An Inverse Kinematic Problem with Internal Sources

Abstract

Given a bounded domain $M$ in ${\mathbb{R}}^n$ with a conformally Euclidean metric $g=\rho d{x}^2$, in this paper we consider the inverse problem of recovering a semigeodesic neighborhood of a domain $\Gamma \subset \partial M$ and the conformal factor $\rho$ in the neighborhood from the travel time data (defined below) and the Cartesian coordinates of $\Gamma$. 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.

7 pages

References in corpus (1)

• The inverse problem for the local geodesic ray transform