Runhai Feng, Dario Grana

Characterization of subsurface reservoirs often requires geological facies models to identify areas with favorable rock properties. With the development of computing powers, deep learning approaches, such as the generative adversarial networks (GANs), became widely used for simulating complex geological models. However, training of the GANs typically requires a large quantity of training data for updating neural parameters. This process is generally done using traditional geostatistical methods based on multiple-point statistics or process-based models to build the training data. In this study, we propose to train the GANs using one single training image, a conceptual model from which the statistics of the geological patterns can be extracted. The training image is first down-sampled to different scales, and the generator and the discriminator are trained alternately for each scale. The training process is implemented from the coarsest to the finest scale to learn the spatial statistics from the training image progressively. We apply the proposed GANs to simulate the 2D Lena river delta and 3D Descalvado aquifer analog model, in which complex geological patterns and structures from the training image are successfully learned and reproduced by GANs. The gradual deformation method is further applied to iteratively calibrate the random realizations by the generator to observed data, in an optimization workflow. The optimization scheme is implemented many times to obtain multiple independent models that all match the observed data.