  Consider the inverse scattering of time-harmonic acoustic scattering by an
infinite rough surface which is supposed to be a local perturbation of a plane.
A novel version of reverse time migration (RTM) is proposed to reconstruct the
shape and location of the rough surface. The method is based on a modified
Helmholtz-Kirchhoff identity associated with a special rough surface, leading
to a modified imaging functional which uses the near-field data generated by
point sources as measurements. The modified imaging functional always reaches a
peak on the boundary of the rough surface for sound-soft case and penetrable
case, and hits a nadir on the boundary of the rough surface for sound-hard
case. Furthermore, we also establish the RTM method associated with the
far-field data generated by plane waves. As far as we know, this is the first
result for the RTM method with the far-filed data. Numerical experiments are
presented to show the powerful imaging quality.
