  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. Recently, generative
adversarial neural networks (GANs) have demonstrated a potential of
synthesizing input textural images and creating equiprobable geomaterial
images. 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. We demonstrate SAGANs can
generate the arbitrary large size of statistical realizations with connectivity
and structural properties 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.
