基于Curvelet变换阈值法的地震数据去噪方法
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摘要
Curvelet变换是一种新的多尺度几何分析方法,属于稀疏函数表示理论的范畴,较之小波和脊波,它能更好地解决高维函数的特征表示问题,对于曲线奇异性特征从理论上能达到最优的表示效果。将Curvelet变换用于地震数据去噪,概述了Curvelet变换的基本原理,介绍了阈值法去噪的概念;对模拟加入随机噪声的地震数据进行了Curvelet阈值法去噪处理,并对比了不同信噪比下的去噪效果。实验结果表明Curvelet变换阈值法去噪效果明显,且有效信号损失少,是一个切实可行的去噪方法。
Curvelet transform is a new multiscale analysis method,it belongs to the range of sparsity represent theory.Compare to wavelet and ridgelet,it can solve the characteristic represent of higher dimension,and it can acquire theoretically the best expression as to curve singularity characteristic.This paper uses curvelet transform in seismic data denosie,summarizes the principle of curvelet transform,introduces the concept of threshold method denoising.We have made curvelet transform to the data including noise,and achieved effective denoising by choosing appropriate threshold.At the same time,we have compared the denoising effects of different signal to noise ratio.The result indicates that the denoising based on curvelet transform can have obvious effect,and it do not loss signal.As a result,it is a practicable method of denoise.
Curvelet transform is a new multiscale analysis method,it belongs to the range of sparsity represent theory.Compare to wavelet and ridgelet,it can solve the characteristic represent of higher dimension,and it can acquire theoretically the best expression as to curve singularity characteristic.This paper uses curvelet transform in seismic data denosie,summarizes the principle of curvelet transform,introduces the concept of threshold method denoising.We have made curvelet transform to the data including noise,and achieved effective denoising by choosing appropriate threshold.At the same time,we have compared the denoising effects of different signal to noise ratio.The result indicates that the denoising based on curvelet transform can have obvious effect,and it do not loss signal.As a result,it is a practicable method of denoise.
引文
[1]Neelamani Ramesh,Baumstein Anatoly I,Gillard Do-minique G,et al.Coherent and random noise attenuationusing the curvelet transform[J].The Leading Edge,2008,27(2):240-248.
[2]Cand埁s E,Donoho D.Curvelets:A surprisingly effectivenonadaptive representation of objects with edges[M].TN:Vanderbilt University Press,1999.
[3]Cand埁s E,Demanet L,Donoho D,Ying L.Fast discretecurvelet transforms[J].SIAM Multiscale Modeling andSimulation,2006,5:861-899.
[4]黄薇.Curvelet变换及其在图像处理中的应用研究[D].西安:西安理工大学,2007.
[5]姚胜利.地震信号的小波去噪方法研究[D].长沙:中南大学,2007.
[6]Deli Wang,Rayan Saab,Ozg櫣r Yilmaz,et al.Bayesianwavefield separation by transform-dom-ain sparsity promo-tion[J].Geophysics,2008,73(5):A33-A38.
[2]Cand埁s E,Donoho D.Curvelets:A surprisingly effectivenonadaptive representation of objects with edges[M].TN:Vanderbilt University Press,1999.
[3]Cand埁s E,Demanet L,Donoho D,Ying L.Fast discretecurvelet transforms[J].SIAM Multiscale Modeling andSimulation,2006,5:861-899.
[4]黄薇.Curvelet变换及其在图像处理中的应用研究[D].西安:西安理工大学,2007.
[5]姚胜利.地震信号的小波去噪方法研究[D].长沙:中南大学,2007.
[6]Deli Wang,Rayan Saab,Ozg櫣r Yilmaz,et al.Bayesianwavefield separation by transform-dom-ain sparsity promo-tion[J].Geophysics,2008,73(5):A33-A38.
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