We consider the wave equation
,
in
,
, where the metric
is known outside an
open and bounded set
with smooth boundary
.
We define a source as a sum of point sources,
, where the points
, form a dense set on
. We show that when
the weights
are chosen
appropriately,
determines
the scattering relation on
,
that is, it determines for all geodesics which pass through
the
travel times together with the entering and exit points and directions. The wave
contains the singularities produced by all point sources, but when
for some
, we can trace
back the point source that produced a given singularity in the data. This gives us the distance in
between a source
point
and an arbitrary
point
. In particular, if
is a simple Riemannian
manifold and
is
conformally Euclidian in
,
these distances are known to determine the metric
in
. In the
case when
is nonsimple, we present a more detailed analysis of the wave fronts yielding the scattering
relation on
.