Signal and noise separation in prestack seismic data using velocity-dependent seislet transform

Separation of primaries and pegleg multiples

Next, we use a synthetic CMP gather (Figure 6a) to test separation of primaries and pegleg multiples by VD-seislet frame. This gather was generated by Lumley et al. (1994) using Haskell-Thompson elastic modeling and a well log from the Mobil AVO dataset (Keys and Foster, 1998). The gather contains primaries and water-bottom multiples of different orders.

To separate pegleg multiples from primaries, we transform the data using VD-seislet frame by involving different VD slope fields (Figure 7a) according to equations 7 and 10. The primary velocities and calculated velocities of different-order pegleg multiples are shown in Figure 6b. The estimated curves of multiple velocities indicate accurate trends in velocity spectra. We use a nonlinear shaping-regularization scheme (equations 12-13) to separate different wavefield components, which are shaped to be sparse in the corresponding VD-seislet frame domain (Figure 7b). In this example, the pattern number in equation 11 $N$ is selected to be 4. The separated wavefields are shown in Figure 8 and display reasonably accurate separation results.

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Figure 6. Synthetic model (a) and velocity trends of primaries and multiples (b).

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Figure 7. VD slopes (a) and VD-seislet coefficients (b).

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Figure 8. Separated wavefields. Primaries (a), first-order multiples (b), second-order multiples (c), and third-order multiples (d).

Signal and noise separation in prestack seismic data using velocity-dependent seislet transform