小波分析技术在地震信号噪声处理中的应用
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摘要
小波分析是20世纪80年代中后期逐渐发展起来的一个新的数学分支,它具有多分辨率分析的优良特性,在许多方面获得了广泛应用。信号中混入噪声之后,会引起信号的奇异性变化。随机噪声和有效信号本身在奇异点的奇异指数大小不同,从而它们的小波变换的模极大值在不同尺度下的传播行为也不一样。依据此区别,对于一个含噪地震道记录信号进行小波分解(即多分辨率分解)之后,在模极大值图上去除那些幅度随尺度增加而减小的极值点(对应噪声的极值点),而保留幅度随尺度增加而增大的点(对应信号突变点位置),这样就可以在模极大值图上达到去除噪声的目的。小波分析技术在地震信号噪声处理中,去噪效果明显优于传统的傅立叶变换方法。
Wavelet analysis is a new math branch that has been developing since the late 1980'sWavelet analysis has excellent characteristics of multiresolution analysis(MRA) and has been widely used in many fieldsThe signal mixed with noise will occur oddity changesBecause the Oddity Index of random noise is different from that of effective signals on the degree,their spread behaviors of module max are different each other under various measuresAccording to this difference,an earthquake signal including noise is divided into different frequency bands by waveletanalysisWe can wipe off the noise's maximum dot,whose scope decreases with the increase of measure,and retain the signal's extremum dot,whose scope increases with the increase of measureSo,we can rebuild the original signal through getting rid of noise from the module max chatIn the denoise of earthquake signal,Wavelet analysis has the obvious advantage over conventional Fourier transform in denoise effect
Wavelet analysis is a new math branch that has been developing since the late 1980'sWavelet analysis has excellent characteristics of multiresolution analysis(MRA) and has been widely used in many fieldsThe signal mixed with noise will occur oddity changesBecause the Oddity Index of random noise is different from that of effective signals on the degree,their spread behaviors of module max are different each other under various measuresAccording to this difference,an earthquake signal including noise is divided into different frequency bands by waveletanalysisWe can wipe off the noise's maximum dot,whose scope decreases with the increase of measure,and retain the signal's extremum dot,whose scope increases with the increase of measureSo,we can rebuild the original signal through getting rid of noise from the module max chatIn the denoise of earthquake signal,Wavelet analysis has the obvious advantage over conventional Fourier transform in denoise effect
引文
〔1〕彭玉华 小波变换与工程应用(修订版)[M] 北京:科学出版社,2002
〔2〕皱长春,杨欣德,潘令枝,等 一种基于小波变换的测井曲线去噪新方法[J] 物探与化探,1999,23(6):462-466
〔3〕李保生,吴 毅,侯再红,等 多分辨率分析去除光斑图像中的背景噪声[J] 量子电子学报,2001,18(6):485-488
〔4〕[美]催锦泰 小波分析导论[M] 程正兴译 西安:西安交通大学出版社,1995
〔5〕彭玉华 小波变换与工程应用[M] 北京:科学出版社,1999
〔2〕皱长春,杨欣德,潘令枝,等 一种基于小波变换的测井曲线去噪新方法[J] 物探与化探,1999,23(6):462-466
〔3〕李保生,吴 毅,侯再红,等 多分辨率分析去除光斑图像中的背景噪声[J] 量子电子学报,2001,18(6):485-488
〔4〕[美]催锦泰 小波分析导论[M] 程正兴译 西安:西安交通大学出版社,1995
〔5〕彭玉华 小波变换与工程应用[M] 北京:科学出版社,1999
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