A reliable Bayesian neural network for the prediction of reservoir thickness with quantified uncertainty

In seismic exploration, reservoir prediction plays a significant role since it can reveal the characteristics of a reservoir through attribute analysis. Multi-attribute reservoir prediction models are the most commonly used methods that aim to establish a reasonable relationship between reservoir parameters and seismic attributes. Although many related approaches have been proposed, their results are unsatisfactory when given limited logging data. Meanwhile, they frequently fail to evaluate how reliable their predictions are. Given the prominent advantages of Bayesian methods to model uncertainty, we propose in this paper a Bayesian neural network (BNN) model to predict reservoir thickness and quantify uncertainty. In particular, we first combine attribute data with spatial information as auxiliary variables to forecast reservoir thickness using a neural network. Meantime, we capture both epistemic and aleatoric uncertainty of the BNN using a Bayesian approximation approach known as Monte Carlo dropout (MC-dropout). Finally, the BNN model is applied to one sparse logging dataset to predict the reservoir thickness as well as the uncertainty in our interested field area. Experimental results demonstrate that our proposed BNN is more appropriate for coping with geostatistical problems in comparison with other methods.