Preconditioned BFGS-based Uncertainty Quantification in elastic Full Waveform Inversion

TL;DR

This paper introduces a preconditioned BFGS method combined with randomized SVD to efficiently approximate the inverse Hessian for uncertainty quantification in large-scale elastic Full Waveform Inversion, demonstrated on the Marmousi benchmark.

Contribution

It presents a novel approach integrating preconditioned BFGS with randomized SVD for efficient inverse Hessian approximation in FWI, enabling uncertainty quantification.

Findings

Effective low-rank inverse Hessian approximation for large-scale FWI.

Preconditioned BFGS improves convergence and stability.

Successful application to elastic Marmousi benchmark.

Abstract

Full Waveform Inversion (FWI) plays a vital role in reconstructing geophysical structures. The Uncertainty Quantification regarding the inversion results is equally important but has been missing out in most of the current geophysical inversions. Mathematically, uncertainty quantification is involved with the inverse Hessian (or the posterior covariance matrix), which is prohibitive in computation and storage for practical geophysical FWI problems. L-BFGS populates as the most efficient Gauss-Newton method; however, in this study, we empower it with the new possibility of accessing the inverse Hessian for uncertainty quantification in FWI. To facilitate the inverse-Hessian retrieval, we put together BFGS (essentially, full-history L-BFGS) with randomized singular value decomposition towards a low-rank approximation of the Hessian inverse. That the rank number equals the number of iterations makes this solution efficient and memory-affordable even for large-scale inversions. Also, based on the adjoint method, we formulate different diagonal Hessian initials as preconditioners and compare their performances in elastic FWI. We highlight our methods with the elastic Marmousi benchmark, demonstrating the applicability of preconditioned BFGS in large-scale FWI and uncertainty quantification.