多子波分解与重构中子波的优选
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摘要
在地震信号的多子波分解与重构中,子波类型与子波分辨率的选择是十分重要的。针对这一问题,首先计算了复数Paul子波和复数Morlet子波的时频谱,并讨论了频率域内子波宽度控制参数对频率域分辨率的影响;然后应用匹配追踪算法对实际地震数据进行多子波分解与重构,从理论上确定了控制复数Paul子波和复数Morlet子波频率域分辨率的最佳子波宽度,对两种子波分解重构地震剖面的差异性进行了对比分析。理论和实际计算结果表明:复数Paul子波与复数Morlet子波的分辨率和频谱能量分布有所不同,在实际应用中需针对不同的研究目的选择不同类型的子波。基于复数Paul子波的重构剖面保留了更多的低频能量,适用于反射同相轴连续的地下构造研究;基于复数Morlet子波的重构剖面高、低频频谱差异大,更适用于地震波吸收衰减研究。
It is very important to select the wavelet and its resolution in multi-wavelet decomposition and reconstruction method.In order to well select wavelet,firstly,we calculate the time-frequency spectrums of complex Paul wavelet and complex Morlet wavelet,and discuss the influence of wavelet width controlling parameters on resolution in frequency domain.Then,matching pursuit algorithm is applied to carry out multi-wavelet decomposition and reconstruction on actual seismic data,and theoretically identify best wavelet width controlling the frequency-domain resolution of complex Paul wavelet and complex Morlet wavelet;meanwhile,the difference of the seismic sections reconstructed from the two wavelets is analyzed.Theoretical model and actual data computation results indicate that the two wavelets have different resolution and different shape of frequency spectrum.In actual application,we should select the wavelet in terms of the target:the reconstruction profile based on complex Paul wavelet preserves more low-frequency energy,which is suitable to study the sub-structures with continuous reflection events;the reconstruction profile based on complex Morlet wavelet has large contrast between low-frequency and high-frequency spectrum,which is more suitable to study the seismic wave absorption and attenuation effect.
It is very important to select the wavelet and its resolution in multi-wavelet decomposition and reconstruction method.In order to well select wavelet,firstly,we calculate the time-frequency spectrums of complex Paul wavelet and complex Morlet wavelet,and discuss the influence of wavelet width controlling parameters on resolution in frequency domain.Then,matching pursuit algorithm is applied to carry out multi-wavelet decomposition and reconstruction on actual seismic data,and theoretically identify best wavelet width controlling the frequency-domain resolution of complex Paul wavelet and complex Morlet wavelet;meanwhile,the difference of the seismic sections reconstructed from the two wavelets is analyzed.Theoretical model and actual data computation results indicate that the two wavelets have different resolution and different shape of frequency spectrum.In actual application,we should select the wavelet in terms of the target:the reconstruction profile based on complex Paul wavelet preserves more low-frequency energy,which is suitable to study the sub-structures with continuous reflection events;the reconstruction profile based on complex Morlet wavelet has large contrast between low-frequency and high-frequency spectrum,which is more suitable to study the seismic wave absorption and attenuation effect.
引文
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[2]赵爽,李仲东,许红梅,等.多子波分解技术检测含煤砂岩储层[J].天然气工业,2007,27(9):44-47 Zhao S,Li Z D,Xu H M,et al.Using multiple wave-let decomposition technique to detect the sandstone reservoir with coal layer[J].Natural Gas Industry,2007,27(9):44-47
[3]王昕,魏刚,刘歆,等.多子波分解与重构技术在复杂储层预测中的应用[J].断块油气田,2010,17(3):289-292 Wang X,Wen G,Liu X,et al.Application of seismic trace-wavelet decomposition and reconfiguration technology in complex reservoir prediction[J].Fault-Block Oil&Gas Field,2010,17(3):289-292
[4]Partyka G,Gridley J,Lopez J.Interpretational appli-cations of spectral decomposition in reservoir charac-terization[J].The Leading Edge,1999,18(3):353-360
[5]Liu J,Wu Y F,Han D H,et al.Time-frequency de-composition based on Ricker wavelet[J].Expanded Abstracts of74 th Annual Internat SEG Mtg,2004,1937-1940
[6]Liu J,Marfure K J.Matching pursuit decomposition using Morlet wavelets[J].Expanded Abstracts of 75 th Annual Internat SEG Mtg,2005,786-789
[7]Wang Y.Multichannel matching pursuit for seismic trace decomposition[J].Geophysics,2010,75(4):61-66
[8]Wang Y.Seismic time-frequency spectral decomposi-tion by matching pursuit[J].Geophysics,2007,72(1):V13-V20
[9]徐天吉,沈忠民,文雪康.多子波分解与重构技术应用研究[J].成都理工大学学报,2010,37(6):660-666 Xu T J,Shen Z M,Wen X K.Research and applica-tion of multi-wavelet decomposition and reconstruc-ting technology[J].Journal of Chengdu University of Technology,2010,37(6):660-666
[10]陈发宇,杨长春.对依据频率的匹配追踪快速算法的改进[J].石油物探,2009,48(1):80-83 Chen F Y,Yang C C.An improvement for frequen-cy-dominated fast matching pursuits algorithm[J].Geophysical Prospecting for Petroleum,2009,48(1):80-83
[11]陈发宇,杨长春.基于MP方法的地震信号快速分解算法[J].地球物理学进展,2007,22(6):1692-1697 Chen F Y,Yang C C.Seismic signal's decomposition based on matching pursuits method[J].Progress in Geophysics,2007,22(6):1692-1697
[12]马朋善,王继强,刘来祥,等.Morlet小波分频处理在提高地震资料分辨率中的应用[J].石油物探,2007,46(3):283-287 Ma P S,Wang J Q,Liu L X,et al.The application of frequency decomposition technique of morlet wavelet in enhancing seismic data resolution[J].Geophysi-cal Prospecting for Petroleum,2007,46(3):283-287
[13]高静怀,吴茜,陈文超,等.小波变换域地震资料瞬时频率分析方法[J].石油物探,2007,46(6):534-540 Gao J K,Wu Q,Cheng W C,et al.Instantaneous fre-quency analysis of seismic data in wavelet transform domain[J].Geophysical Prospecting for Petroleum,2007,46(6):534-540
[14]邹问,陈爱萍,贺振华,等.基于S变换的地震相分析技术[J].石油物探,2006,45(1):48-51 Zhou W,Chen A P,He Z H,et al.Seismic faces a-nalysis based on S transform[J].Geophysical Pros-pecting for Petroleum,2006,45(1):48-51
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