On the left, at the earth's surface, you see the surface ground roll. In frames B and C the slowest events are the asymptotes of successively faster hyperbolas. To my knowledge this method has never been tried. I believe it is worth some serious testing. Even in the most layered of geological regions there are always faults and irregularities to illuminate the full available spectrum.
Difficulty is unlikely to come from weak signals.
More probably, the potential for difficulty lies in near-surface velocity irregularity. As with Stolt migration, your answer should be expressed as a 2-D inverse Fourier transform.