Vol. 3, No. 4, 2021

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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

Vol. 3 (2021), No. 4, 789–811
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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Keywords
Finsler manifold, scattering relation, distance functions, anisotropic elasticity
Mathematical Subject Classification
Primary: 86A22, 53Z05, 53C60
Milestones
Received: 21 May 2021
Revised: 30 August 2021
Accepted: 9 October 2021
Published: 12 February 2022
Authors
Maarten V. de Hoop
Departments of Computational and Applied Mathematics, Earth Science
Rice University
Houston, TX
United States
Joonas Ilmavirta
Department of Mathematics and Statistics
University of Jyväskylä
Jyväskylä
Finland
Matti Lassas
Department of Mathematics and Statistics
University of Helsinki
Helsinki
Finland
Teemu Saksala
Department of Mathematics
North Carolina State University
Raleigh, NC
United States