A machine learning method called sparse modelling has received attention in many different fields. One of the method for achieving sparse modelling includes least absolute shrinkage and selection operator (lasso), which has been used for property estimation and layer boundary detection in subsurface modelling. The estimates by lasso, however, are point estimates and do not provide information on the "uncertainties." This study newly developed a Bayesian method for one-dimensional subsurface modelling using a spike-and-slab prior. The proposed method was demonstrated through numerical examples on 1D subsurface modelling. The proposed method consistently solved two problems, property estimation and layer boundary detection, with high accuracy and can evaluate the posterior PDF of estimates based on Bayes' rule.

Keywords:Subsurface Modelling, Bayes' Rule, Spike-and-Slab Prior, Property Estimation, Layer Boundary Detection.