Work

Fourier method for inverse source problem using correlation of passive measurements*

Year: 2024

Type: article

Abstract: 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.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ad6fc7

Authors: Faouzi Triki, Kristoffer Linder-Steinlein, Mirza Karamehmedović

Institution: Technical University of Denmark

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,165

Funder: Villum Fonden