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dc.contributor.authorde Hoop, Maarten V.
dc.contributor.authorIlmavirta, Joonas
dc.contributor.authorLassas, Matti
dc.contributor.authorSaksala, Teemu
dc.date.accessioned2023-08-30T09:14:41Z
dc.date.available2023-08-30T09:14:41Z
dc.date.issued2023
dc.identifier.citationde Hoop, M. V., Ilmavirta, J., Lassas, M., & Saksala, T. (2023). Stable reconstruction of simple Riemannian manifolds from unknown interior sources. <i>Inverse Problems</i>, <i>39</i>(9), Article 095002. <a href="https://doi.org/10.1088/1361-6420/ace6c9" target="_blank">https://doi.org/10.1088/1361-6420/ace6c9</a>
dc.identifier.otherCONVID_184473625
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/88790
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
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherIOP Publishing
dc.relation.ispartofseriesInverse Problems
dc.rightsCC BY 4.0
dc.subject.otherinverse problem
dc.subject.otherRiemannian geometry
dc.subject.otherdistance function
dc.subject.otherstability
dc.subject.otherdiscrete approximation
dc.titleStable reconstruction of simple Riemannian manifolds from unknown interior sources
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202308304827
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineInversio-ongelmien huippuyksikköfi
dc.contributor.oppiaineMathematicsen
dc.contributor.oppiaineCentre of Excellence in Inverse Problemsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn0266-5611
dc.relation.numberinseries9
dc.relation.volume39
dc.type.versionpublishedVersion
dc.rights.copyright© 2023 The Author(s). Published by IOP Publishing Ltd Printed in the UK
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber284715 HY
dc.subject.ysoinversio-ongelmat
dc.subject.ysoRiemannin monistot
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
jyx.subject.urihttp://www.yso.fi/onto/yso/p39163
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1088/1361-6420/ace6c9
dc.relation.funderSuomen Akatemiafi
dc.relation.funderResearch Council of Finlanden
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundinginformationM V d H was supported by the Simons Foundation under the MATH + X program, the National Science Foundation under Grant DMS-1815143, and the corporate members of the Geo-Mathematical Imaging Group at Rice University. J I was supported by the Academy of Finland (Projects 332890 and 336254). M L was supported by Academy of Finland (Projects 284715 and 303754). T S was supported by the Simons Foundation under the MATH + X program and the corporate members of the Geo-Mathematical Imaging Group at Rice University.
dc.type.okmA1


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