Inverse Problem of Travel Time Difference Functions on a Compact Riemannian Manifold with Boundary

We show that the travel time difference functions, between common interior points and pairs of points on the boundary, determine a compact Riemannian manifold with smooth boundary up to Riemannian isometry if the boundary satisfies a certain visibility condition. This corresponds with the inverse mi...

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Veröffentlicht in:	The Journal of Geometric Analysis 2019-12, Vol.29 (4), p.3308-3327
Hauptverfasser:	de Hoop, Maarten V., Saksala, Teemu
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Cybernetics Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Inverse problems Mathematics Mathematics and Statistics Riemann manifold Smooth boundaries Travel time Visibility
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creator	de Hoop, Maarten V. Saksala, Teemu
description	We show that the travel time difference functions, between common interior points and pairs of points on the boundary, determine a compact Riemannian manifold with smooth boundary up to Riemannian isometry if the boundary satisfies a certain visibility condition. This corresponds with the inverse microseismicity problem. In the proof of this result, we also construct an explicit smooth atlas from the travel time difference functions.
doi_str_mv	10.1007/s12220-018-00111-0
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subjects	Abstract Harmonic Analysis Convex and Discrete Geometry Cybernetics Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Inverse problems Mathematics Mathematics and Statistics Riemann manifold Smooth boundaries Travel time Visibility
title	Inverse Problem of Travel Time Difference Functions on a Compact Riemannian Manifold with Boundary
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