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arXiv · 1810.11088

Inverting the local geodesic ray transform of higher rank tensors

Maarten V. de Hoop·Gunther Uhlmann·Jian Zhai
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Abstract

Consider a Riemannian manifold in dimension $n\geq 3$ with 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 with elastic \textit{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.

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Maarten V. de Hoop, Gunther Uhlmann, Jian Zhai. 2018-11-08. Inverting the local geodesic ray transform of higher rank tensors. https://doi.org/10.1088/1361-6420%2Fab1ace

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