Adaptive subtraction

This step is subdivided into two tasks: adaptive matching of the multiples to the original data and subtraction of the matched multiples to get the primaries Guitton (2005). To assess the ability of adaptive subtraction to restore the amplitudes lost by the migration-adjoint migration process, I applied it to the adjoint-migrated, unmuted SODCIGs (panel (b) of Figure ). Figure  shows the original [panel (a)] and the matched [panel (b)] CMP. Figure  shows the difference between the two panels in Figure  plotted with 100% clip and with the clip of the original data. The adaptive pattern matching has recovered the the original data remarkably well despite the loss of energy on the large offsets of the water-bottom primary and multiple after the migration-adjoint migration process (see panel (b) of Figure ).

 

cmp_comp2
Figure 7 Comparison between a CMP of the original data (a) and the same CMP after migration, adjoint migration and adaptive matching (b).

 

resid1
Figure 8 Residual energy after subtracting the matched CMP from the original, plotted at 100% clip (a) and at the clip of the original CMP (b).

We would like to similarly match the estimated multiples to the original data but we cannot, because nothing prevents the pattern-matching algorithm from attempting to match the primaries as well. This is obviously undesirable because, as much as possible, we want to keep the primaries as they are in the original data. Here is where the estimate of the primaries will help. We can estimate filters to simultaneously match both the estimated primaries and the estimated multiples to the data as in Guitton's thesis 2005 thus preventing the primaries to be matched to the same dataset as the multiples. An easier approach is to use the estimated primaries to compute a mask such that where the primaries are present the mask is zero and therefore the primaries are not matched when attempting to match the multiples Claerbout and Fomel (2002) . This is the approach I used here although in practice the other approach is likely to be better. In order to compute the mask I first computed the envelope of the estimated primaries, and then chose a threshold amplitude above which all samples were set to zero and below which all samples were set to one. This mask was then smoothed with a triangular filter both in offset and in time. Figure  shows the envelope of the estimated primaries and the mask.

 

mask
Figure 9 Envelope of the estimated primaries (a) and mask of ones and zeros derived from it (b).

The result of applying the weighted adaptive matching to the estimated multiples is shown in Figure . The water-bottom multiple has not been well recovered, in contrast to the other multiples. The primaries didn't leak much into the multiples, which is a very satisfactory result. Figure  shows the residual, obtained by subtracting the matched estimated multiples from the data. Here we see that although the result is not perfect, most of the multiple energy has been attenuated except for the water-bottom multiple. In particular, the primaries have been well-recovered.

 

cmp_comp3
Figure 10 Comparison between a CMP of the original data (a) and the same CMP after migration, muting of the primaries, adjoint migration and adaptive matching (b). Some residual energy from the large offset of the water-bottom primary remains and the water-bottom multiple has been imperfectly recovered.

 

resid2
Figure 11 Residual energy after subtracting the matched CMP of the multiples from the original, plotted at 100% clip (a) and at the clip of the original CMP (b).