A Conditional Generative Variational Autoencoder for Uncertainty Quantification of Seismic Images

  • Barbosa, Carlos (Federal University of Rio de Janeiro)
  • Silva, Charlan (Federal University of Rio de Janeiro)
  • Silva, Bruno (Federal University of Rio de Janeiro)
  • Rochinha, Fernando (Federal University of Rio de Janeiro)
  • Coutinho, Alvaro (Federal University of Rio de Janeiro)

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Bayesian seismic imaging provides a natural framework for uncertainty quantification. Nevertheless, its practical implementation is limited by the high computational cost of posterior sampling via full wave equation simulations. Data-driven surrogate modeling offers an effective alternative, in which a machine-learning model learns a functional mapping between inputs and outputs, replacing repeated PDE-based forward simulations [3]. Although the training phase incurs significant computational demands, the resulting surrogate enables fast, low-cost inference and repeated uncertainty-aware estimates [3]. In this context, we propose a deep generative surrogate model based on a conditional variational autoencoder (cVAE) network to sample migrated seismic images from target areas of interest, supporting uncertainty quantification. The cVAE is a two-level generative process with a continuous latent variable sampled conditionally on a discrete (categorical) latent component [2]. Learning the categorical latent variable encodes the multimodality of the original seismic amplitudes across seismic image realizations in an unsupervised manner. We train the cVAE model using a dataset of seismic images generated by a workflow designed for seismic imaging with quantified uncertainty [1]. Our results demonstrate that the proposed cVAE accurately reproduces the multimodality observed in the training seismic image amplitudes, reflecting the system’s variability. This conclusion is supported by comparisons of amplitude histograms from the training and generated samples, together with uncertainty measurements such as the variability index.