The elastic ray transform
Functional Analysis
2025-09-03 v2 Analysis of PDEs
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.
Cite
@article{arxiv.2502.18686,
title = {The elastic ray transform},
author = {Joonas Ilmavirta and Antti Kykkänen and Teemu Saksala},
journal= {arXiv preprint arXiv:2502.18686},
year = {2025}
}
Comments
23 pages, updated introduction