Deep learning for probabilistic salt segmentation using Bayesian inference machines

Salt interpretation is an essential step of velocity model building for seismic imaging workflows in many salt basins around the world. However, conventional techniques are labor intensive and prone to human error due to the inherent complexities of salt geometries, seismic data and the model building process. While deep learning (DL) frameworks using convolutional neural networks provide fully automated solutions for salt interpretation, fully deterministic output models do not provide statistically meaningful probability and uncertainty estimations. Bayesian neural networks address these limitations by providing accurate salt probability values and quantitative uncertainties that arise in data and model parameters; however, Bayesian networks are difficult to train and require more computational resources compared to traditional networks. Here, we propose a hybrid fully convolutional architecture that combines deterministic and probabilistic layers, which provides an efficient DL methodology for obtaining true salt probabilities and model uncertainties. We demonstrate the prediction and generalization capabilities of this network architecture through training and testing on two different seismic data sets.