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PreprintCC BY-NC-ND 4.0arXiv

Rigidity for formally determined point source scattering for an anisotropic acoustic medium

  • Pradipta Chatterjee
  • Rakesh
  • Abhilash Tushir
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Abstract

Consider an acoustic medium, occupying three dimensional space, whose anisotropic sound speed is modeled by a Riemannian metric which is Euclidean outside a compact region D. The medium is probed by acoustic waves generated by a finite number (dimension dependent) of point sources outside D and the medium response is measured on the boundary of D for a finite time period. We show that if these measurements agree with that of an Euclidean metric then the metric is Euclidean up to a diffeomorphism. This result is similar to the result in \cite{ORS26a} where they used plane waves instead of point sources. Using point sources instead of plane waves presents new difficulties, dealt with in this article.

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Cite

BibTeXRIS
BibTeX
@misc{chatterjee2026rigidity,
  title = {{Rigidity for formally determined point source scattering for an anisotropic acoustic medium}},
  author = {Pradipta Chatterjee and Rakesh and Abhilash Tushir},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21258},
  eprint = {2610.21258},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21258},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Rigidity for formally determined point source scattering for an anisotropic acoustic medium
AU  - Pradipta Chatterjee
AU  - Rakesh
AU  - Abhilash Tushir
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21258
UR  - https://arxiv.org/abs/2610.21258
AB  - Consider an acoustic medium, occupying three dimensional space, whose anisotropic sound speed is modeled by a Riemannian metric which is Euclidean outside a compact region D. The medium is probed by acoustic waves generated by a finite number (dimension dependent) of point sources outside D and the medium response is measured on the boundary of D for a finite time period. We show that if these measurements agree with that of an Euclidean metric then the metric is Euclidean up to a diffeomorphism. This result is similar to the result in \cite{ORS26a} where they used plane waves instead of point sources. Using point sources instead of plane waves presents new difficulties, dealt with in this article.
ER  -