  Subsurface earth models (referred to as geo-models) are crucial for
characterizing complex subsurface systems. Multiple-point statistics are
commonly used to generate geo-models. In this paper, a deep-learning-based
generative method is developed as an alternative to the traditional Geomodel
generation procedure. The generative method comprises two deep-learning models,
namely the hierarchical vector-quantized variational autoencoder (VQ-VAE-2) and
PixelSNAIL autoregressive model. Based on the principle of neural discrete
representation learning, the VQ-VAE-2 learns to massively compress the
Geomodels to extract the low-dimensional, discrete latent representation
corresponding to each Geomodel. Following that, PixelSNAIL uses the deep
autoregressive network to learn the prior distribution of the latent codes. For
the purpose of Geomodel generation, PixelSNAIL samples from the newly learned
prior distribution of latent codes, and then the decoder of the VQ-VAE-2
converts the newly sampled latent code to a newly constructed geo-model.
PixelSNAIL can be used for unconditional or conditional geo-model generation.
In an unconditional generation, the generative workflow generates an ensemble
of geo-models without any constraint. On the other hand, in the conditional
geo-model generation, the generative workflow generates an ensemble of
geo-models similar to a user-defined source image, which ultimately facilitates
the control and manipulation of the generated geo-models. To better construct
the fluvial channels in the geo-models, the perceptual loss is implemented in
the VQ-VAE-2 model instead of the traditional mean squared error loss. At a
specific compression ratio, the quality of multi-attribute geo-model generation
is better than that of single-attribute geo-model generation.
