ON THE CONSTRUCTION OF VIRTUAL INTERIOR POINT SOURCE TRAVEL TIME DISTANCES FROM THE HYPERBOLIC NEUMANN-TO-DIRICHLET MAP

摘要

We introduce a new algorithm to construct travel time distances between a point in the interior of a Riemannian manifold and points on the boundary of the manifold, and describe a numerical implementation of the algorithm. It is known that the travel time distances for all interior points determine the Riemannian manifold in a stable manner. We do not assume that there are sources or receivers in the interior, and use the hyperbolic Neumann-to-Dirichlet map, or its restriction, as our data. Our algorithm is a variant of the boundary control method, and to our knowledge, this is the first numerical implementation of the method in a geometric setting.