An improved stochastic inversion for joint estimation of seismic impedance and lithofacies

Abstract

Stochastic seismic inversion works as an important technology to estimate the elastic parameters of subsurface media to guide lithology prediction and fluid discrimination. The subsurface parameters and reservoir properties are usually estimated separately in conventional stochastic seismic inversion methods. In this study, an improved stochastic approach is proposed to invert seismic impedance and lithofacies simultaneously. The Gaussian mixture priori probability density function (PDF) is initially utilized to describe the distribution of the model parameters influenced by subsurface lithofacies. Furthermore, a novel expression of multi-dimensional posteriori PDF conditioned with time and frequency joint-domain seismic data is derived. Then, the differential evolution Markov Chain Monte Carlo (DE-MCMC) sampling algorithm is utilized to implement the optimizations of multi-dimensional posterior PDF in the stochastic inversion approach, which runs multiple Markov chains in parallel and estimates the multiple solutions of model parameters with the theory of population evolutionary. Lithofacies can be clearly discriminated according to the weights of different Gaussian components in the posterior PDF and the continuous model parameters are sampled from the selected Gaussian components to realize the simultaneous prediction of these two parameters. Finally, the feasibility and robustness of the proposed stochastic DE-MCMC inversion approach are illustrated by several synthetic examples and one feld dataset. The estimated P-wave impedance and lithofacies classifcation results of maximum conditional probability density (Cpd) for 10 simulations coincide with well-logging curves and interpreted lithofacies from wells.