Generation of non-stationary stochastic fields using generative adversarial networks

In the context of geoscience and mineral exploration, accurate characterization of subsurface structures and their spatial variability is crucial for resource evaluation and geoenergy applications, such as hydrocarbon extraction and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:msub><mml:mrow><mml:mtext>CO</mml:mtext></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> storage in deep geological formations. When generating geological facies conditioned on observed data, samples corresponding to all possible spatial configurations are not generally available in the training set. This challenge becomes even greater when dealing with non-stationary fields that exhibit spatially varying statistical properties, which is common in mineral deposits and geological formations. Our study investigates the application of Generative Adversarial Networks (GANs) to generate non-stationary channelized patterns and examines the model’s ability to generalize to unseen spatial configurations not present in the training set. The developed method, based on spatial-conditioning, enables effective learning of the correlation between spatial conditioning data (e.g., non-stationary soft maps) and the generated realizations, without requiring additional loss terms or solving optimization problems for each new data. The models can be trained on both 2D and 3D samples, making them particularly valuable for modeling complex geological structures in mineral deposits. Our results on real and synthetic datasets demonstrate the ability to generate geologically-plausible realizations beyond the training samples with strong correlation to target map. These results underscore the potential of advanced AI techniques to enhance decision-making and operational efficiency in geoenergy projects.