Uncertainty aware pre-stack seismic inversion using probabilistic neural networks

Seismic inversion, the process of inferring subsurface properties from seismic signals, is a crucial tool to monitor underground structures in applications such as geotechnical engineering, environmental studies, civil engineering, and archaeology. The predictions derived from seismic inversion play a key role in guiding high-cost decisions, including underground construction, well drilling, and field development. Recent advances in deep neural networks (DNNs) have demonstrated improved accuracy in predicting fine-grained subsurface structures compared to traditional statistical methods. However, most machine learning approaches overlook the uncertainty of predictions due to the ill-posed and noisy inverse problem. By adopting a probabilistic perspective, we maintain the high prediction quality of modern neural networks but advance them with calibrated uncertainty estimates. Tests on two synthetic offshore volumes show that ensembling and probabilistic layers approaches capture the epistemic and aleatoric uncertainties, respectively, and thus provide well-calibrated uncertainty estimates. Compared to the standard linear Bayesian baseline, our method reduces the Mean Squared Error by 39% and the Expected Calibration Error by 44%. Furthermore, we show that the proposed approach remains robust under perturbations of the forward model and training on limited data.