Fast and scalable earth texture synthesis using spatially assembled generative adversarial neural networks

The earth texture with complex morphological geometry and compositions such as shale and carbonate rocks, is typically characterized with sparse field samples because of an expensive and time-consuming characterization process. Accordingly, generating arbitrary large size of the geological texture with similar topological structures at a low computation cost has become one of the key tasks for realistic geomaterial reconstruction and subsequent hydro-mechanical evaluation for science and engineering applications. Recently, generative adversarial neural networks (GANs) have demonstrated a potential of synthesizing input textural images and creating equiprobable geomaterial images for stochastic analysis of hydrogeological properties, for example, the feasibility of CO₂ storage sites and exploration of unconventional resources. However, the texture synthesis with the GANs framework is often limited by the computational cost and scalability of the output texture size. In this study, we proposed a spatially assembled GANs (SAGANs) that can generate output images of an arbitrary large size regardless of the size of training images with computational efficiency. The performance of the SAGANs was evaluated with two and three dimensional (2D and 3D) rock image samples widely used in geostatistical reconstruction of the earth texture and Lattice-Boltzmann (LB) simulations were performed to compare pore-scale flow patterns and upscaled permeabilities of training and generated geomaterial images. We demonstrate SAGANs can generate the arbitrary large size of statistical realizations with connectivity and structural properties and flow characteristics similar to training images, and also can generate a variety of realizations even on a single training image. In addition, the computational time was significantly improved compared to standard GANs frameworks.