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Abstract
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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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Keywords
Finsler manifold, scattering relation, distance functions,
anisotropic elasticity
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Mathematical Subject Classification
Primary: 86A22, 53Z05, 53C60
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Milestones
Received: 21 May 2021
Revised: 30 August 2021
Accepted: 9 October 2021
Published: 12 February 2022
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