基于曲波域的软硬阈值折中地震信号去噪
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摘要
噪声衰减是地震资料处理中的关键步骤之一。根据曲波变换对于光滑且二阶连续可微函数所具有的最优逼近性能,给出了曲波域随机噪声衰减的软硬阈值折中方法。基于模型讨论了有效信号和随机噪声在曲波域不同方向上的分布差异;最后,将该方法应用于实际地震资料处理。结果表明,本文方法不仅有效地压制了地震资料中的随机噪声,提高了地震资料的信噪比,而且较好地保留了地震数据中的有效信号。
The random noise attenuation is a very important step in seismic data processing.According to the optimal approximation property of the second curvelet transform about smooth and second-order continuous differentiable singular function.A new threshold method of random noise attenuation is proposed based on curvelet transform.With regard to the model,the difference in curvelet domain between signal and noise is discussed and the seismic data are processed based on the proposed method.The results show that this method can not only attenuate the random noise and enhance signal to noise ratio in seismic data,but also protect the integrity of seismic data from damage.
The random noise attenuation is a very important step in seismic data processing.According to the optimal approximation property of the second curvelet transform about smooth and second-order continuous differentiable singular function.A new threshold method of random noise attenuation is proposed based on curvelet transform.With regard to the model,the difference in curvelet domain between signal and noise is discussed and the seismic data are processed based on the proposed method.The results show that this method can not only attenuate the random noise and enhance signal to noise ratio in seismic data,but also protect the integrity of seismic data from damage.
引文
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[3]刘伟,杨凯,王征,等.基于SVD的正交多项式变换及其在地震资料处理中的应用[J].工程地球物理学报,2010,7(4):433～437.
[4]陈知富,邓居智,陈辉,等.基于小波变换的大地电磁信号去噪研究[J].工程地球物理学报,2012,9(6):732～737.
[5]张军华,吕宁,田连玉,等.地震资料去噪方法综合评述[J].石油地球物理勘探,2005,40(增刊):121～127.
[6]刘贵忠,宗涛,章珂,等.利用纵向小波包变换和横向多项式拟合提高地震信号的信噪比和分辨率[J].石油地球物理勘探,1995,30(5):584～592.
[7]Candès E J,Guo F.New multiscale transform,mini-mum total variation synthesis:Applications to edge-preserving image reconstruction[J].Signal Pro-cessing,2002,(82):1519～1543.
[8]Candès E J,Donoho D L.Recovering edges inⅢ-posed problems:optimality of curvelet frames[J].Annals of Statistics,2002,(30):784～842.
[9]Candès E J,Roberg J,Tao T.Stable signal recoveryfrom incomplete and inaccurate measurements[J].Communications on Pure and Applied Mathematics,2006,59(8):1207～1223.
[10]张志禹,毕杨.基于曲波变换和独立分量分析的有噪图像盲分离[J].计算机应用,2007,27(2:)438～441.
[11]Candès E J,Donoho D L.Continuous curvelet transformⅡ:Discretization and frames[J].Applied and Computa-tional Harmonic Analysis,2005,19(2):198～222.
[12]Candès E J,Demannet S L,Donoho D L,et al.Fastdiscrete curvelet transforms[J].Multiscale Modelingand Simulation,2006,5(3):861～899.
[13]Starck J L,Candès E J,Donoho D L.The curvelettransform for image denoising[J].IEEE TransactionsOn Image Processing,2002,11(6):670～684.
[14]Candès E J,Donoho D L.New tight frames of curve-lets and optimal representation of objects with piece-wise-singularities[J].Communications on Pure andApplied Mathematics,2004,57(2):219～266.
[15]何劲,李宏伟,张帆.基于curvelet变换与小波包变换联合的图像去噪算法[J].通信技术,2008,41(1):140～142.
[16]Donoho D L.De-noiseing by soft-thresholding[J].IEEETransactions On Image Processing,1995,41(6):613～627.
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