New parameterizations for Bayesian seismic tomography

In this study, we rely on a Bayesian approach to estimate the seismic velocity from first arrival travel times. The advantage of the Bayesian approach compared to linearized ones is its ability to properly quantify the uncertainties associated with the solution. However, this approach remains fairly expensive, and the Markov chain-Monte Carlo algorithms that are used to sample the posterior distribution are efficient only when the number of parameters remains within reason. Therefore, a first step toward an efficient implementation of the Bayesian approach is to properly parameterize the model to reduce its dimensionality. In this article, we introduce new parsimonious parameterizations which enable us to accurately reproduce the wave velocity field and the associated uncertainties. The first parametric model that we propose uses a random Johnson–Mehl tessellation, a generalization of the Voronoi tessellation. The main difference of the Johnson–Mehl model when compared to the Voronoi model is that the shapes of the generated cells are much more general. The cells of a Voronoi tessellation are indeed convex polytopes, while the Johnson–Mehl tessellation model yields cells whose boundaries are portions of hyperboles and which are not necessarily convex, hence allowing for a greater variety of shapes. We demonstrate the gain in efficiency and the better convergence when compared to the Voronoi model. The second parameterization uses Gaussian kernels as basis functions. Its purpose is to provide a way to reproduce localized variations in the seismic velocity field. We first illustrate the tomography results with a synthetic velocity model which contains two small anomalies. We then apply our methodology to a more advanced and realistic synthetic model that serves as a benchmark in the oil industry. We finally present an example where Gaussian kernels outperform Voronoi and Johnson–Mehl models. The tomography results reveal the ability of our algorithm to map the velocity heterogeneities accurately using few parameters.