Iterative PDE-Constrained Optimization for Seismic Full-Waveform Inversion

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 prob...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2024, Vol.64 (5), p.954-966
Main Authors: Malovichko, M. S., Orazbayev, A., Khokhlov, N. I., Petrov, I. B.
Format: Article
Language:English
Subjects:
Acceleration
Algebra
Algorithms
Computational Mathematics and Numerical Analysis
Feasibility
Iterative methods
Linear algebra
Mathematics
Mathematics and Statistics
Numerical methods
Optimal Control
Optimization
Partial differential equations
Seismic analysis
Seismic engineering
Solvers
Waveforms
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524700192