  Deep neural networks offer numerous potential applications across geoscience,
for example, one could argue that they are the state-of-the-art method for
predicting faults in seismic datasets. In quantitative reservoir
characterization workflows, it is common to incorporate the uncertainty of
predictions thus such subsurface models should provide calibrated probabilities
and the associated uncertainties in their predictions. It has been shown that
popular Deep Learning-based models are often miscalibrated, and due to their
deterministic nature, provide no means to interpret the uncertainty of their
predictions. We compare three different approaches to obtaining probabilistic
models based on convolutional neural networks in a Bayesian formalism, namely
Deep Ensembles, Concrete Dropout, and Stochastic Weight Averaging-Gaussian
(SWAG). These methods are consistently applied to fault detection case studies
where Deep Ensembles use independently trained models to provide fault
probabilities, Concrete Dropout represents an extension to the popular Dropout
technique to approximate Bayesian neural networks, and finally, we apply SWAG,
a recent method that is based on the Bayesian inference equivalence of
mini-batch Stochastic Gradient Descent. We provide quantitative results in
terms of model calibration and uncertainty representation, as well as
qualitative results on synthetic and real seismic datasets. Our results show
that the approximate Bayesian methods, Concrete Dropout and SWAG, both provide
well-calibrated predictions and uncertainty attributes at a lower computational
cost when compared to the baseline Deep Ensemble approach. The resulting
uncertainties also offer a possibility to further improve the model performance
as well as enhancing the interpretability of the models.
