Extracting crucial microstructures to characterize the elastic wave velocity and resistivity of Berea sandstone using convolutional neural networks

Abstract

To reveal the internal structure of the earth, rock physical models are insightful for interpreting geophysical observation data and are often used for estimating subsurface structures. However, as the estimated value of each model significantly depends on the assumed microstructure, the obtained subsurface structure may be biased. Despite the innovations of high-resolution imaging technologies and their application to digital rock physics (DRP) and machine learning (ML), the characteristic microstructure controlling rock physical properties remains unclear. We apply ML and extraction of regression activation mapping (RAM) and learned filters to visualize the characteristic microstructure underlying the elastic and electrical properties of rock (P-wave velocity [Formula: see text], S-wave velocity [Formula: see text], [Formula: see text]/[Formula: see text] ratio, and electrical resistivity). This regression task is implemented using convolutional neural networks (CNNs) that are trained on these properties and calculated with the DRP approach using Berea sandstone images as samples. Although the calculated geophysical properties show perturbations even among digital rocks that have the same porosity, the results predicted using the best-performing CNN model exhibit a relative error of 2%–7% with respect to elastic properties. The visualized RAM revealed that the machine focuses on larger grains for predicting P-wave and S-wave velocities, whereas their ratio ([Formula: see text]/[Formula: see text]) takes into account the pore space. In contrast, electrical properties consider grain edges and surrounding pores, which may be related to the tortuosity of the pore space. Moreover, filter visualizations demonstrated that the geometric characteristics of Berea sandstone could be representative of circular or elliptical shapes for determining elastic properties, whereas tube-like shapes were extracted for electrical resistivity. These findings shed new light on the crucial internal structures used for defining each rock property.