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dc.contributor.authorIlmavirta, Joonas
dc.contributor.authorMönkkönen, Keijo
dc.date.accessioned2020-01-28T10:15:48Z
dc.date.available2020-01-28T10:15:48Z
dc.date.issued2020
dc.identifier.citationIlmavirta, J., & Mönkkönen, K. (2020). Unique continuation of the normal operator of the X-ray transform and applications in geophysics. <i>Inverse Problems</i>, <i>36</i>(4), Article 045014. <a href="https://doi.org/10.1088/1361-6420/ab6e75" target="_blank">https://doi.org/10.1088/1361-6420/ab6e75</a>
dc.identifier.otherCONVID_34402315
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/67566
dc.description.abstractWe 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.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherInstitute of Physics
dc.relation.ispartofseriesInverse Problems
dc.rightsCC BY-NC-ND 3.0
dc.subject.otherx-ray transform
dc.subject.othergeophysics
dc.titleUnique continuation of the normal operator of the X-ray transform and applications in geophysics
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202001281820
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineInversio-ongelmien huippuyksikköfi
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineCentre of Excellence in Inverse Problemsen
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.relation.issn0266-5611
dc.relation.numberinseries4
dc.relation.volume36
dc.type.versionacceptedVersion
dc.rights.copyright© 2020 IOP Publishing Ltd.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber309963
dc.relation.grantnumber284715 HY
dc.relation.grantnumber295853
dc.subject.ysotomografia
dc.subject.ysogeofysiikka
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p17798
jyx.subject.urihttp://www.yso.fi/onto/yso/p6800
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/3.0/
dc.relation.doi10.1088/1361-6420/ab6e75
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramTutkijatohtori, SAfi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramPostdoctoral Researcher, AoFen
jyx.fundinginformationJ 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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