The synthetic data

Figure 6a shows a synthetic shot gather for a 1D medium. This gather is corrupted with internal multiples only. In Figure 6b, we display the internal multiple model obtained using the CFP approach Berkhout and Verschuur (1999). This internal multiple model is perfect and could be directly subtracted from the data in Figure 6a. Note that the amplitude of the internal multiples is significantly less than the amplitude of the primaries, making the $\ell^2$-norm unsuitable for estimating the shaping filters. Figure 7 displays the histograms of both the data and the internal multiples. The narrow peak of the noise indicates that the $\ell^1$-norm should be used.

 

inter
Figure 6 (a) A synthetic shot gather infested with internal multiples. (b) The internal multiples model obtained using the CFP technology. This model matches the internal multiples in (a).

 

histodata Figure 7 Histograms of the input data (Figure 6a) and of the noise (Figure 6b). The density function of the noise is much narrower than for the data. The $\ell^1$-norm should be used to estimate the signal.