Generating Subsurface Earth Models using Discrete Representation Learning and Deep Autoregressive Network

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.