dc.contributor.author Ilmavirta, Joonas dc.contributor.author Mönkkönen, Keijo dc.date.accessioned 2020-01-28T10:15:48Z dc.date.available 2020-01-28T10:15:48Z dc.date.issued 2020 dc.identifier.citation Ilmavirta, J., & Mönkkönen, K. (2020). Unique continuation of the normal operator of the X-ray transform and applications in geophysics. Inverse Problems, 36(4), Article 045014. https://doi.org/10.1088/1361-6420/ab6e75 dc.identifier.other CONVID_34402315 dc.identifier.uri https://jyx.jyu.fi/handle/123456789/67566 dc.description.abstract We show that the normal operator of the X-ray transform in $\mathbb{R}^d$, $d\geq 2$, has a unique continuation property in the class of compactly supported distributions. This immediately implies uniqueness for the X-ray tomography problem with partial data and generalizes some earlier results to higher dimensions. Our proof also gives a unique continuation property for certain Riesz potentials in the space of rapidly decreasing distributions. We present applications to local and global seismology. These include linearized travel time tomography with half-local data and global tomography based on shear wave splitting in a weakly anisotropic elastic medium. en dc.format.mimetype application/pdf dc.language eng dc.language.iso eng dc.publisher Institute of Physics dc.relation.ispartofseries Inverse Problems dc.rights CC BY-NC-ND 3.0 dc.subject.other x-ray transform dc.subject.other geophysics dc.title Unique continuation of the normal operator of the X-ray transform and applications in geophysics dc.type article dc.identifier.urn URN:NBN:fi:jyu-202001281820 dc.contributor.laitos Matematiikan ja tilastotieteen laitos fi dc.contributor.laitos Department of Mathematics and Statistics en dc.contributor.oppiaine Inversio-ongelmien huippuyksikkö fi dc.contributor.oppiaine Matematiikka fi dc.contributor.oppiaine Centre of Excellence in Inverse Problems en dc.contributor.oppiaine Mathematics en dc.type.uri http://purl.org/eprint/type/JournalArticle dc.description.reviewstatus peerReviewed dc.relation.issn 0266-5611 dc.relation.numberinseries 4 dc.relation.volume 36 dc.type.version acceptedVersion dc.rights.copyright © 2020 IOP Publishing Ltd. dc.rights.accesslevel openAccess fi dc.relation.grantnumber 309963 dc.relation.grantnumber 284715 HY dc.relation.grantnumber 295853 dc.subject.yso tomografia dc.subject.yso geofysiikka dc.format.content fulltext jyx.subject.uri http://www.yso.fi/onto/yso/p17798 jyx.subject.uri http://www.yso.fi/onto/yso/p6800 dc.rights.url https://creativecommons.org/licenses/by-nc-nd/3.0/ dc.relation.doi 10.1088/1361-6420/ab6e75 dc.relation.funder Suomen Akatemia fi dc.relation.funder Suomen Akatemia fi dc.relation.funder Suomen Akatemia fi dc.relation.funder Academy of Finland en dc.relation.funder Academy of Finland en dc.relation.funder Academy of Finland en jyx.fundingprogram Akatemiahanke, SA fi jyx.fundingprogram Huippuyksikkörahoitus, SA fi jyx.fundingprogram Tutkijatohtori, SA fi jyx.fundingprogram Academy Project, AoF en jyx.fundingprogram Centre of Excellence, AoF en jyx.fundingprogram Postdoctoral Researcher, AoF en jyx.fundinginformation J I was supported by the Academy of Finland (decision 295853) and K M was supported by Academy of Finland (Center of Excellence in Inverse Modeling and Imaging, Grant Numbers 284715 and 309963). We thank Maarten de Hoop and Todd Quinto for discussions. We also thank Mikko Salo for pointing out the connection between our result and the unique continuation of the fractional Laplacian. We are grateful to the anonymous referees for insightful remarks and suggestions.
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