Inverse problem of Travel time difference functions on compact\n Riemannian manifold with boundary

2018/07/06 by Maarten V. de Hoop, de Hoop, Maarten V., Teemu Saksala +1
Computer Science · Engineering · Environmental Science · Mathematics · #53C22 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Landslides and related hazards #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1807.02576

openalex publication_date 2018/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the travel time difference functions, measured on the boundary,\ndetermine a compact Riemannian manifold with smooth boundary up to Riemannian\nisometry, if boundary satisfies a certain visibility condition. This\ncorresponds with the inverse microseismicity problem. The novelty of our paper\nis a new type of a proof and a weaker assumption for the boundary than it has\nbeen presented in the literature before. We also construct an explicit smooth\natlas from the travel time difference functions.\n

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