposed. The performance of this sparse Bayesian lasso (SBLasso) is demonstrated through numerical tests and an actual case study of its accuracy of trend estimation and layer boundary detection. The degree of accuracy or inaccuracy of estimation provided by the SBLasso clearly corresponds to data quality, such as the number of available data points, noise level, and noise correlation. A method of soil stratification based on SBLasso was also proposed, and the stratification results by SBLasso were compared with those produced by existing methods for validation.