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

synt,sdip
Synthetic
data (a) and slopes calculated by PWD (b).
Figure 1. |
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noise,pdip
Synthetic
noisy data (a) and slopes calculated by PWD (b).
Figure 2. |
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svsc2,vdip
Velocity
scanning (dash line: exact velocity, solid line: picked
velocity) (a) and VD slopes (b).
Figure 3. |
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A direct application of the seislet transform is denoising. We apply both PWD-seislet and VD-seislet transforms on the noisy data (Figure 2a). Figure 4a and 4b show the transform coefficients of PWD-seislet and VD-seislet, respectively. The hyperbolic events are compressed in both transform domains. Notice that PWD-seislet coefficients get more concentrated at small scale than those of VD-seislet because parts of the random noise are also compressed along inaccurate PWD slopes. Meanwhile, random noise gets spread over different scales in the VD-seislet domain, while the predictable reflection information gets compressed to large coefficients at small scales, which makes signal and noise display different amplitude characteristics. Figure 4c shows a comparison between the decay of coefficients sorted from large to small in the PWD-seislet transform and the VD-seislet transform. Seislet transform can compress the seismic events with coincident wavelets, if the slopes of the reflections are correct, the sparse large coefficients only correspond to the stacked reflection events. However, when the slopes of the reflections are not accurate, the stacked amplitude values for inconsistent wavelets will create more coefficients with smaller values. VD slopes are less affected by strong random noise than PWD slopes, which results in a faster decay of the VD-seislet coefficients. A simple thresholding method can easily remove the small coefficients of random noise. Figure 5a and 5b display the denoising results by using PWD-seislet transform and VD-seislet transform, respectively. The events after PWD-seislet transform denoising show serious distortion while VD-seislet transform produces a reasonable denoising result. For numerically comparison, we use the signal-to-noise ratio (SNR) defined as , where is the noise-free signal and is the denoised signal. The original SNR of the noisy data (Figure 2a) is -12.53 dB. The SNR of the denoised results using the PWD-seislet transform (Figure 5a) and the VD-seislet transform (Figure 5b) are 0.53 dB and 1.94 dB, respectively.

pseis,vseis,ccomp
PWD-seislet
coefficients (a), VD-seislet coefficients (b), and transform
coefficients sorted from large to small, normalized, and
plotted on a decibel scale (Solid line - VD-seislet
transform. Dashed line - PWD-seislet transform) (c).
Figure 4. |
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pclean,vclean
Denoising
result using different transforms. PWD-seislet transform (a)
and VD-seislet transform (b).
Figure 5. |
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Signal and noise separation in prestack seismic data using velocity-dependent seislet transform |

2015-10-24