Empirical mode decomposition (EMD) Huang et al. (1998) can adaptively decompose a non-stationary signal into different stationary components, which are called intrinsic mode functions (IMF). The oscillating frequency of each IMF decreases according to the separation sequence of each IMF. EMD has found successful applications in seismic data processing Chen (2016); Chen and Ma (2014). EMD is commonly applied in each frequency slice in the frequency-space domain and the highest wavenumber component is removed. The only parameter we need to define in such method is the number of dip components. Considering that, in practice, we commonly choose to remove the first EMD component in order to remove the highest oscillating components, the EMD based filtering is non-parametric. Because of the adaptivity and the superior performance of the EMD based smoothing in field seismic data processing, more and more researchers are turning to use this technique as a blind-processing tool in order to deal with the rapidly increasing data size in modern seismic data processing Chen et al. (2015c).
In this letter, we propose a novel EMD based approach called randomized-order EMD to attenuate multiple reflections noise Weglein et al. (2003); Fomel (2009a); Weglein (2013); Carvalho (1992). The common midpoint (CMP) gather is first flattened by using the automatically picked velocities Fomel (2009b) corresponding to the primary reflections. Then, the primary reflections are flattened while the multiple reflections are not. Since the multiple reflections and primary reflections are much similar in the near-offset part, we propose to first randomize the data along the spatial direction and make the unflattened multiple reflections behave like random incoherent noise along the spatial direction. Then the EMD based smoothing algorithm is applied to remove such incoherent noise. After EMD based smoothing, an inverse randomization step is applied, which is followed by the inverse normal moveout. The proposed approach is compared with median filtering and prediction error filtering based approaches. The performance shows that the EMD based smoothing algorithm can have stronger capability in removing the incoherent noise while preserving more primary reflections energy. The randomized-order EMD approach can not only be used in attenuating multiple reflections noise, but also be used in attenuating other types of coherent noise. The proposed method solves two long-standing problems in existing demutiple algorithms. The first one is the difficulty in separating coherent signal and coherent noise in near-offset traces, because they have very close local slopes and curvatures. The second one is the difficulty in selecting optimal parameters when applying a denoising operator. In many traditional denoising algorithms, the parameters are highly dependent on the input data set. The proposed algorithm solves the first problem by shuffling the traces along the spatial direction that help best distinguish between signal and noise. The proposed algorithm solves the second problem by using the EMD based method to adaptively process the data, where we do not need to specify any input parameter regardless of the complexity of input data set.