An inverse source problem for a variable speed wave equation with discrete-in-time sources

We consider a time-dependent inverse source problem for the inhomogeneous wave equation, with sources that are delta-like in time, and (roughly speaking) non-negative and of limited oscillation in space. We take the displacement of the wave on a fixed detection surface, over some time interval, as our data. We then use time-reversal from the boundary to generate a related waveform, and discuss how to identify sources (as well as artifacts) from this.