by Joonas Ilmavirta, Antti Kykkänen and Teemu Saksala
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.
Reference:
The elastic ray transform (Joonas Ilmavirta, Antti Kykkänen and Teemu Saksala), Inverse Problems, volume 41, number 9, pp. 095008, 2025.
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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.
[arXiv]
Bibtex Entry:
@article{elastic-xrt1,
author = {Joonas Ilmavirta and Antti Kykk\"{a}nen and Teemu Saksala},
title = {{The elastic ray transform}},
month = sep,
year = 2025,
arxiv = {2502.18686},
url = {http://users.jyu.fi/~jojapeil/pub/elastic-xrt1.pdf},
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.},
doi = {10.1088/1361-6420/ae0152},
journal = {Inverse Problems},
volume = {41},
number = {9},
pages = {095008}
}