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
Contributing organizations
Related projects
- Centre of Excellence in Inverse Problems Research
- Salo, Mikko
- Academy of Finland
- Inverse boundary problems: toward a unified theory
- Salo, Mikko
- Academy of Finland
- Ray tomography for imaging the Earth
- Ilmavirta, Joonas
- Academy of Finland
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 2