To equalize the coverage of the irregularly sampled subset I applied three different regularization methods: conventional binning after NMO, partial stacking by calibrated AMO, and inversion to common offset (ICO). The model is a common offset section with zero effective azimuth, 800m nominal offset and regular CMP spacing of 17.5 m. Figure fold17 shows the fold distribution for the subset binned at the model resolution. In addition to the original areas of missing coverage, most of the bins are now empty. This is a perfect test case for ICO using both formulations for data-space and model-space inverse.
The results of regularizing the data by partial stacking using NMO, AMO, normalized AMO, data-space ICO and model-space ICO are shown in Figures time-slice-comp-crossline. As expected, NMO nicely preserved the continuity of flat event However, the NMO action didn't interpolate for missing gaps. Also, due to the low fold of the decimated subset and the fast varying coverage between CMP bins, the signal to noise ratio changes rapidly across the section as shown on the time slice, which displays low resolution image of the channel. With un-normalized AMO, amplitudes of flat events are very distorted and aliasing noise dominates the seismic sections along the in-line and cross-line axes. The time slice shows strong acquisition footprint where the high and low amplitude anomalies are purely fold related. AMO normalization significantly improved the results. The amplitudes along the flat events are better handled as shown on the time slice. However, there is a travel-time error in the filled gaps and aliasing artifacts remain in the sections. The results of regularized ICO with row and column scaling, after 8 iterations, are better than the normalized AMO result. Amplitudes along the flat reflectors are better equalized and aliasing related noise is largely reduced. The result of model-space ICO is better than the data-space result because of better regularization of the model-space solution. A good regularizing operator that can be applied to an irregularly sampled model should improve the quality of the data-space solution.