Unique continuation of the normal operator of the x-ray transform and applications in geophysics. (24th March 2020) - Ilmavirta, Joonas; Mönkkönen, Keijo
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.