Introduction

Multiples are multiplicative events seen in seismic profiles, which undergoes more than one reflections Wu et al. (2016). Multiple attenuation is one of the most important steps in seismic data processing, especially for marine data processing. Instead of being incoherent along the spatial direction like random noise Lin et al. (2015); Chen et al. (2016), the multiple reflections are coherent and behave nearly the same as the primary reflections, which makes it very difficult to remove them using simple signal processing methods. The surface related multiple elimination (SRME) is one of the most appealing approaches to attenuate the multiple reflections, which includes two main steps: multiple prediction and adaptive subtraction Huo and Wang (2009); Verschuur et al. (1992). The surface related multiple reflections are first predicted based on the SRME theory and then adaptively subtracted from the raw data record. The adaptive subtraction step is intended to adjust for the mismatch of amplitude and phase during the SRME prediction step. There have existed several ways for designing the adaptive subtraction filters. Verschuur et al. (1992) proposed the classic least-squares based method for building the adaptive subtraction filter, which is called the stationary matching filter Jiao et al. (2015). Wang (2003b) proposed an expanded multiple multichannel matching filter, which exploits more local time and phase information to match the multiple reflections. The regularized optimization is also adopted for non-stationary matching filtering Chen and Fomel (2015); Fomel (2009a), which better appeals to the real non-stationary seismic data. Another widely used approach to attenuate multiple reflections is by dip filtering after normal moveout (NMO) of primary reflections. While the primary reflections are flattened after NMO, the multiple reflections cannot be flattened in the NMO corrected gather. Usually a Radon transform is used to remove the unflattened multiple reflections Wang (2003a); Foster and Mosher (1992); Donno (2011); Zhuang et al. (2015); Xue et al. (2016); Abbad et al. (2011). The dip filtering based approach can not only attenuate the surface-related multiple reflections, but also can attenuate high-order multiple reflections or interbed multiple reflections. When processing the marine field seismic data, the SRME method and the dip filtering based method are usually combined to obtain the optimal suppression of all types of multiple reflections.

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.