A method is described for seismic depth uncertainty analysis including receiving wavelet basis functions and cutoff thresholds and randomly perturbing wavelet coefficients in reduced wavelet space based on the wavelet basis functions and the cutoff thresholds to generate a plurality of random wavelet fields; receiving a reference model in a depth domain; transforming the plurality of random wavelet fields to the depth domain and combining them with the reference model to form candidate models; performing a hierarchical Bayesian modeling with Markov Chain Monte Carlo (MCMC) sampling methods using the candidate models as input to generate a plurality of realizations; and computing statistics of the plurality of realizations to estimate depth uncertainty. The method may be executed by a computer system.