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
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摘要
提出了一种针对小波地震信号的新型去噪方法,该方法结合了非线性小波阈值去噪算法和递归最优阈值选择算法.阐述了非线性小波阈值去噪算法的基本原理和递归最优阈值选择算法的步骤,并与传统的数据平滑法和流行的基于MAD的小波固定阈值去噪法进行了深入比较.仿真实验和统计数据表明,本方法既保证了处理后数据序列的光滑性,又保证了真实信号的完整性;克服了其他两种方法的不足,在处理效果上取得了较大优势,并在实际震相的判读工作中证明了本方法的有效性.
A new denoising method of seismic signals based on nonlinear wavelet thresholding denoising and recursive optimal thresholding was proposed.The method was compared with data smoothing and wavelet fixed thresholding denoising method via MAD.Simulations and statistic evidences demonstrated that the presented approach could keep the smoothness of processed data and the integrity of real signals.It conquered the shortages of data smoothing and wavelet fixed thresholding denoising,and had much better efficiency and good application value.
A new denoising method of seismic signals based on nonlinear wavelet thresholding denoising and recursive optimal thresholding was proposed.The method was compared with data smoothing and wavelet fixed thresholding denoising method via MAD.Simulations and statistic evidences demonstrated that the presented approach could keep the smoothness of processed data and the integrity of real signals.It conquered the shortages of data smoothing and wavelet fixed thresholding denoising,and had much better efficiency and good application value.
引文
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2 Mallat S.A Wavelet Tour of Signal Processing[M].New York:Academic Press,1998.
3姜弢,林君,陈祖斌.延时参数对地震信号信噪比的改善[J].地球物理学报,2009,52(6):1651-1656.
4 Wang R Q,Li Q,Zhang M.Application of multi-scaled morphology in denoising seismic data[J].Applied Geophysics, 2008(3):197-203.
5武文波,杨志高,秦前清.基于重叠变换的地震数据压缩去噪[J].计算机工程与应用,2004,40(35):196-198.
6柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2):541-545.
7武永胜,师学明,张剑,等.基于小波变换的地震映像法资料去噪研究.[J].工程地球物理学报,2008,5(5):584- 589.
8 Donoho D,Johnstone I.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994,81:425-455.
9 von Sachs R,Neumann J.Wavelet thresholding:Beyond the Gaussian I.I.D.situation[J].Wavelets and Statistics (Springer Lecture Notes in Statistics),1995,103:301-329.
10 von Sachs R,Schneider K.Wavelet smoothing of evolutionary spectra by non-linear thresholding[J].Appl Comput Harmon Anal,1996,3(3):268-282.
11 Logvinenko A D,Byth W,Vityaev E E.In search of an elusive hard threshold:A test of observer's ability to order sub-threshold stimuli[J].Vision Research,2004,44(3):287-296.
12 Kathrin Berkner,Raymond O,Wells Jr.Smoothness estimates for soft-threshold denoising via translation-invariant wavelet transforms[J].Applied and Computational Harmonic Analysis,2002,12(1):1-24.
2 Mallat S.A Wavelet Tour of Signal Processing[M].New York:Academic Press,1998.
3姜弢,林君,陈祖斌.延时参数对地震信号信噪比的改善[J].地球物理学报,2009,52(6):1651-1656.
4 Wang R Q,Li Q,Zhang M.Application of multi-scaled morphology in denoising seismic data[J].Applied Geophysics, 2008(3):197-203.
5武文波,杨志高,秦前清.基于重叠变换的地震数据压缩去噪[J].计算机工程与应用,2004,40(35):196-198.
6柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2):541-545.
7武永胜,师学明,张剑,等.基于小波变换的地震映像法资料去噪研究.[J].工程地球物理学报,2008,5(5):584- 589.
8 Donoho D,Johnstone I.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994,81:425-455.
9 von Sachs R,Neumann J.Wavelet thresholding:Beyond the Gaussian I.I.D.situation[J].Wavelets and Statistics (Springer Lecture Notes in Statistics),1995,103:301-329.
10 von Sachs R,Schneider K.Wavelet smoothing of evolutionary spectra by non-linear thresholding[J].Appl Comput Harmon Anal,1996,3(3):268-282.
11 Logvinenko A D,Byth W,Vityaev E E.In search of an elusive hard threshold:A test of observer's ability to order sub-threshold stimuli[J].Vision Research,2004,44(3):287-296.
12 Kathrin Berkner,Raymond O,Wells Jr.Smoothness estimates for soft-threshold denoising via translation-invariant wavelet transforms[J].Applied and Computational Harmonic Analysis,2002,12(1):1-24.
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