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 language | English |
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Article number | 105009 |
Journal | Inverse Problems |
Volume | 40 |
Issue number | 10 |
Number of pages | 14 |
ISSN | 0266-5611 |
DOIs | |
Publication status | Published - 2024 |
Keywords
- Inverse source problem
- Passive imaging
- Stability
- Wave equation