Transdimensional MCMC inversion of Rayleigh wave dispersion curves: Preliminary results on synthetic data.

We implement a transdimensional Bayesian algorithm to invert Rayleigh wave dispersion curves considering as unknowns the number of model parameters, that is the locations of the layer boundaries together with the shear wave velocity and the Vp/Vs ratio of each layer. A reversible jump Markov Chain Monte Carlo (MCMC) algorithm is used to sample the variable-dimension model space, while the adoption of a parallel tempering strategy and of a delayed rejection updating scheme improve the efficiency of the probabilistic sampling. This work has a mainly theoretical perspective and is aimed at drawing general conclusions about the suitability of our approach for dispersion curve inversion. For this reason, we focus on synthetic data inversions, and we limit to consider the fundamental mode, which is analytically computed from schematic 1D reference models. Our tests prove that the implemented inversion algorithm provides a parsimonious solution and successfully estimates model uncertainty and model dimensionality. In particular, as expected, the posterior uncertainties increase passing from Vs, to layer thicknesses and to Vp/Vs ratio, and changes according to the expected resolution on model parameters.