Application of Reversible Jump Markov Chain Monte Carlo Algorithms to Elastic and Petrophysical Amplitude-Versus-Angle Inversions

Abstract

We infer the elastic and petrophysical properties from pre-stack seismic data through a transdimensional Bayesian inversion. 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 (rjMCMC) algorithm is used to sample the variable-dimension model space. This inversion scheme provides a parsimonious solution, and reliably quantifies the uncertainties affecting the estimated model parameters. Parallel tempering, which employs a sequence of interacting Markov chains in which the likelihood function is successively relaxed, is used to improve the efficiency of the probabilistic sampling. In addition, the delayed rejection updating scheme is employed to speed up the convergence of the rjMCMC algorithm to the stationary regime. Both elastic and petrophysical inversions invert the amplitude versus angle responses and employ a convolutional forward modelling based on the exact Zoeppritz equations. First, synthetic tests are used to assess the reliability of the implemented rjMCMC algorithms, then their applicability is demonstrated by inverting field seismic data acquired onshore. In this case the inversion was aimed at inferring the elastic and petrophysical properties around a gas-saturated reservoir hosted in a shale-sand sequence. In this case, the final outcomes provided by the rjMCMC algorithms are also compared with the predictions of linear Bayesian elastic and petrophysical inversions. The synthetic and field data examples demonstrate that the implemented algorithms can successfully estimate model uncertainty, model dimensionality and subsurface parameters with an affordable computational cost.