Inverting the local geodesic ray transform of higher rank tensors
Abstract
Consider a Riemannian manifold in dimension [ image ] with a strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem is closely related to elastic qP-wave tomography. Under the condition that the manifold can be foliated with a continuous family of strictly convex hypersurfaces, the local invertibility implies a global result. One can straightforwardedly adapt the proof to show similar results for tensor fields of arbitrary rank.
- Publication:
-
Inverse Problems
- Pub Date:
- November 2019
- DOI:
- 10.1088/1361-6420/ab1ace
- arXiv:
- arXiv:1810.11088
- Bibcode:
- 2019InvPr..35k5009D
- Keywords:
-
- tensor tomography;
- elastic-wave travel-time tomography;
- scattering calculus;
- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs
- E-Print:
- doi:10.1088/1361-6420/ab1ace