Fourier method for inverse source problem using correlation of passive measurements

Faouzi Triki, Kristoffer Linder-Steinlein*, Mirza Karamehmedović

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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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.
Original languageEnglish
Article number105009
JournalInverse Problems
Volume40
Issue number10
Number of pages14
ISSN0266-5611
DOIs
Publication statusPublished - 2024

Keywords

  • Inverse source problem
  • Passive imaging
  • Stability
  • Wave equation

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