Enabling Uncertainty Quantification in Seismic Images Employing Generative Variational Autoencoders
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Currently, seismic imaging methods that incorporate quantified uncertainty using a Bayesian approach face limitations due to the high computational costs associated with simulating the full seismic wave equation while sampling the posterior probability distribution. To address this issue, data-driven surrogate models offer computational advantages by creating a mathematical function that maps inputs to outputs, thus bypassing the need for costly differential equation calculations [2]. While significant computational effort is required to initially train the machine learning model to replicate the posterior distribution sampling, the real benefit of these methods lies in the fact that, once trained, subsequent estimations become computationally trivial [2]. In this context, we propose a deep generative surrogate model based on variational autoencoder (VAE) networks to sample migrated seismic images from targeted areas of interest, aiding in uncertainty quantification. The VAE is composed of 2-D convolutional, dropout, and dense layers, with weights optimized by minimizing a loss function that includes both reconstruction error and Kullback-Leibler divergence. We train the VAE model using a dataset of 5,000 seismic images generated from a workflow designed for seismic imaging with quantified uncertainty [1]. Our results demonstrate that the proposed VAE network accurately reproduces the statistics of the training seismic images and reflects the system’s variability. This conclusion is supported by comparing the statistical moments, such as the mean and variance, of both the training and generated samples alongside uncertainty measurements like the confidence index.
