Unique continuation of the normal operator of the x-ray transform and applications in geophysics. (24th March 2020)

• Record Type: Journal Article
• Authors: Ilmavirta, Joonas; Mönkkönen, Keijo
• Is Part Of: Inverse problems. Volume 36:Number 4(2020)
• Publication Date: 2020-03-24
• Subjects: inverse problems -- x-ray tomography -- normal operator -- unique continuation -- theoretical seismology; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab6e75
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We show that the normal operator of the x-ray transform in R d, d ≥ 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.