Joint Bayesian inversion based on rock-physics prior modeling for the estimation of spatially correlated reservoir properties

The joint inversion of seismic data for elastic and petrophysical properties is an inverse problem with a nonunique solution. There are several factors that impact the accuracy of the results, such as the statistical rock-physics relations and observation errors. We have developed a general methodology to incorporate a linearized rock-physics model in a multivariate multimodal prior distribution for Bayesian seismic linearized inversion. The prior distribution is used to define a mixture model for elastic and petrophysical properties and introduce physics-based correlations between the properties. Using the rock-physics prior model and a convolutional seismic forward model in the Bayesian inversion framework, we obtain an analytical expression of the spatially independent conditional distributions to be used as a proposal distribution in a Gibbs sampling algorithm. We then combine the sampling algorithm with geostatistical simulation methods to compute the spatially correlated posterior distribution of the model parameters. We apply our method to a real angle-stack seismic data set to generate multiple geostatistical realizations of facies, P-velocity, S-velocity, density, porosity, and water saturation. The method is validated through a blind well test and a comparison with the standard Bayesian linearized inversion.