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A
foliated and reversible Finsler manifold is determined by its
broken scattering relation
Maarten V. de Hoop, Joonas Ilmavirta, Matti Lassas and Teemu Saksala |
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Vol. 3 (2021), No. 4, 789–811
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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. |
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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Authors |
| Maarten V. de Hoop | |
| Departments of Computational and
Applied Mathematics, Earth Science Rice University Houston, TX United States |
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| Joonas Ilmavirta | |
| Department of Mathematics and
Statistics University of Jyväskylä Jyväskylä Finland |
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| Matti Lassas | |
| Department of Mathematics and
Statistics University of Helsinki Helsinki Finland |
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| Teemu Saksala | |
| Department of Mathematics North Carolina State University Raleigh, NC United States |
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