四参数宽带B样条子波
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摘要
本文基于地震尖脉冲的小波分解及其重构原理,提出一种基于部分尺度下信号重构理论的宽带子波构成方法,利用此方法可以形成一系列各具特色的地震子波。基于复B样条小波,具体讨论四参数宽带B样条地震子波的构成,推导出四参数宽带B样条子波的时间域和频率域的解析表达式。四参数宽带B样条地震子波不仅具有可直接调节旁瓣衰减的参数,而且还可以直接调节相位的个数,与相同主瓣等效频率的雷克子波和俞氏子波相比,四参数宽带B样条子波旁瓣小,非零时间点的延续时间短。楔形模型制作的合成地震记录表明,四参数宽带B样条子波的分辨率更高且参数选择更为灵活,可为地震资料处理提供一个更方便、更灵活的地震理论子波。
Based on the wavelet decomposition and its reconstruction theory,we propose here a method to reconstruct wide-band wavelets.Different seismic wavelets can be reconstructed in this way.In virtue of complex frequency B-spline wavelet,we form a wide-band B-spline wavelet with four parameters and deduce its analytic expressions both in the time domain and in the frequency domain.The side lobes and phase numbers of the wide-band B-spline wavelet with four parameters can be easily adjusted through its parameter.In comparison with the Ricker wavelet and wide-band Ricker wavelet in the condition of the same main lobe equivalent frequency,the wide-band B-spline wavelet with four parameters not only has smaller side lobe but also has shorter non-zero time length.The synthetic result of wedge model indicates that the wide-band B-spline wavelet with four parameters has higher resolution and its parameters are easily adjusted.Therefore,it is a seismic theory wavelet more conveniently to be used in seismic data processing.
Based on the wavelet decomposition and its reconstruction theory,we propose here a method to reconstruct wide-band wavelets.Different seismic wavelets can be reconstructed in this way.In virtue of complex frequency B-spline wavelet,we form a wide-band B-spline wavelet with four parameters and deduce its analytic expressions both in the time domain and in the frequency domain.The side lobes and phase numbers of the wide-band B-spline wavelet with four parameters can be easily adjusted through its parameter.In comparison with the Ricker wavelet and wide-band Ricker wavelet in the condition of the same main lobe equivalent frequency,the wide-band B-spline wavelet with four parameters not only has smaller side lobe but also has shorter non-zero time length.The synthetic result of wedge model indicates that the wide-band B-spline wavelet with four parameters has higher resolution and its parameters are easily adjusted.Therefore,it is a seismic theory wavelet more conveniently to be used in seismic data processing.
引文
[1]李庆忠.走向精确勘探的道路.北京:石油工业出版社,1994
[2]杨培杰,印兴耀.地震子波提取方法综述.石油地球物理勘探,2008,43(1):123~128Yang Pei-jie and Yin Xing-yao,Summary of seismicwavelet pick-up.OGP,2008,43(1):123~128
[3]Eugene Lichm an.Unified approach to gas and fluiddetection on instantaneous seismic wavelets.SEGTechnical Program Expanded Abstracts,2003,22:1699~1702
[4]俞寿朋.宽带Ricker子波.石油地球物理勘探,1996,31(5):605~615Yu Shou-peng.Wide-band Ricker wavelet.OGP,1996,31(5):605~615
[5]Ricker N.The formand nature of seismic waves andthe structure of seismograms.Geophysics,1940,5(4):348~366
[6]Huang Jun-bin,Gao Li-jun,Gao Yong.Side lobes ofwavelets i mpact identification of thin sand bodies.Applied Geophysics,2007,4(2):111~117
[7]Grossmann A and Morlet J.Decomposition of Hardyfunctions into square integrable wavelets of constantshape:SIAM.Journal on Mathematical Analysis,1984,15(4):723~736
[8]http:∥www.mathworks.cn/access/helpdesk/help/toolbox/wavelet/ch06_ad9.ht ml
[9]郑君里,杨为理,应君珩.信号与系统(上).北京:高等教育出版社,1981
[10]俞寿朋.高分辨率地震勘探.北京:石油工业出版社,1993
[11]Taner M T,Koehler F and Sheriff R E.Complexseismic trace analysis.Geophysics,1979,44(6):1041~1063
[12]张海燕,李庆忠.几种常用解析子波的特性分析.石油地球物理勘探,2007,42(6):651~657Zhang Hai-yan and Li Qing-zhong.Analysis on fea-ture of common analytic wavelets.OGP,2007,42(6):651~657
[13]Widess M B.How thin is a thin bed?.Geophysics,1973,38(6):1176~1180
[2]杨培杰,印兴耀.地震子波提取方法综述.石油地球物理勘探,2008,43(1):123~128Yang Pei-jie and Yin Xing-yao,Summary of seismicwavelet pick-up.OGP,2008,43(1):123~128
[3]Eugene Lichm an.Unified approach to gas and fluiddetection on instantaneous seismic wavelets.SEGTechnical Program Expanded Abstracts,2003,22:1699~1702
[4]俞寿朋.宽带Ricker子波.石油地球物理勘探,1996,31(5):605~615Yu Shou-peng.Wide-band Ricker wavelet.OGP,1996,31(5):605~615
[5]Ricker N.The formand nature of seismic waves andthe structure of seismograms.Geophysics,1940,5(4):348~366
[6]Huang Jun-bin,Gao Li-jun,Gao Yong.Side lobes ofwavelets i mpact identification of thin sand bodies.Applied Geophysics,2007,4(2):111~117
[7]Grossmann A and Morlet J.Decomposition of Hardyfunctions into square integrable wavelets of constantshape:SIAM.Journal on Mathematical Analysis,1984,15(4):723~736
[8]http:∥www.mathworks.cn/access/helpdesk/help/toolbox/wavelet/ch06_ad9.ht ml
[9]郑君里,杨为理,应君珩.信号与系统(上).北京:高等教育出版社,1981
[10]俞寿朋.高分辨率地震勘探.北京:石油工业出版社,1993
[11]Taner M T,Koehler F and Sheriff R E.Complexseismic trace analysis.Geophysics,1979,44(6):1041~1063
[12]张海燕,李庆忠.几种常用解析子波的特性分析.石油地球物理勘探,2007,42(6):651~657Zhang Hai-yan and Li Qing-zhong.Analysis on fea-ture of common analytic wavelets.OGP,2007,42(6):651~657
[13]Widess M B.How thin is a thin bed?.Geophysics,1973,38(6):1176~1180
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