1D Elastic Full-Waveform Inversion Through a Reversible Jump MCMC Algorithm

We implement a transdimensional Bayesian approach to solve the 1D elastic full-waveform inversion (FWI) in which the reflectivity algorithm constitutes the forward modelling. In this approach the number of model parameters (i.e. the number of layers) is treated as an unknown, and a reversible jump Markov Chain Monte Carlo algorithm is used to sample the variable-dimension model space. We also treat the noise standard deviation as an unknown parameter to be solved for, thus letting the algorithm infer the appropriate level of data-fitting. A Parallel tempering strategy and a delayed rejection updating scheme are used to improve the efficiency of the probabilistic sampling. We focus the attention to synthetic data inversions, with the aim to draw general conclusions about the suitability of our approach for pre-stack inversion of reflection seismic data. Our tests prove that the implemented inversion algorithm provides a parsimonious solution and successfully estimates model uncertainty, noise level, model dimensionality and elastic parameters. Our experiments also demonstrate that there is a trade-off between property uncertainty and location uncertainty: A strong elastic contrast determines high uncertainty in the model property values, but low uncertainty in the location of the elastic discontinuity