Uncertainty Quantification in Intelligent-Based Electrical Resistivity Tomography Image Reconstruction With Monte Carlo Dropout Strategy

Abstract

The Electrical Resistivity Tomography (ERT) method plays an essential role in researching electrical properties at the core scale, and the resistivity image inversion reconstruction technique is the key to constraining measurement accuracy. In recent years, with the improvement of computer operation capabilities and the acquisition of a large amount of geophysical data, the inversion algorithms represented by machine learning (ML) have made it possible to reconstruct ERT images automatically. However, the solution of ERT image inversion has large uncertainty due to high nonlinearity. Meanwhile, traditional ML methods are not initially developed for evaluating the uncertainty of such reconstruction results. In this paper, we propose a novel MC-Net ML scheme to quantitatively estimate the uncertainty of the ERT image reconstruction by introducing the Monte-Carlo Dropout strategy with a multiple stochastic method to approximate Bayesian inference. As one important evaluation index, the correlation coefficient (CC) between target image and reconstructed image is used to compare the effects of six types of simulated data carried by different ML schemes. The inversion results show that MC-Net increases lower limit of CC on the premise of ensuring average CC. Moreover, the accuracy of regression and classification results defined in this paper also obtained the highest value by MC-Net. With the proposed scheme, we can further provide a quantification of the uncertainty to determine whether reconstructed images are reliable after reconstructing the ERT images, which is of great significance for actual intelligent inversion tasks.