Capturing Uncertainty And Preserving Geological Realism with Attentive Neural Processes for Subsurface Property Modeling

Abstract:

Generating geologically valid subsurface models is a critical step when interpreting the solid Earth. The modeling process usually involves inferring geological properties of the rock over a wide area, given a limited number of measurements and existence of inaccessible ground truth. The geological model should maintain the correct measurements distribution and heterogeneity, and preserve geological meaning.As there are many plausible predictions while modeling the geological properties, understanding the uncertainty is also crucial.

Over the last two decades, the field of geostatistics has been extensively used for subsurface modeling of the rock properties. This consists of the standard multistep geostatistical tools, such as 2-point geostatistics and more complex strategies such as multiple-point geostatistics or geologic process-based modeling. As the procedures become more geologically realistic, it becomes harder to condition proposed geological models to the data. The development of machine learning and the increase of computational power, has allowed geoscientists to exploit a variety of deep learning techniques for subsurface property modeling, e.g. GANs. While GAN does learn to capture the distribution of patterns, it does not provide a quantitative estimate of uncertainty like 2-point geostatistics.

In this study, we use Attentive Neural Processes (ANP) to model geological properties given sparse physical measurements. ANP combines the benefits of stochastic processes and neural networks to learn distributions over functions and make flexible predictions at test time conditioned on context input. Instead of requiring domain knowledge to obtain a prior, e.g., channel orientation, ANPs learn an implicit prior from the available data. Also, ANPs provide a quantitative measure to estimate the uncertainty in the predictions.

We train an ANP network on the open-source Stanford VI dataset, which is a synthetic dataset generated to test any proposed algorithm for subsurface reservoir modeling and characterization. Given sparse physical measurements, our trained ANP model predicts mean and variance for the rock properties at all locations, allowing us to generate multiple realizations of a geological model. The variance provides a quantitative measure of uncertainty in the predictions.