Sampling-Free Bayesian Inference for Local Refinement in Linear Inversion Problems with a Latent Target Property

We present a sampling-free probabilistic inversion of latent target property based on the principles of expectation propagation where we estimate the joint distribution of the target variable in a local region. The prior model matches the prior distribution in the local-focused region but integrates our model parameters outside the focus region using approximate distributions. The approximate distribution includes large spatial structure information while maintaining the dimension of the inversion small. In addition, we map and solve the inversion into a new feature space where we can exclude components where the data have little influence, thereby decreasing the dimensionality of the inversion, and therefore, the inversion runtime. We test the method on seismic amplitude-versus-offset (AVO) inversion examples for the prediction of facies classes, as well as on the estimation of vuggy porosity in computed tomography (CT) images of core from a carbonate reservoir. We demonstrate that our method achieves good-quality predictions while significantly reducing the computational demand, making it particularly interesting to run large-scale inversion studies.