Unique continuation of the normal operator of the X-ray transform and applications in geophysics
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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Inverse ProblemsDate
2020Discipline
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsCopyright
© 2020 IOP Publishing Ltd.
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.
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Institute of PhysicsISSN Search the Publication Forum
0266-5611Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/34402315
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Academy of FinlandFunding program(s)
Academy Project, AoF; Centre of Excellence, AoF; Postdoctoral Researcher, AoF
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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