Following equation (10), we compute offset-domain CIGs with the 2-D deconvolution imaging condition. Figure a shows the offset-domain CIGs computed with the 1-D crosscorrelation imaging condition. As expected, they show less resolution than the offset-domain CIGs computed with the 2-D deconvolution imaging condition (Figure c).
We transform offset-domain CIGs into angle-domain CIGs following the method presented by Sava and Fomel (2000). Figure b shows the angle-domain CIGs computed with the 1-D crosscorrelation imaging condition. They also show less resolution than the angle-domain CIGs computed with the 2-D deconvolution imaging condition (Figure d).
We now compare the previous gathers with the gathers resulting from the migration of the data with a lower velocity. Figures a to d display the offset-domain and the angle-domain CIGS computed with the 1-D crosscorrelation imaging condition and the 2-D deconvolution imaging conditon for the low velocity, respectively. Notice that with the 2-D deconvolution the curvature of the events, due to the low migration velocity, appears more clear.
Finally, we use the angle-domain Radon transform (ART) methodology described in Sava and Guitton (2003) to estimate the curvature of the reflectors in the angle-domain CIGs. Since the curvature of the reflectors in the ART domain is related to velocity errors, a better curvature estimation can lead to a better velocity estimation. A flat reflector in the angle-domain CIG maps at zero q (curvature index) in the ART CIGs. Conversely, a reflector with moveout in the angle-domain CIG should map away from zero q in the ART CIG.
In Figure we compare the ART CIGs with the correct velocity (Figure a and Figure b) and the low velocity (Figure c and Figure d). In both cases we calculated the angle-domain CIGs with 1-D crosscorrelation (Figure a and Figure c) and 2-D deconvolution (Figure b and Figure d).
Notice that 2-D deconvolution imaging condition gives ART CIGs that are easier to interpret. Also notice that due to the lack of resolution, ART CIGs computed with 1-D crosscorrelation and the correct velocity Figure (a) show events that can be misinterpreted as reflectors with the wrong velocity. In addition, ART CIGs computed with 1-D crosscorrelation and the wrong velocity Figure (c) show events that can be misinterpreted as reflectors with the correct velocity. This problem is reduced with the 2-D deconvolution imaging condition (Figure b and Figure d) .