We consider the problem to reconstruct a wave speed
c ∈ C∞(M) in a domain M ⊂ R
n from acoustic boundary measurements
modelled by the hyperbolic Dirichlet-to-Neumann map
Λ. 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−2dx2
) 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
ec
−2 − c
−2
�
(ξ)| ≤ Ce2R|ξ|
Λe − Λ
∗
, ξ ∈ R
n
,
for all ec ∈ U ∩ V , where Λ is the Dirichlet-to-Neumann map corre- e
sponding to the wave speed ec and k·k∗
is a norm capturing certain
regularity properties of the Dirichlet-to-Neumann maps
