双密度双树复小波域统计模型的地震信号降噪
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摘要
随机噪声的存在降低了地震信号的信噪比,淹没了有效信号,影响后续的地质解释。文章根据随机噪声的特性以及地震信号道间相关性,建立双密度双树复小波域统计模型压制地震信号中的随机噪声。首先对含噪地震信号进行双密度双树复小波变换,分别对不同尺度、不同方向上的噪声方差和含噪地震信号方差进行估计,计算阈值;再运用最大后验概率估计方法从含噪地震信号小波系数中估计出源地震信号的小波系数;最后利用双密度双树复小波逆变换对源地震信号的小波系数估计值进行重构,得到降噪后的地震信号。仿真实验和对实际地震信号的处理结果表明该方法能够有效地压制随机噪声,提高了信噪比,较好地保留了有效信号。
The random noise reduces the signal-to-noise ratio of the seismic signal,submerges the effective signal and affects the geological interpretation.The double density dual tree complex wavelet domain statistical model is established to suppress random noise in the seismic signal according to the characteristics of random noise and seismic signal channel correlation.Firstly,the noisy seismic signal is decomposed by double density dual tree complex wavelet.The noise variance and noisy seismic signal variance at different scales and directions are estimated,and the threshold is calculated.The wavelet coefficients of the source seismic signal are estimated from the noisy seismic signal using the maximum a posteriori probability estimation method.Finally,the denoised seismic signal is achieved based on double density dual tree complex wavelet inverse transform.The experimental results show that the proposed method can suppress the random noise effectively,enhance the signal-to-noise ratio and retain the effective signal very well.
The random noise reduces the signal-to-noise ratio of the seismic signal,submerges the effective signal and affects the geological interpretation.The double density dual tree complex wavelet domain statistical model is established to suppress random noise in the seismic signal according to the characteristics of random noise and seismic signal channel correlation.Firstly,the noisy seismic signal is decomposed by double density dual tree complex wavelet.The noise variance and noisy seismic signal variance at different scales and directions are estimated,and the threshold is calculated.The wavelet coefficients of the source seismic signal are estimated from the noisy seismic signal using the maximum a posteriori probability estimation method.Finally,the denoised seismic signal is achieved based on double density dual tree complex wavelet inverse transform.The experimental results show that the proposed method can suppress the random noise effectively,enhance the signal-to-noise ratio and retain the effective signal very well.
引文
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[14]王姣,李振春,王德营.基于CEEMD的地震数据小波阈值去噪方法研究[J].石油物探,2014,53(2):164-172.
[15]刘霞,黄阳,黄敬,等.基于经验模态分解(EMD)的小波熵阈值地震信号去噪[J].吉林大学学报(地球科学版),2016,46(1):262-269.
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[18]殷明,白瑞峰,邢燕,等.基于非下采样双树复小波域的双变量模型去噪算法[J].光子学报,2014,43(10):131-137.
[19]KINGSBURY N G.The dual-tree complex wavelet transform:a new efficient tool for image restoration and enhancement[C]//The 9th European Signal Processing Conference.[S.l.:s.n.],1998:319-322.
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[22]张稳稳.双树复小波域的邻域自适应贝叶斯收缩去噪[J].计算机工程与应用,2012,48(31):156-160.
[2]刘财,王典,刘洋,等.二维多级中值滤波技术在随机噪声消除中的应用初探[J].石油地球物理勘探,2005,40(2):163-167.
[3]BEKARA M,VAN DER BAAN M.Local singular value decompsition for signal enhancement of seismic data[J].Geophysics,2007,72(2):59-65.
[4]薛亚茹,陆文凯,陈小宏,等.基于正交多项式变换的CMP动校正道集随机噪声压制[J].地球物理学进展,2009,24(1):159-163.
[5]袁艳华,王一博,刘伊克,等.非二次幂Curvelet变换及其在地震噪声压制中的应用[J].地球物理学报,2013,56(3):1023-1032.
[6]ZHAI M Y.Seismic data denoising based on the fractional Fourier transformation[J].Journal of Applied Geophysics,2014,109:62-70.
[7]DENG X H,MA H T,LI Y,et al.Seismic random noise attenuation based on adaptive time-frequency peak filtering[J].Journal of Applied Geophysics,2015,113(10):31-37.
[8]YU Z,GAROSSINO P G A.High-energy noise attenuation of seismic data in the wavelet-transform domain[J].Integrated Computer-Aided Engineering,2005,12(1):57-67.
[9]CAO S Y,CHEN X P.The second-generation wavelet transform and its application in denoising of seismic data[J].Applied Geophysics,2005,2(2):70-74.
[10]夏洪瑞,葛川庆,彭涛.小波时空变阈值去噪方法在可控震源资料处理中的应用[J].石油地球物理勘探,2010,45(1):23-27.
[11]张一,成礼智.一种基于递归最优阈值选择算法的小波地震信号的去噪方法[J].南开大学学报(自然科学版),2011,44(4):67-71.
[12]BEENAMOL M,PRABAVATHY S,MOHANALIN J.Wavelet based seismic signal de-noising using Shannon and Tsallis entropy[J].Computers&Mathmatics with Applications,2012,64(11):3580-3593.
[13]李雪英,张晶,孔祥琦,等.基于离散小波变换的地震资料自适应高频噪声压制[J].物探与化探,2013,7(1):165-170.
[14]王姣,李振春,王德营.基于CEEMD的地震数据小波阈值去噪方法研究[J].石油物探,2014,53(2):164-172.
[15]刘霞,黄阳,黄敬,等.基于经验模态分解(EMD)的小波熵阈值地震信号去噪[J].吉林大学学报(地球科学版),2016,46(1):262-269.
[16]BERKNER K,WELLS R O,Jr.Smoothness estimates for soft-threshod denoising via translation-invariant wavelets transforms[J].Applied and Computational Harmonic Analysis,2002,12(1):1-24.
[17]刘鑫,贺振华,黄德济.基于小波变换的地震资料去噪处理研究[J].油气地球物理,2006,4(4):15-18.
[18]殷明,白瑞峰,邢燕,等.基于非下采样双树复小波域的双变量模型去噪算法[J].光子学报,2014,43(10):131-137.
[19]KINGSBURY N G.The dual-tree complex wavelet transform:a new efficient tool for image restoration and enhancement[C]//The 9th European Signal Processing Conference.[S.l.:s.n.],1998:319-322.
[20]SELESNICK I W.The double density DWT[M]//PETROSIAN A,MEYER F G.Wavelets in Signal and Image Analysis:From Theory to Practice.Boston:Kluwer,2001:39-68.
[21]SELESNICK I W.The double-density dual-tree DWT[J].IEEE Transactions on Signal Pocessing,2004,52(5):1304-1314.
[22]张稳稳.双树复小波域的邻域自适应贝叶斯收缩去噪[J].计算机工程与应用,2012,48(31):156-160.