Closed-Loop Bayesian Generative Adversarial Network for Probabilistic Acoustic Impedance Inversion

The inherent non-uniqueness problem challenges acoustic impedance inversion, and thus it is meaningful to explore the possible solutions via advanced strategies, e.g., incorporating uncertainty estimation. At present, several generative adversarial network (GAN)-based inversion methods have been shown to offer advantages in terms of inversion accuracy. However, most of them have primarily focused on deterministic predictions, limiting their ability to explore the range of the solution space. Furthermore, the scarcity of labeled data pairs in field data tasks can reduce inversion accuracy. To address these shortcomings, we introduce a Bayesian GAN (BGAN) based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Bayes by Backprop</i> , and integrate it into a closed-loop framework. Synthetic data experiments demonstrate that the closed-loop BGAN performs better than cycle-consistent GAN (cycle-GAN) with insufficiently labeled data pairs. Moreover, unlike the cycle-GAN, the closed-loop BGAN possesses the capability of assessing prediction uncertainties. Compared with the Bayesian linearized inversion (BLI) and Monte Calor (MC) dropout methods, the closed-loop BGAN is more accurate and robust in the inversion of noisy seismic data with lower uncertainty. Therefore, the closed-loop BGAN can achieve high accuracy inversion while estimating potential solutions more reasonably. The field data example also demonstrates that compared with BLI and MC dropout, the closed-loop BGAN can obtain more reasonable inversion results with more reliable uncertainty estimation.