A practical implementation of data-space Hessian in the time-domain extended-source full-waveform inversion

TL;DR

This paper presents a practical implementation of data-space Hessian in time-domain extended-source full-waveform inversion, combining approximations, iterative refinement, and regularization techniques to improve accuracy and efficiency.

Contribution

It introduces a workflow that reduces computational cost in data-space Hessian estimation for extended-source FWI using filter matching, conjugate-gradient refinement, and multiscale regularization.

Findings

Efficient estimation of data residuals reduces computational burden.

Multiscale frequency continuation improves inversion stability.

Regularization enhances large-contrast reconstruction accuracy.

Abstract

Full-waveform inversion (FWI) with extended sources first computes wavefields with data-driven source extensions, such that the simulated data in inaccurate velocity models match the observed counterpart well enough to prevent cycle skipping. Then, the source extensions are minimized to update the model parameters. This two-step workflow is iterated until both data and sources are matched. It was recently shown that the source extensions are the least-squares solutions of the recorded scattered data fitting problem. As a result, they are computed by propagating backward in time the deblurred FWI data residuals, where the deblurring operator is the inverse of the damped data-domain Hessian of the scattering-source estimation problem. Estimating the deblurred data residuals is the main computational bottleneck of time-domain extended-source FWI (ES-FWI). To mitigate this issue, we first estimate them when the inverse of the data-domain Hessians is approximated by matching filters in Fourier and short-time Fourier domains. Second, we refine them with conjugate-gradient iterations when necessary. Computing the matching filters and performing one conjugate-gradient iteration each require two simulations per source. Therefore, it is critical to design some workflows that minimize this computational burden. We implement time-domain ES-FWI with the augmented Lagrangian method. Moreover, we further extend its linear regime with a multiscale frequency continuation approach, which is combined with grid coarsening to mitigate the computational burden and regularize the inversion. Finally, we use total-variation regularization to deal with large-contrast reconstruction. We present synthetic cases where different inversion workflows carried out with data-domain Hessians of variable accuracy were assessed with the aim at converging toward accurate solutions while minimizing computational cost.