面波衰减处理中小波函数的选择方法
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摘要
在讨论小波域面波衰减处理原理的基础上,总结出了在面波衰减处理中小波分解结果应具有良好分离性的要求,根据支集长度决定局部化特性,消失矩决定低频低波数分量的能量集中程度,分析出在面波衰减处理中应选取短支集长度、高消失矩及具有对称性的小波函数的原则,得出了Symmlet小波函数是最优小波的结论。并通过对实际地震资料和人工合成地震记录面波衰减处理结果中面波衰减程度以及对反射波影响程度的分析,验证了所提出的小波函数选取方法的正确性。
Based on the discussions on the principles of surface wave attenuation processing in wavelet domain,it is concluded that good separability of wavelet decomposition result is needed during surface wave attenuation processing.Because support length decides local features and vanishing moment decides the energy concentration degree of low-frequency and low-wave-number components,a symmetrical wavelet function principle that short support length and high vanishing moment should be chosen is determined,and Symmlet wavelet function is considered as the optimal wavelet.Surface-wave attenuation degree and influence of reflection wave are analyzed regarding surfacewave attenuation processing results obtained from actual seismic data and synthetic seismogram,which validates the method for wavelet function selection.
Based on the discussions on the principles of surface wave attenuation processing in wavelet domain,it is concluded that good separability of wavelet decomposition result is needed during surface wave attenuation processing.Because support length decides local features and vanishing moment decides the energy concentration degree of low-frequency and low-wave-number components,a symmetrical wavelet function principle that short support length and high vanishing moment should be chosen is determined,and Symmlet wavelet function is considered as the optimal wavelet.Surface-wave attenuation degree and influence of reflection wave are analyzed regarding surfacewave attenuation processing results obtained from actual seismic data and synthetic seismogram,which validates the method for wavelet function selection.
引文
[1]曾祥,乔宝平,刘依谋,等.基于小波变换的自适应面波压制方法[J].北京大学学报(自然科学版),2015,51(5):837-842.ZENG Xiangkun,QIAO Baoping,LIU Yimou,et al.Adaptive groun-droll attenuation based on the wavelet transform[J].Acta Scien-tiarum Naturalium Universitatis Pekinensis,2015,51(5):837-842.
[2]孙学文,陈文超,高静怀,等.小波域强面波衰减方法研究[J].石油地球物理勘探,2008,43(1):22-28.SUN Xuewen,CHEN Wenchao,GAO Jinghuai,et al.Study on atten-uation of strong surface wave in wavelet domain[J].Oil GeophysicalProspecting,2008,43(1):22-28.
[3]刘财,王典,杨宝骏,等.二维小波变换在地震勘探面波消除中的应用[J].地球物理学进展,2003,18(4):711-714.LIU Cai,WANG Dian,YANG Baojun,et al.Apply of 2-D wavelettransform in surface wave eliminations of seismic exploration[J].Progress in Geophysics,2003,18(4):711-714.
[4]张华,潘冬明,张兴岩.利用二维小波变换实现叠前分离面波[J].新疆石油地质,2007,28(5):576-578.ZHANG Hua,PAN Dongming,ZHANG Xingyan.Application of 2Dwavelet transform to prestack of surface wave[J].Xinjiang Petro-leum Geology,2007,28(5):576-578.
[5]徐鑫,张学强,徐涛,等.小波变换在压制面波中的应用[J].工程地球物理学报,2008,5(2):196-200.XU Xin,ZHANG Xueqiang,XU Tao,et al.Application of wavelettransform in surface wave elimination[J].Chinese Journal of Engi-neering Geophysics,2008,5(2):196-200.
[6]李彩芹,张华.小波变换与F-K联合滤波在面波分离中的应用[J].中国煤田地质,2007,19(4):60-61.LI Caiqin,ZHANG Hua.Application of combining wavelet trans-form and F-K filtering in surface wave separation[J].Coal Geologyof China,2007,19(4):60-61.
[7]张华,陈小宏,杨海燕.地震信号去噪的最优小波基选取方法[J].石油地球物理勘探,2011,46(1):70-75.ZHANG Hua,CHEN Xiaohong,YANG Haiyan.Optimistic waveletbasis selection in seismic signal noise elimination[J].Oil Geophysi-cal Prospecting,2011,46(1):70-75.
[8]陈钢花,余杰,张孝珍.基于小波时频分析的测井层序地层划分方法[J].新疆石油地质,2007,28(3):355-358.CHEN Ganghua,YU Jie,ZHANG Xiaozhen.Logging sequencestratigraphic division based on wavelet time-frequency analysis[J].Xinjiang Petroleum Geology,2007,28(3):355-358.
[9]MALLAT S.A wavelet tour of signal processing(Second Edition)[M].Beijing:China Machine Press,2003:303-312.
[10]白泉,韩晶晶,盛国华,等.地震动反应谱拟合过程中小波基函数的选取[J].地震学报,2015,37(6):1 037-1 044.BAI Quan,HAN Jingjing,SHENG Guohua,et al.Selection of wave-let basis function in the simulation of seismic response spectrum[J].Acta Seismologica Sinica,2015,37(6):1 037-1 044.
[11]郑钧,侯锐锋.小波去噪中小波基的选择[J].沈阳大学学报,2009,21(2):108-110.ZHENG Jun,HOU Ruifeng.Selection of wavelet base in denoisingof wavelet transform[J].Journal of Shenyang University,2009,21(2):108-110.
[12]DAUBECHIES I.Orthonormal bases of compactly supported wave-lets[J].Communications on Pure and Applied Mathematics,1988,41(7):909-996.
[13]DAUBECHIES I.Ten lectures on wavelets[M].PA,USA:Societyfor Industrial and Applied Mathematics,1992.
[14]查显杰,傅容珊,戴志阳,等.小波基函数选择对SAR干涉图去噪的影响[J].遥感信息,2008,23(2):17-20.ZHA Xianjie,FU Rongshan,DAI Zhiyang,et al.The influence onSAR interferograms noise reduction due to the selection of waveletbase function[J].Remote Sensing Information,2008,23(2):17-20.
[15]曾宪伟,赵卫明,师海阔,等.利用小波包变换对地震信号进行时频分析时小波基函数的选取[J].地震研究,2010,33(4):323-328.ZENG Xianwei,ZHAO Weiming,SHI Haikuo,et al.Selection ofwavelet basis function in process of time-frequency analysis of earth-quake signals using wavelet packet transform[J].Journal of Seis-mological Research,2010,33(4):323-328.
[16]胡明顺,潘冬明,李娟娟,等.基于频散曲线合成面波地震记录的方法[J].煤田地质与勘探,2010,38(2):59-62.HU Mingshun,PAN Dongming,LI Juanjuan,et al.The method ofsynthesizing surface-wave seismogram based on dispersion curves[J].Coal Geology&Exploration,2010,38(2):59-62.
[2]孙学文,陈文超,高静怀,等.小波域强面波衰减方法研究[J].石油地球物理勘探,2008,43(1):22-28.SUN Xuewen,CHEN Wenchao,GAO Jinghuai,et al.Study on atten-uation of strong surface wave in wavelet domain[J].Oil GeophysicalProspecting,2008,43(1):22-28.
[3]刘财,王典,杨宝骏,等.二维小波变换在地震勘探面波消除中的应用[J].地球物理学进展,2003,18(4):711-714.LIU Cai,WANG Dian,YANG Baojun,et al.Apply of 2-D wavelettransform in surface wave eliminations of seismic exploration[J].Progress in Geophysics,2003,18(4):711-714.
[4]张华,潘冬明,张兴岩.利用二维小波变换实现叠前分离面波[J].新疆石油地质,2007,28(5):576-578.ZHANG Hua,PAN Dongming,ZHANG Xingyan.Application of 2Dwavelet transform to prestack of surface wave[J].Xinjiang Petro-leum Geology,2007,28(5):576-578.
[5]徐鑫,张学强,徐涛,等.小波变换在压制面波中的应用[J].工程地球物理学报,2008,5(2):196-200.XU Xin,ZHANG Xueqiang,XU Tao,et al.Application of wavelettransform in surface wave elimination[J].Chinese Journal of Engi-neering Geophysics,2008,5(2):196-200.
[6]李彩芹,张华.小波变换与F-K联合滤波在面波分离中的应用[J].中国煤田地质,2007,19(4):60-61.LI Caiqin,ZHANG Hua.Application of combining wavelet trans-form and F-K filtering in surface wave separation[J].Coal Geologyof China,2007,19(4):60-61.
[7]张华,陈小宏,杨海燕.地震信号去噪的最优小波基选取方法[J].石油地球物理勘探,2011,46(1):70-75.ZHANG Hua,CHEN Xiaohong,YANG Haiyan.Optimistic waveletbasis selection in seismic signal noise elimination[J].Oil Geophysi-cal Prospecting,2011,46(1):70-75.
[8]陈钢花,余杰,张孝珍.基于小波时频分析的测井层序地层划分方法[J].新疆石油地质,2007,28(3):355-358.CHEN Ganghua,YU Jie,ZHANG Xiaozhen.Logging sequencestratigraphic division based on wavelet time-frequency analysis[J].Xinjiang Petroleum Geology,2007,28(3):355-358.
[9]MALLAT S.A wavelet tour of signal processing(Second Edition)[M].Beijing:China Machine Press,2003:303-312.
[10]白泉,韩晶晶,盛国华,等.地震动反应谱拟合过程中小波基函数的选取[J].地震学报,2015,37(6):1 037-1 044.BAI Quan,HAN Jingjing,SHENG Guohua,et al.Selection of wave-let basis function in the simulation of seismic response spectrum[J].Acta Seismologica Sinica,2015,37(6):1 037-1 044.
[11]郑钧,侯锐锋.小波去噪中小波基的选择[J].沈阳大学学报,2009,21(2):108-110.ZHENG Jun,HOU Ruifeng.Selection of wavelet base in denoisingof wavelet transform[J].Journal of Shenyang University,2009,21(2):108-110.
[12]DAUBECHIES I.Orthonormal bases of compactly supported wave-lets[J].Communications on Pure and Applied Mathematics,1988,41(7):909-996.
[13]DAUBECHIES I.Ten lectures on wavelets[M].PA,USA:Societyfor Industrial and Applied Mathematics,1992.
[14]查显杰,傅容珊,戴志阳,等.小波基函数选择对SAR干涉图去噪的影响[J].遥感信息,2008,23(2):17-20.ZHA Xianjie,FU Rongshan,DAI Zhiyang,et al.The influence onSAR interferograms noise reduction due to the selection of waveletbase function[J].Remote Sensing Information,2008,23(2):17-20.
[15]曾宪伟,赵卫明,师海阔,等.利用小波包变换对地震信号进行时频分析时小波基函数的选取[J].地震研究,2010,33(4):323-328.ZENG Xianwei,ZHAO Weiming,SHI Haikuo,et al.Selection ofwavelet basis function in process of time-frequency analysis of earth-quake signals using wavelet packet transform[J].Journal of Seis-mological Research,2010,33(4):323-328.
[16]胡明顺,潘冬明,李娟娟,等.基于频散曲线合成面波地震记录的方法[J].煤田地质与勘探,2010,38(2):59-62.HU Mingshun,PAN Dongming,LI Juanjuan,et al.The method ofsynthesizing surface-wave seismogram based on dispersion curves[J].Coal Geology&Exploration,2010,38(2):59-62.