Transdimensional Seismic-Petrophysical AVA Inversion

We implement a transdimensional Bayesian inversion that infers petrophysical reservoir properties, layer boundary locations, and the associated uncertainties from pre-stack seismic data. Our algorithm employs a convolutional forward modelling based on the exact Zoeppritz equations and treats the number of model parameters (i.e. the number of layers) as an unknown to be inferred from the data. A reversible jump Markov Chain Monte Carlo (rjMCMC) algorithm is used to sample the variable-dimension model space, whereas a parallel tempering approach, a delayed rejection updating scheme, and a parameter perturbation defined in a principal-component rotated parameter space are used to improve the efficiency of the probabilistic sampling and to speed up the convergence of the rjMCMC algorithm toward the stationary regime. The adopted inversion scheme provides a parsimonious solution, and reliably quantifies the uncertainties affecting the estimated model parameters. First, synthetic tests are used to assess the reliability of the implemented rjMCMC algorithm, then its applicability is demonstrated by the inversion of field data acquired onshore and investigating a gas-saturated reservoir hosted in a shale-sand sequence. Our inversion tests prove that the implemented algorithm can successfully estimate model uncertainty, model dimensionality, and petrophysical properties with an affordable computational cost.