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

Introduction

The rapid development of the exploration for unconventional resource raise a higher demand for random noise attenuation of pre- and post-stack seismic profile because of the higher demand for processing noisy land seismic data. Existing denoising techniques can be divided into four categories. The first is based on the predictive property of useful signal, such as predictive filtering (Wang, 1999; Liu et al., 2012; Abma and Claerbout, 1995; Canales, 1984; Chen and Ma, 2014). These types of methods can achieve good result for linear events but may fail in handling complex or hyperbolic events. The way to deal with this linear-events dependence limitation is to use small local windows. However, different window size will results in different denoising effects and window size is actually data dependent. Thus, localized versions of the first type of methods with small processing windows are often hard to be implemented in practice. The second is based on statistical properties of seismic data, such as mean filter (Bonar and Sacchi, 2012), median filter (Chen et al., 2014c; Chen, 2014). These types of methods are often used to attenuate specific types of random noise. For example, a mean filter is only effective to attenuate highly Gaussian white noise, and a median filter can only remove spike-like random noise with excellent performance. The third is based on extracting the principal components of seismic data, such as singular spectrum analysis (SSA) (Oropeza and Sacchi, 2011; Chen et al., 2014b), and $f-x$ EMD (Bekara and van der Baan, 2009; Chen et al., 2014d). For these methods, first several components are selected to represent the main useful signals. These types of methods are based on a pre-known mode or rank of the seismic data. However, for complex seismic data, the mode or rank is hard to select, and for curved events, the rank or mode tends to be high and thus will involve a serious rank-mixing problem. The fourth is based on a transformed domain thresholding strategy, such as the papers of Chen et al. (2014a); Neelamani et al. (2008); Gao et al. (2006); Fomel and Liu (2010). The transformed domain thresholding methods can be easily implemented, however, they require strictly that the transformed domain is sparse. For complicated seismic profiles, seldom sparsity-promoting transform can obtain an ideal sparse representation, which limits the use of the fourth type of methods.

Huang et al. (1998) proposed empirical mode decomposition (EMD) to prepare stable input for the Hilbert Transform. The essence of EMD is to stabilize a non-stationary signal. That is, to decompose a signal into a series of intrinsic mode functions (IMF). Each IMF has a relatively local-constant frequency. The frequency of each IMF decreases according to the separation sequence of each IMF. EMD is a breakthrough in the analysis of linear and stable spectra. It adaptively separates non-linear and non-stationary signals, which are features of seismic data, into different frequency ranges. Bekara and van der Baan (2009) applied $f-x$ EMD to attenuation of random noise, which was demonstrated to perform better than $f-x$ predictive filtering. Recently a type of hybrid denoising approaches using EMD is becoming attractive. Chen et al. (2012) proposed to combine EEMD, an enhanced version of EMD, with wavelet domain thresholding, to obtained a better denoised result. Similarly, Dong et al. (2013) combined $f-x$ EMD with curvelet domain thresholding, and also obtained better results compared with individual denoising performances. Chen and Ma (2014) noticed the problem of $f-x$ EMD in dealing with complex structure and solve it by introducing $f-x$ empirical mode decomposition predictive filtering (EMDPF), which combine the advantage of both $f-x$ EMD and $f-x$ predictive filtering. A combination between $f-x$ EMD and one other random noise attenuation approach is becoming more and more attractive because of the special property of $f-x$ EMD in preserving horizontal events.

In this paper, we demonstrate the horizontal-preservation ability of $f-x$ EMD and show the problem of $f-x$ EMD in handling with dipping events. We summarize the connections between the currently existing EMD based denoising approaches and generalize the methods into a general hybrid framework. The principle is to first separate the events in a seismic profile into two parts: horizontal events and dipping events, and then denoise them individually. Because of the strong horizontal-preservation ability of $f-x$ EMD, the horizontal events can be effectively denoised and fully preserved. The dipping events can be preserved by applying a dipping-events retriever that can denoise and preserve dipping events effectively. The hybrid approach solves the problem of $f-x$ EMD in preserving the dipping events, and improve the dipping-event retrieving operator by obtaining cleaner denoised horizontal events.

Considering that in most seismic profiles, dipping events or steeply dipping events takes up a small percent of the total signals, a selective hybrid strategy is also proposed. In the selective hybrid framework, only specific processing windows are processed twice by two different denoising operators, which can helps to maximize the effectiveness of $f-x$ EMD and the whole processing efficiency. Instead of combining $f-x$ EMD with $f-x$ predictive filtering, wavelet thresholding or curvelet thresholding, a novel hybrid approach is to combine $f-x$ EMD with $f-x$ singular spectrum analysis (SSA). Both synthetic and field data examples demonstrate the superior property of the proposed approach.

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