EMD-seislet transform |

real-0,real-z,real-eseist-0,real-eseist-dif-g,real-eseist-z,real-seist-0,real-seist-dif-g,real-seist-z,real-fx-0,real-fx-dif-g,real-fx-z
Denoising test. (c) Denoised data using EMD-seislet domain thresholding. (d) Noise section corresponding to (c). (f) Denoised data using seislet domain thresholding. (g) Noise section corresponding to (f). (i) Denoised data using FX Decon. (j) Noise section corresponding to (i). (b),(e),(h) and (k): Zoomed sections for the frame boxes in (a), (c), (f), and (i), respectively.
Figure 6. |
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real-femdr-seis0-3d,real-femdr-seis-thr-3d
(a) EMD-seislet domain before thresholding. (b) EMD-seislet domain after thresholding.
Figure 7. |
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We use a real data example shown in Figure 6a to demonstrate the performance of the proposed EMD-seislet in attenuating random noise. Figure 6c shows the denoised result by thresholding in the EMD-seislet transform domain. Figure 6d shows the removed noise section using EMD-seislet thresholding. 2% of EMD-seislet coefficients were retained. Despite the complicated structures of the seismic image, the proposed approach obtains a successful denoising performance. Figure 6f shows the denoised result using the traditional seislet thresholding method. Figure 6i shows the denoised result using the FX Decon method. Figures 6g and 6j show the removed noise corresponding to the seislet thresholding method and the FX Decon method, respectively. Figures 6b, 6e, 6h, and 6k show the enlarged sections (corresponding to the frame boxes in Figure 6). From the comparison in Figure 6 the proposed approach obtains the best result, while the seislet thresholding is over-smoothing, and the FX Decon harms some of the signal energy. The over-smoothing effect of the seislet thresholding method may be due to the over-smooth local slope calculated using the PWD algorithm. The signal-leakage problem of the FX Decon method has been widely studied in the literature, e.g., in Chen and Ma (2014). The EMD-seislet domains before and after applying the thresholding operator are plotted in Figures 7a and 7b, respectively. It is clear that the thresholding removes most low-amplitude coefficients in the sparse EMD-seislet domain.

EMD-seislet transform |

2019-02-12