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

  • *Corresponding author: Teemu Saksala

    *Corresponding author: Teemu Saksala

EP was supported by the AWM and NSF-DMS grant # 1953892 for presenting this paper at the 2022 Joint Mathematics Meetings

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  • 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 microseismicity. 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.

    Mathematics Subject Classification: 53C21, 53C24, 53C80, 86A22.

    Citation:

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  • Figure 1.  A domain where partial data is insufficient

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