Subsurface modeling is important for subsurface resource development, energy storage, and CO2 sequestration. Many geostatistical and machine learning methods are developed to quantify the subsurface uncertainty by generating subsurface model realizations. Good subsurface models should reproduce depositional patterns in training images (satellite images, outcrops, digital rock, or conceptual models) that are important to fluid flow. However, current methods are computationally demanding, which makes it prohibitively expensive for building large-scale, detailed subsurface model realizations.

In this work, we develop the sequential patch generative adversarial neural network (GAN), a computationally efficient method to perform machine learning- and patch-based, sequential subsurface modeling. The new machine learning method uses shift-invariant neural network structures to allow efficient sequential modeling. In addition, it maps subsurface models to a Gaussian latent space, which allows easier data conditioning and better model parameterization. Three optimization methods for well data conditioning are compared based on pattern reproduction in subsurface model realizations.

Compared to conventional multiple-point statistics (MPS) methods, the new method is faster, requires fewer computational resources, and does not present artifacts in realizations. Compared to previous generative models, the new method is more interpretable and efficient in large geological modeling. For data conditioning, we find the posterior latent variables need to have the same statistical distribution as the prior to reproduce patterns. The sequential patch GAN method is proven to be an efficient machine learning method for large-scale, detailed, subsurface modeling.

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