Seismic image filtering machines, systems, program products, and computer implemented methods are provided to generate a filtered seismic image responsive to filtered seismic image data generated by attenuating coherent seismic noise from surface waves of an unfiltered wavefield constructed from unfiltered seismic image data through a single downward extrapolation of the unfiltered wavefield using a plurality of nonstationary convolution operators to perform localized filtering at each of a plurality of spatial locations of the unfiltered wavefield. Various embodiments, for example, can beneficially handle strong lateral velocity variations thus making various embodiments effective tools to remove complicated coherent seismic noise which is typically in the form of exponentially decaying evanescent waves. Embodiments of the present invention, for example, can use, as a part of the filtering mechanism, specially designed nonstationary convolution operators that are implemented in the space-frequency domain as nonstationary filters.