First Arrival Travel Time Tomography - Bayesian Approach

First arrival time tomography aims at determining the propagation velocity of seismic waves from experimental measurements of their first arrival time. This problem is usually ill-posed and is classically tackled by considering various iterative linearised approaches. However, these methods can yield wrong seismic velocity for highly nonlinear cases and they fail to estimate the uncertainties associated to the model. In our study, we rely on a Bayesian approach coupled with an interacting Markov chain-Monte Carlo (MCMC) algorithm to estimate the wave velocity and the associated uncertainties. The main difficulty associated to this approach is that traditional MCMC algorithms can be inefficient when multimodal probability distributions or complex velocity models involving a great number of parameters come into play. Therefore, a first step toward an efficient implementation of the Bayesian approach is to properly parametrize the model to reduce its dimension and to select adequate prior distribution for the parameters. In this paper, we present a ten layers probabilistic model for the velocity, that we illustrate on tomography results.