Invertible neural networks for uncertainty quantification in refraction tomography

Uncertainty quantification (UQ) should be an essential ingredient of geophysical inversion because it measures the confidence in the results and enables the assessment of the value of information in the data. However, UQ using established methods ranges from very expensive to prohibitively costly, and estimating noise levels and integrating prior information is challenging, so it is not yet widely undertaken. In this paper, we explore the capabilities of a machine learning-based UQ tool known as the invertible neural network (INN) and focus on its application to a 2D tomography problem within a complex foothills environment. We propose a novel approach to handle realistic problem dimensions that uses variational autoencoders to compress the velocity model and data. The INN relates the respective latent spaces, significantly reducing memory requirements. Our findings reveal that this INN-based workflow can perform tomographic inversion while integrating an implicit prior in the form of a set of velocity models with pertinent features. Furthermore, we can address both epistemic and aleatoric uncertainties by adopting a deep ensemble strategy. This integrated approach yields plausible estimates of relative confidence in the inverted velocities, showcasing the potential of INN as a tool for UQ in geophysical inversion.