Iterative PDE-constrained optimization for seismic full-waveform inversion

TL;DR

This paper introduces a new PDE-constrained optimization method for seismic full-waveform inversion that uses a full-space approach with novel preconditioners, significantly reducing runtime compared to standard methods.

Contribution

It presents a PDE-constrained Newton FWI method with innovative preconditioning strategies, demonstrating improved efficiency and potential for further acceleration.

Findings

Significant runtime reduction over standard FWI

Feasibility of Newton-type optimization for seismic FWI

Potential for further computational acceleration

Abstract

This paper presents a novel numerical method for the Newton seismic full-waveform inversion (FWI). The method is based on the full-space approach, where the state, adjoint state, and control variables are optimized simultaneously. Each Newton step is formulated as a PDE-constrained optimization problem, which is cast in the form of the Karush-Kuhn-Tucker (KKT) system of linear algebraic equitations. The KKT system is solved inexactly with a preconditioned Krylov solver. We introduced two preconditioners: the one based on the block-triangular factorization and its variant with an inexact block solver. The method was benchmarked against the standard truncated Newton FWI scheme on a part of the Marmousi velocity model. The algorithm demonstrated a considerable runtime reduction compared to the standard FWI. Moreover, the presented approach has a great potential for further acceleration. The central result of this paper is that it establishes the feasibility of Newton-type optimization of the KKT system in application to the seismic FWI.