Seismic Denoising Based On Statistical Models In The Dual-Tree Complex Wavelet Domain

Seismic signal denoising is a significant step in seismic signal processing and it is of great importance in processing and interpreting seismic signal subsequently. Dual-tree complex wavelet transform provides a new kind of multi-scale analysis tool,which is an improvement of the standard wavelets and overcomes its shortcomings. It has approximate shift-invariance and multi-Directional Selectivity. Moreover the coefficient provides a richer statistical feature information.This paper’s main work is as follows:1. We overview the development status of seismic denoising,and briefly describe the performance evaluation criteria of seismic denoising. We briefly introduce the concept of dual-tree complex wavelet,and further focus on the advantage and of the dual-tree complex wavelet transform.2. We propose two dual-tree complex wavelet transform domain bivariate methods for seismic signal random noise elimination. After the dual-tree complex discrete wavelet transform, the real and imaginary parts of the wavelet coefficients have dependency in the same direction and scale. The real or imaginary parts and the corresponding magnitudes of the wavelet coefficients have dependency in the same direction and scale. So we construct bivariate model for the real and imaginary parts in the same direction and scale. Using the model the wavelet coefficients of original seismic signal are estimated. We get the denoised seismic signal based on dual-tree complex wavelet inverse transform. The proposed algorithm is also extended to the real or imaginary parts and the corresponding magnitudes of dual-tree complex wavelet coefficients in the same direction and scale. The synthetic and field data examples show that the proposed two methods can eliminate random noise effectively.3. In order to improve the resolution of seismic data for facilitating the interpretation of seismic data, the ground roll attenuation is an important problem. A method for ground roll attenuation is proposed combined the dual-tree complex wavelet transform with the local singular value decomposition (SVD). The distribution of the ground roll and the reflected wave in the dual-tree complex wavelet domain is analyzed. The low frequency coefficients are processed by the local SVD because they contain the ground roll and the reflected wave coefficients. For each scale the high frequency coefficients for the ±45° orientation are processed by the local SVD. The high frequency coefficients for the ±75° orientation are processed by the threshold based on the quantile. The high frequency coefficients for the ±15° orientation are unchanged. The synthetic and field data examples show that the proposed method can attenuate the ground roll effectively.