  We consider boundary measurements for the wave equation on a bounded domain
$M \subset \R^2$ or on a compact Riemannian surface, and introduce a method to
locate a discontinuity in the wave speed. Assuming that the wave speed consist
of an inclusion in a known smooth background, the method can determine the
distance from any boundary point to the inclusion. In the case of a known
constant background wave speed, the method reconstructs a set contained in the
convex hull of the inclusion and containing the inclusion. Even if the
background wave speed is unknown, the method can reconstruct the distance from
each boundary point to the inclusion assuming that the Riemannian metric tensor
determined by the wave speed gives simple geometry in $M$. The method is based
on reconstruction of volumes of domains of influence by solving a sequence of
linear equations. For $\tau \in C(\p M)$ the domain of influence $M(\tau)$ is
the set of those points on the manifold from which the distance to some
boundary point $x$ is less than $\tau(x)$.
