奇异性分析方法在地震资料解释及反演研究中的应用
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摘要
本文引入启动函数拓展传统的地层转换模型,在该模型中利用奇异性信息量化地层速度的突变特征,并基于传统的褶积模型研究奇异性信息在波阻抗到合成地震记录之间的传递性。研究结果表明,地震记录中较好地保留了地层介质的奇异性特征,因而从地震记录中提取的奇异性信息除了可以帮助进行地震解释外,还可以作为介质波阻抗反演的有力的支持工具.
In this paper,we introduce the onset function to generalize the traditional geologic boundaries variations model which uses,singularity information to represent the abruptness of the lithologic velocity transition.We study the singularity information passage from acoustic impedance to seismogram based on the convolution seismic-model theory.Our results indicate that stratum singularity information is preserved well by seismic data,so it is a powerful tool for delineating stratigraphy boundaries and inversing acoustic impedance based on singularity analysis of seismic data.
In this paper,we introduce the onset function to generalize the traditional geologic boundaries variations model which uses,singularity information to represent the abruptness of the lithologic velocity transition.We study the singularity information passage from acoustic impedance to seismogram based on the convolution seismic-model theory.Our results indicate that stratum singularity information is preserved well by seismic data,so it is a powerful tool for delineating stratigraphy boundaries and inversing acoustic impedance based on singularity analysis of seismic data.
引文
[1]李春峰.分形介质与分形地层[J].地层学杂志,2005,29(4):348~354.Li C F.Fractal media and fractal stratigraphy[J].Journal ofstratigraphy,2005,29(4):348~354.
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[3]Chang X,Liu Y K.Ashida Yuzuru.Hausdorff fractal algo-rithm for picking first break in seismic traces[J].BUTSURI-TANSA.1999,52(4):316~322.
[4]常旭,刘伊克.地震记录的广义分维及其应用[J].地球物理学报,2002,45(6):839~846.Chang X,Liu Y K.The generalized fractal dimension of seis-mic records and its application[J].Chinese J.Geophys.(inchinese),2002,45(6):839~846.
[5]Payton C,Ed.Seismic stratigraphy?applications to hydro-carbon exploration AAPG,1977.
[6]Verhelst F.Integration of seismic data with well-log data:Ph.D.thesis,Delft University of Technology,2000.
[7]Muller J,Bokn I,McCauley J L.Multifractal analysis ofpetrophysical data:Ann.Geophysicae,1992,10,735~761.
[8]Herrmann F J.Multiscale analysis of well and seismic data,Mathematical Methods in Geophysical Imaging V.1998,180~208.
[9]Dessing F J.A wavelet transform approach to seismic process-ing:Ph.D.thesis,Delft University of Technology,Delft,theNetherlands,1997.
[10]Herrmann F J.A scaling medium representation,a discus-sion on well-logs,fractals and waves:Ph.D.thesis,DelftUniversity of Technology,Delft,the Netherlands,1997.
[11]Herrmann F J,Stark C.A scale attribute for texture in well-and seismic data.70th Ann.Internat Mtg[M].Soc.Expl.Geophys.Expanded Abstracts,2000.
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[13]李春峰,Christopher Liner.基于小波多尺度分析的奇性指数:一种新地震属性[J].地球物理学报,2005,48(4):882~888.Li C F,Christopher L.Singularity exponent from wavelet-based multiscale analysis:A new seismic attribute[J].Chi-nese J.Geophys.(in chinese),2005,48(4):882~888.
[14]Zemanian A H.Distribution theory and transform analysis:An introduction to generalized functions[J].with applica-tions.New York:McGraw-Hill.1965,1~371.
[15]Holschneider M.Wavelets an analysis tool[M].Oxford Sci-ence Publications,1995.
[16]Le Mehaute A.Fractal geometries Boco Raton[M].FL,USA.CRC Press Inc.1991,1~181.
[17]Gorenflo R F.Fractional Calculus in Continuum Mechanics,chapter Fractional Calculus[M].Springer Verlag,1997.
[18]Mallat S,Hwang W L.Singularity detection and processingwith wavelets[J].IEEE Transactions on Information Theo-ry,1992,38:617~642.
[19]Struzik Z R.Determining local singularity strengths and theirspectra with the wavelet transform[J].Fractals,2000,8(2):163~179.
[20]Bony J M.Two-microlocalization and propagation of singu-larities for semilinear hyperbolic equations[M].In Proc.ofTanaguchi Symp.,HERT.Katata,October 1984:11~49.
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[22]Jaffard S.Pointwise smoothness,two-microlocalization andwavelet coefficients[J].Publicacions Matematiques,1991,35:155~168.
[23]Kolwankar K M,Levy Vehel J.A time domain characteriza-tion of the fine local regularity of functions[J].JFAA,2002,8:319~334.
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[25]曹茂森,任青文,王怀洪.基于小波与分形理论的地震异常检测[J].地球物理学报,2005,48(3):672~679.Cao M S,Ren Q W,Wang H H.A method of detecting seis-mic singularities using combined wavelet with fractal[J].Chinese J.Geophys.(in Chinese),2005,48(3):672~679.
[26]李庆春,朱光明.基于小波变换的薄层地震信号奇点的检测[J].地震学报,2000,22(1):54~58.Li Q C,Zhu G M.Wavelet-based singularity detection ofthin-layer seismic signal[J].Acta Seismologica Sinica(inChinese),2000,22(1):54~58.
[27]李世雄.一维波动方程的奇性反演与小波[J].地球物理学报,1995,38(1):93~104.Li S X.Analysis and inversion of singularities of one-dimen-sional wave equations and wavelets[J].Chinese J.Geophys.(in Chinese),1995,38(1):93~104.
[28]Herrmann F J,Stark C.Monoscale analysis of edges Preflec-tors using fractional differentiations Pintegrations.69thAnn.Internat Mtg.,Soc.Expl[M].Geophys.ExpandedAbstracts,1999.
[29]Herrmann F J.Singularity characterization by monoscale a-nalysis:Application to seismic imaging[J].Appl.Comput.Harmon.Anal.,2001,11:64~88.
[30]Herrmann F J.Fractional spline matching pursuit:a quanti-tative tool for seismic stratigraphy.In Expanded Abstracts,Tulsa,2001a.Soc.Expl.Geophys.
[31]Herrmann F J.Multifractional splines:application to seismicimaging.In M.Unser,A.Aldroubi,Andrew,and Laine,editors,Proceedings of SPIE Technical Conference on Wave-lets:Applications in Signal and Image Processing X,volume5207,pages 240?258.SPIE,2003.
[32]Wapenaar K,Gouswaard J.Van Wijngaarden A-J.Multian-gle,multiscale inversion of migrated seismic data[J].TheLeading Edge,1999,18:928~932.
[33]Lyons W J,Herrmann F J,Grotzinger J.Singularity analy-sis:a tool for extracting lithologic and stratigraphic contentfrom seismic data.71st Ann.Internat Mtg,Soc.Expl[M].Geophys.Expanded Abstracts,2001.
[34]Smythe J,Gersztenkorn A,Radovich B,Liner C,and Li C.SPICE:Layered Gulf of Mexico Shelf Framework from Spec-tral Imaging[JM].The Leading Edge,2004,23:921~926.
[35]Liner C,Li C F,Gersztenkorn A,Smythe A.SPICE:A newgeneral seismic attribute:72nd Annual International Meet-ing,SEG,Expanded Abstracts,2004,433~436.
[36]Li C F.Scaling and wavelet-based singularity analyses for ge-ological and geophysical interpretation[Ph.D.dissertation].Tulsa:Univ.of Tulsa,2002.
[2]常旭,刘伊克.Hausdorff分数维识别地震道初至走时[J].地球物理学报,1998,41(6):826~832.Chang X,Liu Y K.Distinguishing seismic first break bymeans of Hausdorff fractal dimension[J].Chinese J.Geo-phys.(in chinese),1998,41(6):826~832.
[3]Chang X,Liu Y K.Ashida Yuzuru.Hausdorff fractal algo-rithm for picking first break in seismic traces[J].BUTSURI-TANSA.1999,52(4):316~322.
[4]常旭,刘伊克.地震记录的广义分维及其应用[J].地球物理学报,2002,45(6):839~846.Chang X,Liu Y K.The generalized fractal dimension of seis-mic records and its application[J].Chinese J.Geophys.(inchinese),2002,45(6):839~846.
[5]Payton C,Ed.Seismic stratigraphy?applications to hydro-carbon exploration AAPG,1977.
[6]Verhelst F.Integration of seismic data with well-log data:Ph.D.thesis,Delft University of Technology,2000.
[7]Muller J,Bokn I,McCauley J L.Multifractal analysis ofpetrophysical data:Ann.Geophysicae,1992,10,735~761.
[8]Herrmann F J.Multiscale analysis of well and seismic data,Mathematical Methods in Geophysical Imaging V.1998,180~208.
[9]Dessing F J.A wavelet transform approach to seismic process-ing:Ph.D.thesis,Delft University of Technology,Delft,theNetherlands,1997.
[10]Herrmann F J.A scaling medium representation,a discus-sion on well-logs,fractals and waves:Ph.D.thesis,DelftUniversity of Technology,Delft,the Netherlands,1997.
[11]Herrmann F J,Stark C.A scale attribute for texture in well-and seismic data.70th Ann.Internat Mtg[M].Soc.Expl.Geophys.Expanded Abstracts,2000.
[12]Li C F.Information passage from acoustic impedance to seis-mograms:perspective from wavelet-based multiscale analysis[M].J.Geophys.Res.,2004,109.
[13]李春峰,Christopher Liner.基于小波多尺度分析的奇性指数:一种新地震属性[J].地球物理学报,2005,48(4):882~888.Li C F,Christopher L.Singularity exponent from wavelet-based multiscale analysis:A new seismic attribute[J].Chi-nese J.Geophys.(in chinese),2005,48(4):882~888.
[14]Zemanian A H.Distribution theory and transform analysis:An introduction to generalized functions[J].with applica-tions.New York:McGraw-Hill.1965,1~371.
[15]Holschneider M.Wavelets an analysis tool[M].Oxford Sci-ence Publications,1995.
[16]Le Mehaute A.Fractal geometries Boco Raton[M].FL,USA.CRC Press Inc.1991,1~181.
[17]Gorenflo R F.Fractional Calculus in Continuum Mechanics,chapter Fractional Calculus[M].Springer Verlag,1997.
[18]Mallat S,Hwang W L.Singularity detection and processingwith wavelets[J].IEEE Transactions on Information Theo-ry,1992,38:617~642.
[19]Struzik Z R.Determining local singularity strengths and theirspectra with the wavelet transform[J].Fractals,2000,8(2):163~179.
[20]Bony J M.Two-microlocalization and propagation of singu-larities for semilinear hyperbolic equations[M].In Proc.ofTanaguchi Symp.,HERT.Katata,October 1984:11~49.
[21]Guiheneuf B,Levy Vehel J.2-microlocal analysis and ap-plications in signal processing[M].In:Proceedings of Inter-national Wavelets Conference,Tangier,1998.
[22]Jaffard S.Pointwise smoothness,two-microlocalization andwavelet coefficients[J].Publicacions Matematiques,1991,35:155~168.
[23]Kolwankar K M,Levy Vehel J.A time domain characteriza-tion of the fine local regularity of functions[J].JFAA,2002,8:319~334.
[24]曹聿明.地震道的奇性特征与分辨率[J].石油地球物理勘探,1995,30(4):480~486.Cao Y M.Resolution and singularity of seismic trace[J].OilGeophysical Prospecting(in Chinese),1995,30(4):480~486.
[25]曹茂森,任青文,王怀洪.基于小波与分形理论的地震异常检测[J].地球物理学报,2005,48(3):672~679.Cao M S,Ren Q W,Wang H H.A method of detecting seis-mic singularities using combined wavelet with fractal[J].Chinese J.Geophys.(in Chinese),2005,48(3):672~679.
[26]李庆春,朱光明.基于小波变换的薄层地震信号奇点的检测[J].地震学报,2000,22(1):54~58.Li Q C,Zhu G M.Wavelet-based singularity detection ofthin-layer seismic signal[J].Acta Seismologica Sinica(inChinese),2000,22(1):54~58.
[27]李世雄.一维波动方程的奇性反演与小波[J].地球物理学报,1995,38(1):93~104.Li S X.Analysis and inversion of singularities of one-dimen-sional wave equations and wavelets[J].Chinese J.Geophys.(in Chinese),1995,38(1):93~104.
[28]Herrmann F J,Stark C.Monoscale analysis of edges Preflec-tors using fractional differentiations Pintegrations.69thAnn.Internat Mtg.,Soc.Expl[M].Geophys.ExpandedAbstracts,1999.
[29]Herrmann F J.Singularity characterization by monoscale a-nalysis:Application to seismic imaging[J].Appl.Comput.Harmon.Anal.,2001,11:64~88.
[30]Herrmann F J.Fractional spline matching pursuit:a quanti-tative tool for seismic stratigraphy.In Expanded Abstracts,Tulsa,2001a.Soc.Expl.Geophys.
[31]Herrmann F J.Multifractional splines:application to seismicimaging.In M.Unser,A.Aldroubi,Andrew,and Laine,editors,Proceedings of SPIE Technical Conference on Wave-lets:Applications in Signal and Image Processing X,volume5207,pages 240?258.SPIE,2003.
[32]Wapenaar K,Gouswaard J.Van Wijngaarden A-J.Multian-gle,multiscale inversion of migrated seismic data[J].TheLeading Edge,1999,18:928~932.
[33]Lyons W J,Herrmann F J,Grotzinger J.Singularity analy-sis:a tool for extracting lithologic and stratigraphic contentfrom seismic data.71st Ann.Internat Mtg,Soc.Expl[M].Geophys.Expanded Abstracts,2001.
[34]Smythe J,Gersztenkorn A,Radovich B,Liner C,and Li C.SPICE:Layered Gulf of Mexico Shelf Framework from Spec-tral Imaging[JM].The Leading Edge,2004,23:921~926.
[35]Liner C,Li C F,Gersztenkorn A,Smythe A.SPICE:A newgeneral seismic attribute:72nd Annual International Meet-ing,SEG,Expanded Abstracts,2004,433~436.
[36]Li C F.Scaling and wavelet-based singularity analyses for ge-ological and geophysical interpretation[Ph.D.dissertation].Tulsa:Univ.of Tulsa,2002.
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