Image gather reconstruction using StOMP |
For the correlation gather construction problem, I attempted to encode multiple different correlations into each data sample. In terms of operators, we can think of the subsampling of correlations as applying a subsampling operator to all possible correlations . In the phase encoded case, we are going to add another operator that first sums a number of different correlations together and then subsamples them leaving a new dataset . This in turn changes the operator in algorithm 1 to . For this test, I combined 20 different correlations in a random pattern to form each data point. Figure 8 shows the same three offset and angle gathers seen in Figures 4 and 6. Note the noticeably better job recovering the deeper portion of subsurface offsets. Figure 9 shows the angle gathers from the fully sampled correlation gathers and the subsampled, phase encoded gathers muted to the believable angle range. The gathers with the notable exception of more lower frequency noise in the recovered gathers.
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Figure 8. A, B, and C show the recovered subsurface offset gathers using compressive sensing as shown in plot A, B and C of Figure 4 and 6. D, E, and F show the corresponding angle gathers. Note the noticeable improvement in A, B, and C compared to the data shown in Figure 6. |
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Figure 9. A comparison of the angle gathers after muting of the fully sampled correlation gathers (A, B, and C) and the phase encoded, subsampled correlation gathers (D, E, and F). |
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Image gather reconstruction using StOMP |