Geostatistical inversion of pre-stack seismic data for the joint estimation of facies and seismic velocities using stochastic sampling from Gaussian mixture posterior distributions

摘要

In this work, we propose a seismic inversion method for the joint estimation of facies and elastic velocities from pre-stack seismic data based on a geostatistical approach. The objective of the proposed inversion methodology is to obtain the posterior distribution of P-wave velocity, S-wave velocity and density and to simultaneously classify the lithology conditioned by seismic data. The inversion algorithm is a sequential Gaussian mixture inversion developed based on Bayesian linearized AVO inverse theory and sequential geostatistical simulations. To mathematically represent the multimodal behavior of elastic properties due to their variations within different facies, we adopt a Gaussian mixture distribution for the prior model of the elastic properties and use the prior probability of the facies as weights of the Gaussian components of the mixture. The solution of the inverse problem is achieved by deriving the explicit analytical expression for the posterior distribution of the elastic properties and facies. A sampling algorithm is then introduced to sequentially simulate several realizations of the estimated model. The inversion methodology has been validated using well logs and synthetic seismic data with different noise levels, and then applied to a 2D seismic section.