Rigidity for formally determined point source scattering for an anisotropic acoustic medium

Abstract

Consider an acoustic medium, occupying three dimensional space, whose anisotropic sound speed is modeled by a Riemannian metric which is Euclidean outside a compact region $D$. The medium is probed by acoustic waves generated by a finite number (dimension dependent) of point sources outside $D$ and the medium response is measured on the boundary of $D$ for a finite time period. We show that if these measurements agree with that of an Euclidean metric then the metric is Euclidean up to a diffeomorphism. This result is similar to the result in \cite{ORS26a} where they used plane waves instead of point sources. Using point sources instead of plane waves presents new difficulties, dealt with in this article.