Unique continuation of the normal operator of the X-ray transform and applications in geophysics
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.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Institute of Physics
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202001281820Use this for linking
Review status
Peer reviewed
ISSN
0266-5611
DOI
https://doi.org/10.1088/1361-6420/ab6e75
Language
English
Published in
Inverse Problems
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
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Funder(s)
Research Council of Finland
Research Council of Finland
Research Council of Finland
Funding program(s)
Postdoctoral Researcher, AoF
Centre of Excellence, AoF
Academy Project, AoF
Tutkijatohtori, SA
Huippuyksikkörahoitus, SA
Akatemiahanke, SA
Additional information about funding
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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