Work

The elastic ray transform

Year: 2025

Type: article

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.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ae0152

Authors: Joonas Ilmavirta, Antti Kykkänen, Teemu Saksala

Institutions: University of Jyväskylä, Rice University, North Carolina State University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta, Division of Mathematical Sciences