Reverse time migration for inverse acoustic scattering by locally rough surfaces

Consider the inverse scattering of time-harmonic acoustic scattering by an infinite rough surface which is supposed to be alocal 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 the sound-soft case and the penetrable case, and hits a nadir on the boundary of the rough surface for the 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-field data. Numerical experiments are presented to show the powerful imaging quality.