Uniqueness of the partial travel time representation of a compact Riemannian manifold with strictly convex boundary

2022/01/06 by Ella Pavlechko, Pavlechko, Ella, Teemu Saksala +1
Mathematics · Medicine · #53C21 #53C24 #53C80 #86A22 #Differential Geometry (math.DG) #FOS: Mathematics #Medical Imaging Techniques and Applications #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2201.01887

openalex publication_date 2022/01/06 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper a compact Riemannian manifold with strictly convex boundary is reconstructed from its partial travel time data. This data assumes that an open measurement region on the boundary is given, and that for every point in the manifold, the respective distance function to the points on the measurement region is known. This geometric inverse problem has many connections to seismology, in particular to micro seismicity. The reconstruction is based on embedding the manifold in a function space. This requires the differentiation of the distance functions. Therefore this paper also studies some global regularity properties of the distance function on a compact Riemannian manifold with strictly convex boundary.

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