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PreprintarXiv licencearXiv

An inverse moving point source problem in inhomogeneous acoustic media: uniqueness, stability and reconstruction

  • Dong Qiu
  • Xiang Xu
  • Yue Zhao
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Abstract

This paper is concerned with the simultaneous recovery of the trajectory and intensity of an unknown moving point source in an inhomogeneous acoustic medium. We prove that the whole-boundary measurements over a finite time interval uniquely determine the moving source. Furthermore, under suitable propagation and rank assumptions, Lipschitz stability of determining both the trajectory and intensity is derived using waveforms measured at four fixed receivers outside the source region. A novel Volterra--Euler reconstruction scheme is developed for solving the inverse problem, and the error estimate is derived for the proposed scheme. Numerical experiments are presented to demonstrate the effectiveness of the proposed numerical method.

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Cite

BibTeXRIS
BibTeX
@misc{qiu2026inverse,
  title = {{An inverse moving point source problem in inhomogeneous acoustic media: uniqueness, stability and reconstruction}},
  author = {Dong Qiu and Xiang Xu and Yue Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36830},
  eprint = {2610.36830},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36830},
}
RIS
TY  - UNPB
TI  - An inverse moving point source problem in inhomogeneous acoustic media: uniqueness, stability and reconstruction
AU  - Dong Qiu
AU  - Xiang Xu
AU  - Yue Zhao
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36830
UR  - https://arxiv.org/abs/2610.36830
AB  - This paper is concerned with the simultaneous recovery of the trajectory and intensity of an unknown moving point source in an inhomogeneous acoustic medium. We prove that the whole-boundary measurements over a finite time interval uniquely determine the moving source. Furthermore, under suitable propagation and rank assumptions, Lipschitz stability of determining both the trajectory and intensity is derived using waveforms measured at four fixed receivers outside the source region. A novel Volterra--Euler reconstruction scheme is developed for solving the inverse problem, and the error estimate is derived for the proposed scheme. Numerical experiments are presented to demonstrate the effectiveness of the proposed numerical method.
ER  -