基于减阶模型的一维赫尔姆霍兹方程非线性波形反演

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2024-11-13 DOI:10.1007/s10440-024-00700-y

Andreas Tataris, Tristan van Leeuwen

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引用次数: 0

摘要

我们研究了一种基于减阶模型（ROM）的波形反演方法，该方法适用于具有阻抗边界条件和可变折射率的亥姆霍兹问题。本文的第一个目标是获得能够将连续问题的 Galerkin 投影重构到 Helmholtz 方程解所跨空间的关系。第二个目标是研究基于 ROM 的非线性优化方法，旨在从反射和透射数据中估算折射率。最后，我们在数值上比较了我们的方法和传统的最小二乘反演法，后者的基础是最小化模拟数据与测量数据之间的距离。

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Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation

We study a reduced order model (ROM) based waveform inversion method applied to a Helmholtz problem with impedance boundary conditions and variable refractive index. The first goal of this paper is to obtain relations that allow the reconstruction of the Galerkin projection of the continuous problem onto the space spanned by solutions of the Helmholtz equation. The second goal is to study the introduced nonlinear optimization method based on the ROM aimed to estimate the refractive index from reflection and transmission data. Finally we compare numerically our method to the conventional least squares inversion based on minimizing the distance between modelled to measured data.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.