Learning by example: fast reliability-aware seismic imaging with normalizing flows

TL;DR

This paper introduces a data-driven normalizing flow approach for fast, reliability-aware seismic imaging that leverages neighboring survey data to efficiently generate high-fidelity images and quantify uncertainty.

Contribution

It presents a novel training of normalizing flows conditioned on neighboring seismic images to improve image quality and reliability assessment in large-scale inverse problems.

Findings

Normalizing flow enables fast posterior sampling for seismic images.

The method improves image quality using neighboring survey data.

Provides a quantitative reliability measure for seismic imaging results.

Abstract

Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of ill-posed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for accurate Bayesian inference and are often computationally infeasible for large-scale inverse problems, such as seismic imaging. Our main contribution is a data-driven variational inference approach where we train a normalizing flow (NF), a type of invertible neural net, capable of cheaply sampling the posterior distribution given previously unseen seismic data from neighboring surveys. To arrive at this result, we train the NF on pairs of low- and high-fidelity migrated images. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image's reliability. To our knowledge, this is the first attempt to train a conditional network on what we know from neighboring images to improve the current image and assess its reliability.