Intelligent random noise modeling by the improved variational autoencoding method and its application to data augmentation

Deep-learning methods facilitate the development of seismic data processing methods; however, they also offer some challenges. The primary challenges are the lack of labeled samples for training, due to heterogeneity in seismic data, expensive acquisition apparatus, and data confidentiality. These problems limit the acquisition of high-quality training data. To solve this problem, we have developed variational autoencoding (VAE) to generate synthetic noise for data augmentation; however, the simplified Kullback-Leibler (KL) distance definition and parameter learning result in the outputs of the original VAE being blurry. To optimize VAE for simulating random desert noise and improve its simulation capability, here we have developed an improved VAE based on KL redefinition and learning parameter replacement. Specifically, we (1) build a training set containing desert random noise samples, (2) redefine the KL distance calculated between two Gaussian mixture densities (rather than two simple Gaussians) because the KL distance plays an important role in the learning accuracy of VAE, and (3) use [Formula: see text] rather than [Formula: see text] to improve the learning efficiency. Statistical analysis indicates that the simulated random noise is statistically indistinguishable from real noise, indicating that our improved VAE is suitable for noise modeling. We also trained a denoising convolutional neural network (DnCNN) using the simulated noise. Data augmentation conducted using the simulated noise improved the effect of DnCNN, proving that our method contributes to data augmentation.