Generative adversarial network as a stochastic subsurface model reconstruction

In geosciences, generative adversarial networks have been successfully applied to generate multiple realizations of rock properties from geological priors described by training images, within probabilistic seismic inversion and history matching methods. Here, the use of generative adversarial networks is proposed not as a model generator but as a model reconstruction technique for subsurface models where we do have access to sparse measurements of the subsurface properties of interest. We use sets of geostatistical realizations as training datasets combined with observed experimental data. These networks are applied to reconstruct nonstationary sedimentary channels and continuous elastic properties, such as P-wave propagation velocity, in the presence and absence of conditioning data. The reconstruction examples shown herein can be considered a post-processing step applied after seismic inversion and performed at those locations where the convergence of the inversion is low, and therefore, the inverted models are associated with high uncertainty. The application examples show the suitability of generative adversarial networks in learning the spatial structure of the data from sets of geostatistical realizations. The generated models reproduce the first- and second-order statistical moments and the spatial covariance matrix of the training dataset.