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arXiv · 2502.18686

The elastic ray transform

Joonas Ilmavirta·Antti Kykkänen·Teemu Saksala
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Abstract

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.

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Joonas Ilmavirta, Antti Kykkänen, Teemu Saksala. 2025-02-25. The elastic ray transform. https://arxiv.org/abs/2502.18686

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