A two-step inversion approach for seismic-reservoir characterization and a comparison with a single-loop Markov-chain Monte Carlo algorithm

We describe a two-step Bayesian algorithm for seismic-reservoir characterization, which, thanks to some simplifying assumptions, is computationally very efficient. The applicability and reliability of this method are assessed by comparison with a more sophisticated and computer intensive Markov Chain Monte Carlo (MCMC) algorithm, which in a single-loop directly estimates petrophysical properties and litho-fluid facies from pre-stack data. The two-step method first combines a linear rock-physics model with the analytical solution of a linearized amplitude versus angle (AVA) inversion, to directly estimate petrophysical properties, and related uncertainties, from pre-stack data under the assumptions of a Gaussian prior model and weak contrasts at the reflecting interface. In particular, we use an empirical, linear rock-physics model, properly calibrated for the investigated area, to reparametrize the linear time-continuous P-wave reflectivity equation in terms of petrophysical contrasts instead of elastic constants. In the second step, a downward 1-D Markov chain prior model is used to infer the litho-fluid classes from the outcomes of the first step. The single-loop MCMC algorithm uses a convolutional forward modelling based on the exact Zoeppritz equations, and adopts a non-linear rock-physics model. Moreover, it assumes a more realistic Gaussian mixture distribution for the petrophysical properties. Both approaches are applied on an onshore 3-D seismic dataset for the characterization of a gas-bearing, clastic reservoir. Notwithstanding the differences in the forward-model parameterization, in the considered rock-physics model, and in the assumed a-priori probability density functions, the two methods yield maximum a-posteriori solutions that are consistent with well log data, although the Gaussian mixture assumption adopted by the single-loop method slightly improves the description of the multimodal behavior of the petrophysical parameters. However, in the considered reservoir, the main difference between the two approaches remains the very different computational times, being the single-loop method much more computationally intensive than the two-step approach