Mapping back to the x-t domain

The mapping from $p-\tau$ to x-t is a simple superposition of linear events. Each sample in $p-\tau$ becomes a line in x-t. Figure  has three panels. The top panel is the original data in x-t; it is a single dipping event. The amplitude is constant along the event and there are no negative values in the data. The middle panel shows the x-t data reconstructed from the aliased $p-\tau$ data. The high frequency energy scattered over the plot is the, mispositioned, aliased data. The bottom panel shows the x-t data reconstructed from the slant stack data after application of the anti-alias mask. The dispersed aliased data is removed but there are still some artifacts. The frequency content of the original data has not been correctly recovered. This is despite the fact that a ``rho'' filter was applied to correct for the high frequencies lost in the slant stack transform. The rho filter is a correction derived under the assumption that the data is continuous and has infinite aperture. The artifacts result from the finite sampling and finite aperture of the original x-t data.

 

single-rec
Figure 4 Top: original data, Middle: data reconstructed from the aliased slant stack, Bottom: data reconstructed from the slant stack with the aliased data masked out.