1. A computer implemented method to generate a filtered seismic image on a display responsive to seismic image data filtered by attenuating coherent seismic noise from surface waves of an unfiltered wavefield through a single downward extrapolation using specially-constructed nonstationary convolution operators to perform localized filtering at each of a plurality of spatial locations of the unfiltered wavefield, the computer implemented method comprising the steps of: constructing, by a computer in a first computer process, an unfiltered wavefield delineated by a plurality of spatial locations from unfiltered, unsorted seismic image data generated responsive to a plurality of seismic energy signals propagated through a surface wave propagation zone and received from a seismic image receiver; building, by the computer in a second computer process, a plurality of nonstationary convolution operators, one for each of the plurality of spatial locations of the unfiltered wavefield, responsive to constructing the unfiltered wavefield in the first computer process for each of the plurality of spatial locations of the unfiltered wavefield, each of the plurality of nonstationary convolution operators being based on a coordinate location of each of the plurality of spatial locations of the unfiltered wavefield within the unfiltered wavefield, and a space-variant velocity, temporal frequency, transverse wavenumber, and wavelength of the unfiltered wavefield at each of the plurality of spatial locations; extrapolating, by the computer in a third computer process, responsive to building each of the plurality of nonstationary convolution operators, the unfiltered wavefield at each of the plurality of spatial locations of the unfiltered wavefield to a depth level below the surface wave propagation zone of the seismic energy signals using, at each of the plurality of spatial locations, at least one of the plurality of nonstationary convolution operators built by the computer in the second computer process associated with that one of the plurality of spatial locations, to thereby locally filter each of the plurality of spatial locations of the unfiltered wavefield; and generating, by the computer in a fourth computer process, a filtered seismic image on a display, adapted to be in communication with the computer, responsive to each of the plurality of spatial locations of the unfiltered wavefield locally filtered by the computer in the third computer process.