  We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a
domain $M \subset \R^n$ from acoustic boundary measurements modelled by the
hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction
formula for $c$ that is based on the Boundary Control method and incorporates
features also from the complex geometric optics solutions approach. Moreover,
we show that the reconstruction formula is locally Lipschitz stable for a low
frequency component of $c^{-2}$ under the assumption that the Riemannian
manifold $(M, c^{-2} dx^2)$ has a strictly convex function with no critical
points. That is, we show that for all bounded $C^2$ neighborhoods $U$ of $c$,
there is a $C^1$ neighborhood $V$ of $c$ and constants $C, R > 0$ such that
|\F\ll(\tilde c^{-2} - c^{-2}\rr)(\xi)| \le C e^{2R |\xi|} \norm{\tilde \Lambda
- \Lambda}_*, \quad \xi \in \R^n, for all $\tilde c \in U \cap V$, where
$\tilde \Lambda$ is the Dirichlet-to-Neumann map corresponding to the wave
speed $\tilde c$ and $\norm{\cdot}_*$ is a norm capturing certain regularity
properties of the Dirichlet-to-Neumann maps.
