  A new parallel-in-time iterative method is proposed for solving the
homogeneous second-order wave equation. The new method involves a coarse scale
propagator, allowing for larger time steps, and a fine scale propagator which
fully resolves the medium using finer spatial grid and shorter time steps. The
fine scale propagator is run in parallel for short time intervals. The two
propagators are coupled in an iterative way that resembles the standard
parareal method developed by Lions, Maday and Turinici. We present a
data-driven strategy in which the computed data gathered from each iteration
are re-used to stabilize the coupling by minimizing the energy residual of the
fine and coarse propagated solutions. An example of Marmousi model is provided
to demonstrate the performance of the proposed method.
