Field data example

Next we apply the proposed method to the real migrated 3D land seismic dataset shown in Figure 18. The 3D seismic image corresponds to a land dataset after time migration. The field dataset goes through a normal seismic processing workflow, e.g., muting the dead traces, ground roll removal, surface-consistent deconvolution, pre-stack noise attenuation by the FX method, NMO-based velocity analysis, and kirchhoff time migration. The temporal sampling interval is 4 ms. There are 200 inlines and 50 crosslines, with trace spacings of 5 m and 10 m, respectively. Figure 19 shows the denoising comparison using different methods. From the previous synthetic examples, we understand the differences for different rank-reduction related methods. Therefore, in this example we examine the denoising performance using the seislet transform (Fomel and Liu, 2010). The seislet transform is deemed to be the sparsest transform for seismic data. The denoised data using the seislet thresholding method, the rank-reduction method, and the proposed method are shown in the left column of Figure 19, respectively. The middle column of Figure 19 shows the corresponding noise cubes of the three methods. Since for the field data example we do not have the pure signal for calculating the SNR, we can only use the local similarity metric to evaluate the denoising performance. The general criterion is that the local similarity between the denoised data and removed noise should be negligible provided that there is no signal leakage in the removed noise. The local similarity cubes corresponding to the three methods are shown in the right column of Figure 19. To make the removed noise comparably strong, we preserve 8% largest coefficients in the seislet domain. We use rank $N=21$ for the rank-reduction method and use rank $N=30$ for the proposed method. Comparison of the local similarity shows that the seislet transform and the rank-reduction methods both cause significant signal leakage, while the proposed method is almost damage-free for the useful signals. It is clear that when removing the same amount of random noise, it is able to preserve the most signal energy for the proposed method. At the same time, the new method can get a smoother result than the rank-reduction method, and same smoothness level compared with the seislet thresholding method. The spectrum comparison for the field data example is plotted in Figure 20, where the proposed method preserves more signal spectra than the seislet method, but removes more noise spectra than the rank-reduction method. The zoomed comparison in Figure 21 makes this even more obvious.

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Figure 18. Real 3D seismic data. The green box highlights the zooming area for detailed comparison.

r3d-seis,r3d-seis-n,r3d-simi3,r3d-lr,r3d-lr-n,r3d-simi1,r3d-olr,r3d-olr-n,r3d-simi2
Figure 19. Denoising comparison. (a) Result using the seislet thresholding method. (b) Removed noise corresponding to (a). (c) Local similarity between (a) and (b). (d) Removed noise using the rank-reduction method. (e) Removed noise corresponding to (d). (f) Local similarity between (d) and (e). (g) Result using the proposed method. (h) Removed noise using the proposed method. (i) Local similarity between (g) and (h).

r3d-fk,r3d-seis-fk,r3d-lr-fk,r3d-olr-fk
Figure 20. Spectrum comparison for the field data example. Spectrum of (a) real seismic data, (b) result using the seislet thresholding method, (c) result using the rank-reduction method, and (d) result using the proposed method.

r3d-z,r3d-seis-z0,r3d-lr-z,r3d-olr-z0
Figure 21. Zoomed denoising comparison for the field data example. (a) Real seismic data. (b) Result using the seislet thresholding method. (c) Result using the rank-reduction method. (d) Result using the proposed method. The arrows highlight the difference between (b) and (d).