Noncausal $f$ -$x$ -$y$ regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data

Application on field poststack data

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Figure 6. The 3D field data cube after time migration.

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Figure 7. The imaginary part of $f$ -$x$ -$y$ NRNA coefficients at a given shift ${{a}_{x,y,{{i}_{0}}}}(f)$ for real dataset.

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Figure 8. The slice X of field data cube. (a) Original data; (b) $f$ -$x$ NRNA; (c) $f$ -$x$ -$y$ NRNA.

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Figure 9. The slice Y of field data cube. (a) Original data; (b) $f$ -$x$ NRNA; (c) $f$ -$x$ -$y$ NRNA.

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Figure 10. The time slice of field data cube. (a) Original data; (b) $f$ -$x$ NRNA; (c) $f$ -$x$ -$y$ NRNA.

The $f$ -$x$ -$y$ NRNA method is applied to a 3D image after time migration (Fig. 6). The shallow structures are simple plane layers (above 1 s) and the deep structures are complex curved layers (below 1 s). We respectively apply $f$ -$x$ NRNA and $f$ -$x$ -$y$ NRNA to enhance the reflectors of this 3D image cube. Fig. 7 shows the imaginary part of $f$ -$x$ -$y$ NRNA coefficients at a given shift ${{a}_{x,y,{{i}_{0}}}}(f)$ . Similar to synthetic example, the $f$ -$x$ -$y$ NRNA coefficients are smooth and reflect the information of event dips. In this example, we use M=2 for $f$ -$x$ -$y$ NRNA and M=8 for $f$ -$x$ NRNA, respectively. Figs. 8(a)- 8(c) and 9(a)- 9(c) respectively shows the X and Y slices after $f$ -$x$ NRNA noise attenuation and $f$ -$x$ -$y$ NRNA noise attenuation. We can find that $f$ -$x$ -$y$ NRNA method can give a better result than $f$ -$x$ NRNA method. The result of $f$ -$x$ -$y$ NRNA has a much better lateral continuity. These two methods not only improve the shallow plane events evidently (e.g. 0s -0.5s), but also improve the deep curved surface events (e.g. the area indicated by ellipse). This is because these two methods both are nonstationary methods, which is suitable for curved events. In addition, comparing $f$ -$x$ NRNA and $f$ -$x$ -$y$ NRNA methods from time slices (Fig. 10(a)- 10(c)), one can also see that the $f$ -$x$ -$y$ NRNA gives more consistent result. The lateral continuity and trace-by-trace consistency of the reflections are crucial in structural interpretation of seismic data by reflection picking especially for the auto-picking tools of interactive interpretation systems (Fomel, 2010).

Noncausal $f$ -$x$ -$y$ regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data