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 ${\mathbb{R}}^d$, $d\ge 2$, 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.

21 pages, 4 figures