  To investigate the dynamics of driven vortices in superconductors, noise in
the local vortex density was investigated in the mixed state of a high-$T_c$
superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_y$, using a two-dimensional electron gas
(2DEG) micro-Hall probe array. We studied the cross-correlation function,
together with the auto-correlation function, both parallel and perpendicular to
the direction of flow of the vortices. The broadband noise (BBN) did not have
large spatial correlations. This suggests that the BBN is due to the
fluctuation of the local vortex density generated by bulk pinning centers under
the area of each probe. On the other hand, the narrow-band noise (NBN) (with
the the time scale of the transit time of vortices) had large translational
correlations. These definitely shows that the NBN was generated by
semimacroscopic imperfections like the surface, and macroscopic line defects
{\it etc.}. In relation to the dynamic phase diagram, large BBN was observed
when the vortices started moving. The dependence of the spatial correlations on
the direction of the array relative to the direction of the driving current
suggested that plastic flow was present when the large BBN was observed. The
gross features of our data agree well with some of the theoretically proposed
dynamical phase diagrams of vortices in superconductors.
