High signal-to-noise ratio (SNR) is necessary for many procedures in seismic exploration such as amplitude variation with offset (AVO) analysis, seismic attribute analysis and microseismic monitoring. The attenuation of random noise is an important subject in improving the signal-to-noise ratio (SNR) (Chen and Ma, 2014). If signal is eliminated with the noise, continuity of seismic events may be disrupted and the resulting image quality will be negatively affected. Enhancing the useful signal while preserving edge properties of the seismic profiles by attenuating random noise can help reduce interpretation difficulties and risks for oil & gas detection (Yang et al., 2015; Gan et al., 2015).

There are several classical ways for random noise attenuation: prediction based noise-attenuation approaches (Liu et al., 2011; Abma and Claerbout, 1995) such as the $f-x$ deconvolution (Gulunay, 1986; Canales, 1984) and $f-xy$ deconcolution (Liu et al., 2012; Gulunay, 2000), median filtering (Chen, 2015; Liu, 2013; Gan et al., 2016), Karhunen-Loeve transform (Jones and Levy, 1987), sparse transform domain thresholding strategies (Donoho, 1995; Fomel and Liu, 2010; Chen et al., 2016,2014; Neelamani et al., 2008) and Cadzow filtering (Trickett, 2008; Trickett and Burroughs, 2009) or multichannel singular spectrum analysis (Gao et al., 2013; Chiu, 2013; Oropeza and Sacchi, 2011). The principle of all these denoising approaches is to distinguish between noise and signal based on certain characteristics, such as the spatial coherency or the sparsity in a sparse transform domain. Chen and Fomel (2015) proposed a two-step denoising approach in order to retrieve the lost useful information from the removed noise based on local signal-and-noise orthogonalization.

In this paper, we focused on attenuating random noise in 3D seismic data using the multichannel singular spectrum analysis (MSSA) algorithm. MSSA is a data-driven algorithm developed from research on alternative tools for the analysis of multichannel time series, which is based on the truncated singular value decomposition (TSVD) (Golub and Loan, 1996) of the Hankel matrix. MSSA is also an extension of singular spectrum analysis (SSA), which is used to analyze 1D time series. Like other noise-attenuation methods, MSSA transforms the data into a domain where signal and noise are mapped onto separate subspaces and then removes the noise. However, many numerical experiments suggest that the random noise can not be completely removed using the MSSA algorithm (Huang et al., 2015). One perspective is that the TSVD can only decompose the data into a noise subspace and a signal-plus-noise subspace. In this paper, we analyzed how to theoretically decompose the input data into signal subspace and noise subspace and proposed a practical solution to apply a variable damping factor to different singular values to obtain results with higher SNR. We used both synthetic and field 3D seismic datasets to demonstrate our proposed approach.