Hoop, Maarten V. deMaarten V. deHoopKykk?nen, AnttiAnttiKykk?nenMishra, Rohit KumarRohit KumarMishra2025-10-132025-10-132025-092331-842210.48550/arXiv.2509.01623http://repository.iitgn.ac.in0/handle/IITG2025/33090We 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.en-USArticle123456789/555