Quantifying microstructures of Earth materials using higher-order spatial correlations and deep generative adversarial networks

Abstract

Key to most subsurface processes is to determine how structural and topological features at small length scales, i.e., the microstructure, control the effective and macroscopic properties of earth materials. Recent progress in imaging technology has enabled us to visualise and characterise microstructures at different length scales and dimensions. However, one limitation of these technologies is the trade-off between resolution and sample size (or representativeness). A promising approach to this problem is image reconstruction which aims to generate statistically equivalent microstructure but at a larger scale and/or additional dimension. In this work, a generative adversarial network (GAN), trained with Wasserstein-loss and gradient penalty, is used to reconstruct two-dimensional images of two hydrothermally rock samples with varying degrees of complexity. Moreover, we employ multi-point spatial correlation functions - known as statistical microstructural descriptors (SMDs) to evaluate the reconstruction performance of our GAN and show that it can reconstruct higher-order, spatially-correlated patterns of complex earth materials, capturing underlying structural and morphological properties. Comparing our results with a stochastic reconstruction method based on a two-point correlation function, we show the importance of coupling training/assessment of GANs with higher-order SMDs, especially in the case of complex microstructures.