A computer-implemented method for analyzing reflection seismic data, the method comprising: sorting the reflection seismic data into sets of data sections acquired from cross-spread gathers, each cross-spread gather corresponding to a source line of shot sources from which seismic impulses were transmitted and a receiver line of recording instruments where the set of data sections for the particular cross-spread gather were recorded; performing data enhancement on the sets of data sections to generate enhanced traces for each set of data sections acquired from a particular cross-spread gather, the performing step includes: applying, for each set of data sections acquired from the particular crossspread gather, forward normal-moveout corrections such that arrival times of primary reflection events in the particular set of data sections become more flat; estimating, for the particular set of data sections, beamforming parameters including a nonlinear traveltime surface and a summation aperture; beamforming, for the particular set of data sections and according to the beamforming parameters, to generate enhanced traces that combine contributions from original traces in the sets of data sections, each enhanced trace azimuthally surrounded by one or more original traces in the sets of data sections, and each enhanced trace located along the estimated nonlinear traveltime surface and from the summation aperture; characterized by: applying inverse normal-moveout corrections to the enhanced traces such that temporal rearrangements due to the forward normal-moveout corrections are undone, and performing additional data processing steps based on the enhanced traces with the temporal rearrangements due to the forward normal-moveout corrections undone leading to an improved image of the subsurface. sorting the reflection seismic data into sets of data sections acquired from cross-spread gathers, each cross-spread gather corresponding to a source line of shot sources from which seismic impulses were transmitted and a receiver line of recording instruments where the set of data sections for the particular cross-spread gather were recorded; performing data enhancement on the sets of data sections to generate enhanced traces for each set of data sections acquired from a particular cross-spread gather, the performing step includes: applying, for each set of data sections acquired from the particular crossspread gather, forward normal-moveout corrections such that arrival times of primary reflection events in the particular set of data sections become more flat; estimating, for the particular set of data sections, beamforming parameters including a nonlinear traveltime surface and a summation aperture; beamforming, for the particular set of data sections and according to the beamforming parameters, to generate enhanced traces that combine contributions from original traces in the sets of data sections, each enhanced trace azimuthally surrounded by one or more original traces in the sets of data sections, and each enhanced trace located along the estimated nonlinear traveltime surface and from the summation aperture; characterized by: applying inverse normal-moveout corrections to the enhanced traces such that temporal rearrangements due to the forward normal-moveout corrections are undone, and applying, for each set of data sections acquired from the particular crossspread gather, forward normal-moveout corrections such that arrival times of primary reflection events in the particular set of data sections become more flat; estimating, for the particular set of data sections, beamforming parameters including a nonlinear traveltime surface and a summation aperture; beamforming, for the particular set of data sections and according to the beamforming parameters, to generate enhanced traces that combine contributions from original traces in the sets of data sections, each enhanced trace azimuthally surrounded by one or more original traces in the sets of data sections, and each enhanced trace located along the estimated nonlinear traveltime surface and from the summation aperture; characterized by: applying inverse normal-moveout corrections to the enhanced traces such that temporal rearrangements due to the forward normal-moveout corrections are undone, and performing additional data processing steps based on the enhanced traces with the temporal rearrangements due to the forward normal-moveout corrections undone leading to an improved image of the subsurface.