Bayesian Convolutional Neural Networks for Seismic Facies Classification

The seismic response of geological reservoirs is a function of the elastic properties of porous rocks, which depends on rock types, petrophysical features, and geological environments. Such rock characteristics are generally classified into geological facies. We propose to use the convolutional neural networks in a Bayesian framework to predict facies based on seismic data and quantify the uncertainty in the classification. A variational approach is adopted to approximate the posterior distribution of neural parameters that is mathematically intractable. The network is trained on labeled examples. The mean and the standard deviation of the distribution of neural parameters are randomly drawn from predefined Gaussian functions for the initialization, and are updated by minimizing the negative evidence lower bound. The facies classification is applied to seismic sections not included in the training data set. We draw multiple random samples from the trained variational posterior distribution to simulate an ensemble predictor and classify the most probable seismic facies. We implement the proposed network in the open-source library of TensorFlow Probability, for its convenience and flexibility. The applications show that the internal regions of the seismic sections are generally classified with higher confidence than their boundaries, as measured by the predictive entropy that is calculated based on a multiclass probability across the possible facies. A plain neural network is also applied for comparison, by assigning fixed values to the neural parameters using a classical backpropagation technique. The comparison shows consistent results; however, the proposed approach is able to assess the uncertainty in the predictions.