Fourier method for inverse source problem using correlation of passive measurements

被引：0

作者：

Triki, Faouzi ^{[1
]}

Linder-Steinlein, Kristoffer ^{[2
]}

Karamehmedovic, Mirza ^{[2
]}

机构：

[1] Univ Grenoble Alpes, Lab Jean Kuntzmann, Grenoble, France

[2] Tech Univ Denmark, Dept Appl Math, Lyngby, Denmark

来源：

INVERSE PROBLEMS | 2024年 / 40卷 / 10期

关键词：

passive imaging; wave equation; stability; inverse source problem; PHASE RETRIEVAL; CONTROLLABILITY;

D O I：

10.1088/1361-6420/ad6fc7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the inverse source problem for the time-dependent, constant-coefficient wave equation with Cauchy data and passive cross-correlation data.We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we show that the cross-correlation solves a wave equation, and we reconstruct the cross-correlation from boundary data to recover the source in the original Cauchy wave equation. In addition, we show the inverse source problem is ill-posed and suffers from non-uniqueness when the mean of the source is zero and provide a uniqueness result and stability estimate in case of non-zero mean sources.

引用

页数：14

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