Direction-adaptive Complex Diffusion Algorithm For Desert Seismic Noise Suppression

Seismic noise suppression is an important method to improve the quality of seismic data.The effect of seismic noise reduction is often affected by the characteristics of seismic noise,and the characteristics of desert random noise are far from the white Gaussian noise.The energy of desert random noise is mainly concentrated in the low frequency band and overlaps with the effective signals.Therefore,it is difficult to suppress the noise without losing the effective signal.In addition,desert random noise is weakly spatially correlated,and have the similar structural features with the effective seismic signals in some areas,further increasing the difficulty in identifying effective signals.Therefore,developing the denoising technology adapted to remove the desert random noise from low signal-to-noise-ratio seismic data has a fundamental role in improving the accuracy of seismic exploration.Nonlinear complex diffusion(NCD)is an effective method for suppressing random noise.This method expands the real domain to the complex domain by constructing a nonlinear complex-value diffusion coefficient,so that imaginary part can be approximated as the smoothed second derivative.The imaginary part can characterize the edge structure and avoid the sensitivity to noise.Therefore,the NCD can adjust the diffusion intensity under the guidance of the imaginary part,and apply different diffusion strengths to different structural features.Complex diffusion filtering shows good adaptability in suppressing seismic noise,and has the ability to suppress low-frequency colored desert random noise.However,the NCD filter algorithm uses a gradient operator to calculate the gradient direction.This gradient operator based on neighborhood information is difficult to characterize the complex structural characteristics of the seismic reflection events,especially for the reflection events with large slopes.In the case of low signal-to-noise ratio,the structural characteristics of the weakly similar desert random noise and the seismic reflection events have a certain similarity,which further affects the accuracy of the estimation of the reflection orientation.The complex diffusion filter causes distortion of the seismic reflection events while suppressing noise.Based on the structural characteristics of the reflection events,an adaptive structure-oriented complex diffusion(ASOCD)method is proposed for desert random noise suppression.This method uses the non-local radial scanning method to calculate the orientation of the reflection event.Based on the estimated the orientation of the reflection event,a direction-adaptive complex diffusion model is constructed so that diffusion can proceed along the orientation of the reflection event.In addition,an adaptive threshold is constructed,which can not only adjust the diffusion intensity according to the structure described by the imaginary part,but also use the threshold to better identify weakly similar noise and effective signals.Simulation experiments and real seismic data processing verify the effectiveness of the ASOCD algorithm.Compared with the structure characterization method based on neighborhood information,the radial scan based on non-local information can more accurately estimate the orientation of the reflection event in desert seismic data,suppress the influence of noise on the direction estimation.The adaptive threshold based on the local covariance matrix can well adjust the intensity of the diffusion,thereby enhancing the suppression of noise while preserving the effective signal.In order to alleviate the distortion of reflection events with rapidly varying slopes,a tensor complex diffusion(TCD)model is further developed for desert random noise suppression.In this paper,the TCD model is constructed by combining the directional structure tensor(DST)and the complex diffusion coefficient.The eigenvectors of DST are used to obtain an accurate estimate of the orientations of the reflection events with rapidly varying slopes and large slopes,thereby achieving the diffusion along the reflection events of complex structures.At the same time,combining the imaginary part and the structure adaptive threshold will extend the traditional real domain diffusion tensor to the complex domain,applying strong diffusion in the weakly similar noise region to enhance the ability to suppress weakly similar noise and reducing the diffusion strength in the effective signal region to effectively preserve the edges.Compared with the traditional structural tensor,DST calculates the orientation of the reflection event in the eigenvectors space of the structural tensor,which can more effectively describe the reflection events with complex structures.Simulation experiments and real seismic data processing verify that the TCD algorithm can adapt to seismic data with complex structural features.Compared with the classical real domain anisotropic diffusion method,the TCD can more effectively preserve signals while suppressing weakly similar desert background noise.