The elastic ray transform
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.
Authors
- Teemu Saksala (ORCID: https://orcid.org/0000-0002-3785-9623)
- Antti Kykkänen (ORCID: https://orcid.org/0009-0001-3867-9480)
- Joonas Ilmavirta (ORCID: https://orcid.org/0000-0002-2399-0911)
Institutions
- North Carolina State University (US)
- Rice University (US)
- University of Jyväskylä (FI)
Publication Details
- Journal
- Inverse Problems
- Published
- 2025-09-01
- DOI
- https://doi.org/10.1088/1361-6420/ae0152
- Citations
- 1
- Primary Topic
- Composite Material Mechanics
- Type
- article
- Field-Weighted Citation Impact
- 0.86
Funders
- Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta
- Division of Mathematical Sciences