Subtracting the coherent noise in real data

For purposes of comparison, I used the CMP gather of Figure 6 again. The filter size is as before (a=30,1). I iterated 45 times before estimating the PEF for the coherent noise. Then I iterated 20 times, for a total of 65 iterations.

The coherent noise attenuation again resembles that obtained with the filtering approach. In Figure 15, I show the result of the inversion. Figure 15a displays the model space, Figure 15b the reconstructed data from 15a, Figure 15c the noise model for the data (${\bf A_n^{-1}m_n}$), and Figure 15d the residual. The noise model is mainly composed of the coherent noise I am trying to attenuate. The residual shows linear events scattered throughout the panel. I think this problem can be partially solved using nonstationary filters as opposed to a stationary one Guitton et al. (2001). The importance of the linear events in the residual does not, however, negate the efficiency of this method. Because the amplitude spectrum of the residual in Figure 16b is whiter than the spectrum of the input data in Figure 16a, the fitting of the data was successful.

 

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Figure 15 Subtracting the coherent noise in real data. (a) An estimated model space. (b) The reconstructed data from the model space. (c) The estimated coherent noise ${\bf A_n^{-1}m_n}$. (d) The residual after inversion. Click Movie to see how the four panels evolve as the iterations continue.

 

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Figure 16 (a) The amplitude spectrum of the input data in Figure 6a. (b) The amplitude spectrum of the residual after inversion. (c) The normalized objective function. Click Movie to see how the two panels b and c evolve as the iterations continue.