Iterative PDE-Constrained Optimization for Seismic Full-Waveform Inversion

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI:10.1134/s0965542524700192

M. S. Malovichko, A. Orazbayev, N. I. Khokhlov, I. B. Petrov

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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.

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地震全波形反演的迭代 PDE 约束优化

摘要本文提出了一种新的牛顿地震全波形反演（FWI）数值方法。该方法以全空间方法为基础，同时对状态、邻接状态和控制变量进行优化。每个牛顿步骤都被表述为一个 PDE 受限优化问题，以线性代数方程的 Karush-Kuhn-Tucker (KKT) 系统的形式呈现。KKT 系统通过预处理 Krylov 求解器精确求解。我们引入了两种预处理方法：一种是基于分块三角形因式分解的预处理方法，另一种是基于非精确分块求解器的预处理方法。我们以标准的截断牛顿 FWI 方案为基准，对 Marmousi 速度模型的一部分进行了测试。与标准 FWI 相比，该算法大大缩短了运行时间。此外，所提出的方法还有进一步加速的巨大潜力。本文的核心成果是确定了 KKT 系统牛顿型优化在地震 FWI 应用中的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.