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

International audienceWith the increasing development of remote sensing platforms and the evolution of sampling facilities in mining and oil industry, spatial datasets are becoming increasingly large, inform a growing number of variables and cover wider and wider areas. Therefore, it is often necessary to split the domain of study to account for radically different behaviors of the natural phenomenon over the domain and to simplify the subsequent modeling step. The definition of these areas can be seen as a problem of unsupervised classification, or clustering, where we try to divide the domain into homogeneous domains with respect to the values taken by the variables in hand. The application of classical clustering methods, designed for independent observations, does not ensure the spatial coherence of the resulting classes. Image segmentation methods, based on e.g. Markov random fields, are not adapted to irregularly sampled data. Other existing approaches, based on mixtures of Gaussian random functions estimated via the expectation-maximization algorithm, are limited to reasonable sample sizes and a small number of variables. In this work, we propose two algorithms based on adaptations of classical algorithms to multivariate geostatistical data. Both algorithms are model free and can handle large volumes of multivariate, irregularly spaced data. The first one proceeds by agglomerative hierarchical clustering. The spatial coherence is ensured by a proximity condition imposed for two clusters to merge. This proximity condition relies on a graph organizing the data in the coordinates space. The hierarchical algorithm can then be seen as a graph-partitioning algorithm. Following this interpretation, a spatial version of the spectral clustering algorithm is also proposed. The performances of both algorithms are assessed on toy examples and a mining dataset