Deep Bayesian Inference for Task-based Seismic Imaging

High dimensionality, complex physics, and lack of access to the ground truth make seismic imaging one of the most challenging inversion problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks conducted on these images. By making use of a Markov-chain Monte Carlo (McMC) sampling technique, we demonstrate how uncertainty in the data can be propagated to the task of seismic horizon tracking. While this example shows that uncertainty can in principle be handled in a systematic manner by using neural nets as deep priors, it unfortunately also reveals that the McMC method fundamentally lacks ability to scale to relevant problem sizes. To overcome this shortcoming, we introduce a variational formulation based on normalizing flows. In this approach, invertible neural networks are trained to generate samples from the posterior. There are strong indications that this approach has the capability to scale better to problems where the forward operator is expensive to evaluate.

https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2021/herrm...