Inverting the local geodesic ray transform of higher rank tensors. (4th October 2019)

• Record Type: Journal Article
• Authors: de Hoop, Maarten V; Uhlmann, Gunther; Zhai, Jian
• Is Part Of: Inverse problems. Volume 35:Number 11(2019)
• Publication Date: 2019-10-04
• Subjects: tensor tomography -- elastic-wave travel-time tomography -- scattering calculus; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab1ace
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Consider a Riemannian manifold in dimension 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.