Inverting the local geodesic ray transform of higher rank tensors
Inverse Problems, 2019•iopscience.iop.org
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.
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.
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.
iopscience.iop.org
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