Abstract
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.
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Acknowledgements
We would like to thank M. Lassas and S. Ivanov for their invaluable comments. MVdH was partially supported by the Simons Foundation under the MATH \(+\) X program, the National Science Foundation under grant DMS-1559587, and by members of the Geo-Mathematical Imaging Group at Rice University. TS was supported by the Simons Foundation under the MATH \(+\) X program.
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de Hoop, M.V., Saksala, T. Inverse Problem of Travel Time Difference Functions on a Compact Riemannian Manifold with Boundary. J Geom Anal 29, 3308–3327 (2019). https://doi.org/10.1007/s12220-018-00111-0
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DOI: https://doi.org/10.1007/s12220-018-00111-0