Poststack land data multiple removal example

In this section we attenuate in the poststack domain surface-related multiples with shaping filters that we estimate with the 312#312- and 1#1-norm. These filters are non-stationary. Figure a shows the multiple-infested data. Figure b displays the multiple model computed with the Delft modeling approach (). Note that for this gather, the amplitude differences between the primaries and the multiples are not very strong. Our goal is to illustrate the use of the 1#1-norm in a more general case when surface-related multiples are present in the data. We specifically focus on the event at 1.6s in Figure . This event is a primary that we want to preserve during the subtraction.

Figures displays the estimated signal when the non-stationary shaping filters are computed with the 312#312 and 1#1-norm. The amplitude of the primary at 1.6s is well preserved with the 1#1-norm in Figure a. However, the amplitude of this primary is attenuated with the 312#312-norm as displayed in Figure b. Figure shows a comparison between the subtracted noise with the 1#1 (Figure a) and the 312#312-norm (Figure b). We conclude that the 312#312-norm tends to subtract too much energy.

This last example proves that the estimation of shaping filters can always be done with the 1#1-norm. The good thing about our inversion scheme and the objective function in equation () is that only one parameter (12#12) controls the 321#321 behavior. Thus we can decide to switch from one norm to another very easily. In Figure , I show a histogram of the input data and of the estimated noise with the 1#1 and 312#312-norms. The theory predicts that the distribution of the 312#312 result should be gaussian and that distribution of the 1#1 result should be exponential. Figure corroborates this.

 

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Figure 10 (a) Stack infested with multiples. (b) The multiple model computed with the Delft modeling approach. The subtraction is done poststack.

 

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Figure 11 (a) The estimated primaries with 1#1-norm adaptive subtraction. (b) The estimated primaries with 312#312-norm subtraction. The primary at 1.6s is very attenuated with the 312#312-norm. The 1#1 technique preserves its amplitude better.

 

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Figure 12 (a) The estimated multiples with the 1#1-norm subtraction. (b) The estimated multiples with the 312#312-norm subtraction. The 312#312-norm tends to over-fit some multiples that creates some leaking of primaries in the estimated noise.

 

hist7636 Figure 13 Histograms of the input data and of the estimated noise with the 1#1- and 312#312-norms. As predicted by the theory, the density function with the 1#1-norm is much narrower than with the 312#312-norm.