A foliated and reversible Finsler manifold is determined by its broken scattering relation (bibtex)
by Maarten V. de Hoop, Joonas Ilmavirta, Matti Lassas, Teemu Saksala
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.
Reference:
A foliated and reversible Finsler manifold is determined by its broken scattering relation (Maarten V. de Hoop, Joonas Ilmavirta, Matti Lassas, Teemu Saksala), Pure and Applied Analysis, volume 4, number 4, pp. 789–811, 2021. [show abstract] [hide 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. [arXiv]
Bibtex Entry:
@article{foliated-finsler-bsr,
        author = {Maarten V. de Hoop and Joonas Ilmavirta and Matti Lassas and Teemu Saksala},
        title = {{A foliated and reversible Finsler manifold is determined by its broken scattering relation}},
        journal = {Pure and Applied Analysis},
        month = dec,
        year = {2021},
        volume = 4,
        number = 4,
        pages = {789--811},
        doi = {10.2140/paa.2021.3.789},
        arxiv = {2003.12657},
        url={http://users.jyu.fi/~jojapeil/pub/foliated-finsler-bsr.pdf},
		gsid={9850333438724223486},
        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.}
}
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