DE-MCMC Based Stochastic Seismic Inversion Incorporating Gaussian Mixture Model

Summary Stochastic seismic inversion works as an important technology to estimate elastic parameters of subsurface media to guide the lithology prediction and fluid discrimination. In this study, an improved stochastic simulation is proposed to invert seismic impedance and lithofacies simultaneously. The Gaussian mixture priori probability density (PDF) is initially utilized to describe the distribution of 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. And, the differential evolution Markov Chain Monte Carlo (DE-MCMC) algorithm is utilized to implement the optimizations of multi-dimensional posterior PDF in our approach, which runs multiple Markov chains in parallel and estimates the multiple solutions of model parameters with the theory of population evolutionary. The lithofacies is clearly discriminated according to the weights of different Gaussian components in the posterior PDF and the model parameters are sampled from the selected Gaussian components to realize the simultaneous prediction of these two parameters. Finally, the feasibility and robustness of DE-MCMC model are illustrated by several synthetic examples and field datasets. The estimated P-wave impedance and lithofacies classification results of maximum conditional probability density (Cpd) coincide with the well logging curves and interpreted lithofacies.