Randomized-order EMD

EMD was thought to be useful only in attenuating spatially incoherent noise. However, the multiple reflections noise in seismic data is spatially coherent. Here, we propose a novel randomized-order EMD in order to make EMD capable of attenuating spatially coherent noise. The randomized-order EMD can be summarized in five main procedures. Firstly, each common midpoint (CMP) gather is flattened according to the normal moveout (NMO) velocity of primary reflections. This step will require NMO velocity analysis Gan et al. (2016); Chen et al. (2015b). An automatic velocity picking approach is used to pick the NMO velocities that corresponds to the primary reflections Fomel (2009b). After the first step, the primary reflections are flattened while the multiple reflections noise of different orders are not. Secondly, the traces are shuffled randomly in order to make the unflattened multiple reflections noise spatially random. Because the primary reflections have small spatial variations, a random trace randomization along the spatial direction will not change the shape of primary reflections too much but will greatly change the spatial coherency of multiple reflections noise. More specifically, the spatially coherent multiple reflections noise can be transformed into spatially incoherent random noise. Thirdly, EMD based smoothing is applied to the randomized CMP gather to attenuate all spatially incoherent noise. Finally, the inverse trace randomization is implemented to the smoothed CMP gather, which is followed by the inverse NMO.

In this letter, EMD is utilized to attenuate noise other than random noise. The randomized order EMD is used for attenuating multiple reflections noise. Since the randomized-order EMD is a generally framework, it can also be used to attenuate any types of unwanted spatially coherent noise, such as ground roll noise Chen et al. (2015a) and point source diffraction.

Fig. 1 shows an example of the randomization process. Fig. 1a is a NMO corrected CMP gather with multiple reflections not flattened. Fig. 1d shows the section after random permutation of all the traces along the spatial direction. It is obvious that after random shuffling, the multiple reflections turn into random spikes from the spatial view while the primary reflections are still coherent. The spikes can be removed using any type of coherency-based denoising approach. Fig. 1b shows demultipled data using a common PEF filter Abma and Claerbout (1995). Fig. 1c shows the demultipled data using EMD based smoothing. Figs. 1e and 1f show the removed multiple reflections using PEF and EMD based approaches, respectively. The performance using the PEF method is not acceptable since there is still some noise left. Since we know the true signal in this example, we can quantitively compare the denoising performance between two methods. We use the signal-to-noise ratio (SNR) defined below to measure the denoising performance Gan et al. (2015); Huang et al. (2016); Chen et al. (2014a); Zu et al. (2016):

$\displaystyle SNR=10\log_{10}\frac{\Arrowvert \mathbf{s} \Arrowvert_2^2}{\Arrowvert \mathbf{s} -\hat{\mathbf{s}}\Arrowvert_2^2},$ (4)

where $\mathbf{s}$ and $\hat{\mathbf{s}}$ denote the true and estimated signals, respectively. The calculated SNRs of the original noisy data, denoised data using PEF and denoised data using EMD are 0.168 dB, 8.344 dB, and 9.061 dB, respectively. The SNR comparison confirms the better denoising performance using the EMD method.

ncmp back nrand-emd-back rand dif emd-dif
Figure 1.
(a) CMP gather. (b) Demultipled using PEF method. (c) Demultipled using the proposed approach. (d) Trace randomization result of (a). (e) Noise corresponding to (b). (f) Noise corresponding to (c).
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