The elastic ray transform
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866909764662853632 |
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| author | Ilmavirta, Joonas Kykkänen, Antti Saksala, Teemu |
| author_facet | Ilmavirta, Joonas Kykkänen, Antti Saksala, Teemu |
| contents | We introduce and study a new family of tensor tomography problems. At rank 2 it corresponds to linearization of travel time of elastic waves, measured for all polarizations. We provide a kernel characterization for ranks up to 2. The kernels consist of potential tensors, but in an unusual sense: the associated differential operators have degree 2 instead of the familiar 1. The proofs are based on Fourier analysis, Helmholtz decompositions, and cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The elastic ray transform Ilmavirta, Joonas Kykkänen, Antti Saksala, Teemu Functional Analysis Analysis of PDEs We introduce and study a new family of tensor tomography problems. At rank 2 it corresponds to linearization of travel time of elastic waves, measured for all polarizations. We provide a kernel characterization for ranks up to 2. The kernels consist of potential tensors, but in an unusual sense: the associated differential operators have degree 2 instead of the familiar 1. The proofs are based on Fourier analysis, Helmholtz decompositions, and cohomology. |
| title | The elastic ray transform |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2502.18686 |