Method for seismic signal denoising based on generalized S-transform and nonlinear complex diffusion

This paper aims to improve the problem of seismic signal enhancement and noise filtering by utilizing the generalized S-transform (GST) and nonlinear complex diffusion (NCD) methods. GST and its inverse transform (IGST) can decompose the original seismic signal into several sub-component signals in terms of the instantaneous frequencies to discern the distribution of various frequencies in the entire signal. The imaginary value generated by the NCD process, which can be used as the directional structure indicator to suppress the noise and enhance the effective signal. Therefore, we present a denoise method of seismic signal based on generalized S-transform and nonlinear complex diffusion (GSNCD). GSNCD, is a decomposition, denoise, and reconstruction method, with three key features: (1) A new GST transform is proposed under the GST framework, which uses the characteristic of the higher frequency resolution in high frequency and the higher time resolution in low frequency to decompose the signal into sub-component signals as different frequencies, and the sub-component signals are used to determine the structural tensor of seismic signal; (2) a fixed diffusion coefficient of complex diffusion is improved to adjust the adaptive iteration step size; (3) the sub-component seismic signals are calculated to avoid filtering deviation caused by fixed inclination angle. Finally, we reconstruct the processed sub-component signals into a complete signal. The simulations and real example fully verify the effectiveness of GSNCD in seismic signal denoising, with particular improvements in the attenuation at the data edge. In the ground motion signal test, the signal-to-noise ratio (SNR) after denoising by GSNCD increased from −2.50 dB to 13.83 dB. In two scenarios tests of exploration signals, the SNR of GSNCD is 12.09 dB and 11.19 dB, respectively, demonstrating better relative error and stability compared to other denoise methods such as Wavelet, empirical mode decomposition (EMD), adaptive NCD (ANCD), damped rank-reduction (DRR) and structural filtering method applied in the low-SNR seismic signal.