Seismic Noise Attenuation Using Variational Mode Decomposition and the Schroedinger Equation

We propose a robust seismic noise attenuation method by an alternative denoising procedure using variational mode decomposition (VMD) combined with the Schrodinger equation thresholding, referred as VMD-Schrodinger interval-thresholding (VMD-Schrodinger IT) method. In the proposed method, VMD is used as a subband-like filter to get a series of uncorrelated intrinsic mode functions (IMFs) from low frequency to high frequency. For IMFs having strong correlations with the original signal, the Schrodinger equation thresholding-based denoising is used to obtain the denoised IMFs. For IMFs existing weak correlations with the original signal, the noise extracted from these IMFs is used to generate several different versions of noise by altering the sample positions. These different versions of noise combined with the information extracted from these IMFs are used to reconstruct different noisy versions of the original IMFs existing weak correlations. Then, the Schrodinger equation thresholding-based denoising is applied to these different noisy data. The denoised IMFs existing weak correlations are the average of these denoised noisy versions signals. Finally, the denoised seismic data are the sum of these denoised IMFs. Compared with the wavelet thresholding method, iterative empirical mode decomposition (EMD) interval-thresholding method, and quantum mechanics-based signal denoising method, the proposed method can more effectively extract weak signals from the noise-dominant components of seismic data, while protecting both the low-frequency and high-frequency components of the seismic trace, especially exhibiting good performance for complex dipping events. The synthetic and field data applications illustrate the robustness and the superiority of the proposed method.