Stochastic Facies Inversion with Prior Sampling by Conditional Generative Adversarial Networks Based on Training Image

Probabilistic methods for geophysical inverse problems allow the use of arbitrarily complex prior information in principle. Geostatistical techniques, such as multiple-point statistics (MPS), for describing spatial correlation models and higher-order statistics have been proposed to achieve this inversion task, in which stochastic algorithms such as Markov chain Monte Carlo (McMC) are incorporated. However, stochastic sampling and optimization often require a large number of iterations, and thus geostatistical sampling of the prior model can become computationally demanding. To overcome this challenge, a deep learning model, namely conditional generative adversarial networks (CGANs), is proposed, which allows one to perform a random walk to sample the complex prior distribution. CGANs simulate conditional realizations conditioned to the available hard conditioning data, that is, direct measurements, while preserving the geometrical structure of the model parameters of interest and replicating the sequential Gibbs sampling algorithm. Despite the need for a training step, for a large number of simulations, CGANs are more efficient than traditional geostatistical simulation algorithms such as single normal equation simulation (SNESIM). The proposed methodology is used as part of the extended Metropolis algorithm to predict the distributions of categorical facies in two examples, a dune environment in the Gobi Desert and a channel system in an idealized subsurface reservoir, from indirect observational data such as acoustic impedance. The inversion results are compared to the extended Metropolis algorithm using standard MPS sampling.