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arXiv · 1409.7863

An Inverse Kinematic Problem with Internal Sources

Leonid Pestov·Gunther Uhlmann·Hanming Zhou
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Abstract

Given a bounded domain $M$ in $\mathbb{R}^n$ with a conformally Euclidean metric $g=ρ\,dx^2$, in this paper we consider the inverse problem of recovering a semigeodesic neighborhood of a domain $Γ\subset \partial M$ and the conformal factor $ρ$ in the neighborhood from the travel time data (defined below) and the Cartesian coordinates of $Γ$. We develop an explicit reconstruction procedure for this problem. The key ingredient is the relation between the reconstruction and a Cauchy problem of the conformal Killing equation.

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Leonid Pestov, Gunther Uhlmann, Hanming Zhou. 2014-09-28. An Inverse Kinematic Problem with Internal Sources. https://doi.org/10.1088/0266-5611%2F31%2F5%2F055006

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