Complex variational mode decomposition for slop-preserving denoising

We have introduced a new decomposition method for seismic data, termed complex variational mode decomposition (VMD), and we have also designed a new filtering technique for random noise attenuation in seismic data by applying the VMD on constant-frequency slices in the frequency–offset (f–x) domain. The motivation behind this paper is to overcome the potential low performance of empirical mode decomposition (EMD) for energy preservation of the steeply dipping events when used for noise attenuation, and low resolution when used for signal decomposition. The VMD is proposed to decompose a signal into an ensemble of band-limited modes. For seismic data consisting of linear events, the constant-frequency slices of its f–x spectrum are exactly band-limited. The noise attenuation algorithm is summarized as follows. First, the Fourier transform is applied on the time axis of the 2-D seismic data. Next, the VMD is applied on each frequency slice of the f–x spectrum and the decomposed modes are combined to obtain the filtered frequency slice. Finally, an inverse Fourier transform is applied on the frequency axis of the f–x spectrum to obtain the denoised result. The resulting VMD-based noise attenuation method is equivalent to applying a Wiener filter on each decomposed mode, which is achieved during the decomposition progress. We also applied 2-D VMD on 3-D seismic data for denoising. Numerical results show that the proposed VMD-based method achieves a higher denoising quality than both the f–x deconvolution method and the EMD-based denoising method, especially for preserving the steep slopes.