The head wave transform
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909765368545280 |
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| author | de Hoop, Maarten V. Kykkänen, Antti Mishra, Rohit Kumar |
| author_facet | de Hoop, Maarten V. Kykkänen, Antti Mishra, Rohit Kumar |
| contents | We introduce and study a new integral ray transform called the head wave transform. The head wave transform integrates a function along a piecewise linear (in general geodesic) path consisting of three parts. The geometry of such paths corresponds to ray paths of head waves propagating in a medium with sharp changes in sound speed. The middle part of the ray paths corresponds to gliding along the so-called gliding surface. As our main results, we prove inversion formulas and kernel characterizations under multiple different sets of assumptions on the geometry of gliding surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The head wave transform de Hoop, Maarten V. Kykkänen, Antti Mishra, Rohit Kumar Classical Analysis and ODEs 44A12, 44A99, 47G10 We introduce and study a new integral ray transform called the head wave transform. The head wave transform integrates a function along a piecewise linear (in general geodesic) path consisting of three parts. The geometry of such paths corresponds to ray paths of head waves propagating in a medium with sharp changes in sound speed. The middle part of the ray paths corresponds to gliding along the so-called gliding surface. As our main results, we prove inversion formulas and kernel characterizations under multiple different sets of assumptions on the geometry of gliding surface. |
| title | The head wave transform |
| topic | Classical Analysis and ODEs 44A12, 44A99, 47G10 |
| url | https://arxiv.org/abs/2509.01623 |