Noniterative f-x-y streaming prediction filtering for random noise attenuation on seismic data

3D synthetic CMP gather

A 3D synthetic CMP gather created by Liu and Chen (2013) shows hyperbolic events (Fig. 5a). The data size is 126-sample (time) $\times$ 101-sample (X) $\times$ 101-sample (Y). The corresponding noisy data is shown in Fig. 5b. The challenge in this case is to account for both strong random noise and nonstationary events. Fig. 6a shows the denoised result using the 2D $f$ -$x$ SPF with 5-sample ($x$ ) filter size, which uses the scale parameters of 1.0 ( $\lambda_{f}$ ) and 4.5 ( $\lambda_{x}$ ). Note that the $f$ -$x$ SPF can attain relatively high SNR (Table 2). However, it cannot provide sufficient protection for curve events; the events at far offsets can be destroyed (Fig. 6a) and part of the signals are left (Fig. 6b). Figure 6c is the denoised result by using the 3D curvelet transform, we adopted the percentage threshold with 10% to mute the random noise, and the 3D curvelet transform effectively suppresses the noise, but part of the signal energy leaks into the noise profile at $-0.5 \sim 0.5$ km (X) (Figure 6d). We compared the proposed method with the 3D $f$ -$x$ -$y$ RNA, and the filter size is 5-sample ($x$ ) $\times$ 5-sample ($y$ ). The denoised result (Fig. 6e) and the removed noise (Fig. 6f) illustrate that the $f$ -$x$ -$y$ RNA protects more signal by removing less noise. The parameters of the 3D $f$ -$x$ -$y$ SPF are selected as 1.0 ( $\lambda_{f}$ ), 4.5 ( $\lambda_{x}$ ), and 4.5 ( $\lambda_{y}$ ), respectively. The filter size of the 3D SPF is the same as that of the 3D RNA. The proposed method recovers the curved events reasonable well (Fig. 6g), similar to the $f$ -$x$ -$y$ RNA. However, the $f$ -$x$ -$y$ SPF saves more computational resources and reveals a higher SNR than the $f$ -$x$ -$y$ RNA (Table 2).

cmpmod,cmpnoise
Figure 5. Synthetic 3D CMP gather (a) and noisy data (b).

cmpspf2,cmperrspf2,cmpct,cmperrct,cmprna,cmperrrna,cmpspf3,cmperrspf3
Figure 6. Denoised result by the $f$ -$x$ SPF (a), noise removed by the $f$ -$x$ SPF (b), denoised result by the 3D curvelet transform (c), noise removed by the 3D curvelet transform (d), denoised result by the $f$ -$x$ -$y$ RNA (e), noise removed by the $f$ -$x$ -$y$ RNA (f), denoised result by the $f$ -$x$ -$y$ SPF (g), noise removed by the $f$ -$x$ -$y$ SPF (h).

Table 2: Comparison of the SNR and time consumption among different methods.

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Noniterative f-x-y streaming prediction filtering for random noise attenuation on seismic data