A1 Journal article (refereed)
Unique continuation of the normal operator of the X-ray transform and applications in geophysics (2020)


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


JYU authors or editors


Publication details

All authors or editors: Ilmavirta, Joonas; Mönkkönen, Keijo

Journal or series: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Publication year: 2020

Volume: 36

Issue number: 4

Article number: 045014

Publisher: Institute of Physics

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1088/1361-6420/ab6e75

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67566

Publication is parallel published: https://arxiv.org/abs/1909.05585


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.


Keywords: geophysics; tomography

Free keywords: x-ray transform; geophysics


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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2


Last updated on 2021-07-07 at 21:34