Abstract—In this paper, we propose a Bayesian methodology for receiver function analysis, a key tool in determining the deep structure of the Earth’s crust. We exploit the assumption of sparsity for receiver functions to develop a Bayesian deconvolution method as an alternative to the widely used iterative deconvolution. We model samples of a sparse signal as i.i.d. Student-t random variables. Gibbs sampling and variational Bayes techniques are investigated for our specific posterior inference problem. We used those techniques within the expectation-maximization (EM) algorithm to estimate our unknown model parameters. The superiority of the Bayesian deconvolution is demonstrated by the experiments on both simulated and real earthquake data. Index Terms—Bayesian inference, deconvolution, expectationmaximization