论文标题
迭代PDE受限的优化用于地震全波反转
Iterative PDE-constrained optimization for seismic full-waveform inversion
论文作者
论文摘要
本文介绍了牛顿地震全波倒置（FWI）的新型数值方法。该方法基于全空间方法，该方法同时优化了状态，伴随状态和控制变量。每个牛顿步骤均以PDE约束优化问题进行配合，该问题以线性代数均衡的Karush-Kuhn-Tucker（KKT）系统的形式施放。 KKT系统用预处理的Krylov求解器不精确地求解。我们介绍了两个预处理：一个基于块 - 三角分解及其具有不精确块求解器的变体。该方法是针对Marmousi速度模型的一部分的标准截断牛顿FWI方案进行了基准测试的。与标准FWI相比，该算法显示出大量的运行时减少。此外，提出的方法具有进一步加速的巨大潜力。本文的主要结果是，它确定了KKT系统在应用于地震FWI中的牛顿型优化的可行性。
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.
