Stable reconstruction of simple Riemannian manifolds from unknown interior sources

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dc.citation.articleNumber095002en_US
dc.citation.journalTitleInverse Problemsen_US
dc.citation.volumeNumber39en_US
dc.contributor.authorHoop, Maarten V. deen_US
dc.contributor.authorIlmavirta, Joonasen_US
dc.contributor.authorLassas, Mattien_US
dc.contributor.authorSaksala, Teemuen_US
dc.date.accessioned2024-05-08T18:56:13Zen_US
dc.date.available2024-05-08T18:56:13Zen_US
dc.date.issued2023en_US
dc.description.abstractConsider the geometric inverse problem: there is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to get an approximate reconstruction, and we indeed provide a discrete metric approximation to the manifold with explicit data-driven error bounds when the manifold is simple. This is the geometrization of a seismological inverse problem where we measure the arrival times on the surface of waves from an unknown number of unknown interior microseismic events at unknown times. The closeness of two metric spaces with a marked boundary is measured by a labeled Gromov–Hausdorff distance. If measurements are done for infinite time and spatially dense sources, our construction produces the true Riemannian manifold and the finite-time approximations converge to it in the metric senseen_US
dc.identifier.citationHoop, M. V. de, Ilmavirta, J., Lassas, M., & Saksala, T. (2023). Stable reconstruction of simple Riemannian manifolds from unknown interior sources. Inverse Problems, 39, 095002. https://doi.org/10.1088/1361-6420/ace6c9en_US
dc.identifier.digitalde_Hoop_2023_Inverse_Problems_39_095002en_US
dc.identifier.doihttps://doi.org/10.1088/1361-6420/ace6c9en_US
dc.identifier.urihttps://hdl.handle.net/1911/115699en_US
dc.language.isoengen_US
dc.publisherIOP Publishing Ltden_US
dc.rightsExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license. Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleStable reconstruction of simple Riemannian manifolds from unknown interior sourcesen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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