  This paper is devoted to the identification of the unknown smooth coefficient
c entering the hyperbolic equation $c(x)\partial_{t}^{2}u - \Delta u = 0$ in a
bounded smooth domain in $\R^{d}$ from partial (on part of the boundary)
dynamic boundary measurements. In this paper we prove that the knowledge of the
partial Cauchy data for this class of hyperbolic PDE on any open subset
$\Gamma$ of the boundary determines explicitly the coefficient $c$ provided
that $c$ is known outside a bounded domain. Then, through construction of
appropriate test functions by a geometrical control method, we derive a formula
for calculating the coefficient $c$ from the knowledge of the difference
between the local Dirichlet to Neumann maps.
