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 qPwave 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:
 10.1088/13616420/ab1ace
 arXiv:
 arXiv:1810.11088
 Bibcode:
 2019InvPr..35k5009D
 Keywords:

 tensor tomography;
 elasticwave traveltime tomography;
 scattering calculus;
 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs
 EPrint:
 doi:10.1088/13616420/ab1ace