3D Probabilistic Site Characterization by Sparse Bayesian Learning

In this paper, the sparse Bayesian learning (SBL) approach previously proposed for the characterization of one-dimensional (1D) soil spatial variability is extended to a more realistic three-dimensional (3D) setting. Direct extension is not computationally feasible because of significant runtime associated with inverting very large matrices and errors associated with computing their determinants. Based on the separability assumption in the autocorrelation function, the current paper successfully extends the SBL to 3D that is computable in practice. The numerical errors associated with large matrices are also mitigated. The second contribution of the current paper is a new efficient method of simulating conditional random fields in 3D based on a dense-lattice assumption. The analysis results for two real case histories show that it is now computationally feasible to characterize the statistical uncertainties in the autocorrelation parameters and trend function as well as to simulate conditional random field samples for 3D problems using the proposed method. To our knowledge, this is the first time we achieve realism in probabilistic site characterization and practicality in runtime at the same time.