Sequential Bayesian-Gaussian mixture linear inversion combined with sequential indicator simulation

He, Dongyang (China University of Petroleum-East China) | Yin, Xingyao (China University of Petroleum-East China) | Zong, Zhaoyun (China University of Petroleum-East China) | Li, Kun (China University of Petroleum-East China)

OnePetro 

Summary Gaussian mixture model can be used to describe the multimodal behaviour of reservoir properties due to their variations within different discrete variables, such as facies. The weights of the Gaussian components represents the probabilities of the discrete variables. However, Bayesian linear inversion based on Gaussian mixture may misclassify discrete variables at some points, which may lead to a bad inversion result. In this study, we consider the spatial variability of discrete variables and combine Gaussian mixture model with the Sequential indicator simulation to determine the weight of each discrete variable in Sequential Bayesian linear inversion problems. We then can obtain the analytical solution of the Bayesian linear inverse problem and simultaneously classify the discrete variables.