Lipschitz Stability of Travel Time Data
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909357899251712 |
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| author | Ilmavirta, Joonas Kykkänen, Antti Lassas, Matti Saksala, Teemu Shedlock, Andrew |
| author_facet | Ilmavirta, Joonas Kykkänen, Antti Lassas, Matti Saksala, Teemu Shedlock, Andrew |
| contents | We prove that the reconstruction of a certain type of length spaces from their travel time data on a closed subset is Lipschitz stable. The travel time data is the set of distance functions from the entire space, measured on the chosen closed subset. The case of a Riemannian manifold with boundary with the boundary as the measurement set appears is a classical geometric inverse problem arising from Gel'fand's inverse boundary spectral problem. Examples of spaces satisfying our assumptions include some non-simple Riemannian manifolds, Euclidean domains with non-trivial topology, and metric trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lipschitz Stability of Travel Time Data Ilmavirta, Joonas Kykkänen, Antti Lassas, Matti Saksala, Teemu Shedlock, Andrew Metric Geometry Differential Geometry 51F30, 53C23, 30L05 We prove that the reconstruction of a certain type of length spaces from their travel time data on a closed subset is Lipschitz stable. The travel time data is the set of distance functions from the entire space, measured on the chosen closed subset. The case of a Riemannian manifold with boundary with the boundary as the measurement set appears is a classical geometric inverse problem arising from Gel'fand's inverse boundary spectral problem. Examples of spaces satisfying our assumptions include some non-simple Riemannian manifolds, Euclidean domains with non-trivial topology, and metric trees. |
| title | Lipschitz Stability of Travel Time Data |
| topic | Metric Geometry Differential Geometry 51F30, 53C23, 30L05 |
| url | https://arxiv.org/abs/2410.16224 |