The head wave transform
Classical Analysis and ODEs
2025-09-03 v1
Abstract
We introduce and study a new integral ray transform called the head wave transform. The head wave transform integrates a function along a piecewise linear (in general geodesic) path consisting of three parts. The geometry of such paths corresponds to ray paths of head waves propagating in a medium with sharp changes in sound speed. The middle part of the ray paths corresponds to gliding along the so-called gliding surface. As our main results, we prove inversion formulas and kernel characterizations under multiple different sets of assumptions on the geometry of gliding surface.
Cite
@article{arxiv.2509.01623,
title = {The head wave transform},
author = {Maarten V. de Hoop and Antti Kykkänen and Rohit Kumar Mishra},
journal= {arXiv preprint arXiv:2509.01623},
year = {2025}
}
Comments
15 pages, 1 figure