  This paper presents a methodology and workflow that overcome the limitations
of the conventional Generative Adversarial Networks (GANs) for geological
facies modeling. It attempts to improve the training stability and guarantee
the diversity of the generated geology through interpretable latent vectors.
The resulting samples are ensured to have the equal probability (or an unbiased
distribution) as from the training dataset. This is critical when applying GANs
to generate unbiased and representative geological models that can be further
used to facilitate objective uncertainty evaluation and optimal decision-making
in oil field exploration and development.
  We proposed and implemented a new variant of GANs called Info-WGAN for the
geological facies modeling that combines Information Maximizing Generative
Adversarial Network (InfoGAN) with Wasserstein distance and Gradient Penalty
(GP) for learning interpretable latent codes as well as generating stable and
unbiased distribution from the training data. Different from the original GAN
design, InfoGAN can use the training images with full, partial, or no labels to
perform disentanglement of the complex sedimentary types exhibited in the
training dataset to achieve the variety and diversity of the generated samples.
This is accomplished by adding additional categorical variables that provide
disentangled semantic representations besides the mere randomized latent vector
used in the original GANs. By such means, a regularization term is used to
maximize the mutual information between such latent categorical codes and the
generated geological facies in the loss function.
  Furthermore, the resulting unbiased sampling by Info-WGAN makes the data
conditioning much easier than the conventional GANs in geological modeling
because of the variety and diversity as well as the equal probability of the
unconditional sampling by the generator.
