Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition

Field example

The field data is a multi-component p-wave image, shown in Figure 12. The seismic section is very noisy, especially in the shallow part.The denoising results using three mentioned approaches and their corresponding noise sections are shown in Figure 13. Most of the profile are horizontal, which makes $f-x$ EMD a potential denoising approach. However, applying $f-x$ EMD will result in loss of some details, as shown in the noise section of $f-x$ EMD (Figure 13b). The denoising performance for $f-x$ SSA and the proposed approach seems quite similar. However, when we look at the zoomed sections pointed out by the frame box A, shown in Figures 14a and 14b, we find that the denoised result for the proposed selective hybrid approach is much cleaner. To compare the signal preservation effect, we can look at the zoomed sections pointed out by the frame box B, shown in Figures 14c and 14d. It's obvious that even though the proposed approach preserve more useful dipping energy, the region of the processing window indeed becomes noisier. However, this is not important considering the preservation of useful signal. We only use one selective processing window in this test, as shown in Figure 13b.

clean,linear
Figure 6. Synthetic data example for testing. (a) Clean data. (b) Noisy data (SNR=-4.725).

linear-fxemd0,linear-fxmssa0,linear-fxemdmssa0,linear-fxemd-noise0,linear-fxmssa-noise0,linear-fxemdmssa-noise0
Figure 7. Comparison of denoising effects. (a) Denoised using $f-x$ EMD (SNR=1.174). (b) Denoised using $f-x$ SSA (SNR=-1.217). (c) Denoised using the proposed selective hybrid approach (SNR=3.044). (d) Noise section corresponding to (a). (e) Noise section corresponding to (b). (f) Noise section corresponding to (c).

traces
Figure 8. Amplitude comparison for the 25th trace of the linear example.

hyper-clean,hyper
Figure 9. Synthetic data example for testing. (a) Clean data. (b) Noisy data (SNR=3.439).

hyper-fxemd0,hyper-fxmssa0,hyper-fxemdmssa0,hyper-fxemd-noise0,hyper-fxmssa-noise0,hyper-fxemdmssa-noise0
Figure 10. Comparison of denoising effects. (a) Denoised using $f-x$ EMD (SNR=3.136). (b) Noise section corresponding to (a). (c) Denoised using $f-x$ SSA (SNR=3.899). (d) Noise section corresponding to (b). (e) Denoised using the proposed selective hybrid approach (SNR=5.334). (f) Noise section corresponding to (c). The frame boxes in (b) are the two selective hybrid processing windows.

hyper-traces
Figure 11. Amplitude comparison for the 15th trace of the hyperbolic example.

pp
Figure 12. Field data example for testing.

pp-fxemd,pp-fxemd-noise0,pp-fxmssa,pp-fxmssa-noise0,pp-fxemdmssa,pp-fxemdmssa-noise0
Figure 13. Comparison of denoising effects. (a) Denoised using $f-x$ EMD. (b) Noise section corresponding to (a). (c) Denoised using $f-x$ SSA. (d) Noise section corresponding to (b). (e) Denoised using the proposed selective hybrid approach. (f) Noise section corresponding to (c). The frame box in (b) is the selective hybrid processing window.

pp-mssa-zoom,pp-emdmssa-zoom,pp-emd-zoom,pp-emdmssa-zoom1
Figure 14. Comparison of zoomed sections. (a) & (b): comparison for frame box A in Figure 13. (c) & (d): comparison for frame box B in Figure 13.

Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition