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arXiv · 2410.16224

Lipschitz Stability of Travel Time Data

Joonas Ilmavirta·Antti Kykkänen·Matti Lassas·Teemu Saksala·Andrew Shedlock
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Abstract

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.

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Joonas Ilmavirta, Antti Kykkänen, Matti Lassas, Teemu Saksala, Andrew Shedlock. 2024-10-21. Lipschitz Stability of Travel Time Data. https://arxiv.org/abs/2410.16224

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