  Although travelling faster than the speed of light in vacuum is not
physically allowed, the analogous bound in medium can be exceeded by a moving
particle. For an electron in dielectric material this leads to emission of
photons which is usually referred to as Cherenkov radiation. In this article a
related mathematical system for waves in inhomogeneous anisotropic medium with
a maximum of three polarisation directions is studied. The waves are assumed to
satisfy $P^k_j u_k (x,t) = S_j(x,t)$, where $P$ is a vector-valued wave
operator that depends on a Riemannian metric and $S $ is a point source that
moves at speed $\beta < c$ in given direction $\theta \in \mathbb{S}^2$. The
phase velocity $v_{\text{phase}}$ is described by the metric and depends on
both location and direction of motion. In regions where
$v_{\text{phase}}(x,\theta) < \beta <c $ holds the source generates a
cone-shaped front of singularities that propagate according to the underlying
geometry. We introduce a model for a measurement setup that applies the
mechanism and show that the Riemannian metric inside a bounded region can be
reconstructed from partial boundary measurements. The result suggests that
Cherenkov type radiation can be applied to detect internal geometric properties
of an inhomogeneous anisotropic target from a distance.

Analysis of PDEs;Differential Geometry