A foliated and reversible Finsler manifold is determined by its broken scattering relation
arXiv:2003.12657 · doi:10.2140/paa.2021.3.789
Abstract
The broken scattering relation consists of the total lengths of broken geodesics that start from the boundary, change direction once inside the manifold, and propagate to the boundary. We show that if two reversible Finsler manifolds satisfying a convex foliation condition have the same broken scattering relation, then they are isometric. This implies that some anisotropic material parameters of the Earth can be in principle reconstructed from single scattering measurements at the surface.
References in corpus (1)
Cited by in corpus (6)
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- Survey on Broken Ray Transforms
- Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity