Abstract: Seismic imaging apparatus for receiving data propagated through sub-surface structure from a seismic source to at least one seismic receiver and forming an image therefrom, the apparatus comprising: an imager for forming an initial image from said data including initial locations of seismic features indicated in said data, a migrator, associated with said imager, for carrying out seismic migration over at least two layers or depth levels to provide corrections to said initial locations, said migrator comprising a krylov space expander for carrying out a krylov space expansion of the exponent of a square root operator, the operator being for defining a wave propagation between respective layers, and a corrector, for using said corrections with said initial locations to form a seismic image indicating said features.