粘弹性介质单程波法非零偏移距地震数值模拟与偏移
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摘要
地震资料分辨率降低,得不到深层介质的精确信息实际上是由于大地吸收效应的影响.同时与双程波动方程相比单程波动方程避免了多次波的干扰并且计算效率高、占用内存少.本文首先基于开尔芬粘弹性介质模型将品质因子与单程波分步傅立叶法波场延拓算子相结合,实现了粘弹性介质波场延拓,从而将单程波弹性介质波场延拓推广到了粘弹性介质.然后在定位原理,数学检波器原理以及等时叠加原理的基础之上实现了粘弹性介质非零偏移距叠前正演模拟.最后将数值模拟得到的正演记录进行弹性偏移和粘弹性偏移并进行对比分析.通过数值算例可以看出,粘弹性介质叠前正演深层的反射波能量减弱,同相轴变粗,频带变窄,主频减小,分辨率降低;粘弹性偏移不但实现了振幅的恢复,而且同时偏移剖面的垂向空间分辨率也得到了提高.
Due to absorption of the earth,the seismic data has lower resolution and could not get the precise information.At the same time,one-way wave equation methods have many advantages in seismic forward modeling than full way equation,for example,high calculation efficiency,less memory.In this paper,we combine the quality factor Q with the SSF operator using one-way wave equation to realize wave-field extrapolation arithmetic used for viscoelastic medium.Then,we realize viscoelastic medium nonzero-offset seismic pre-stack forward modeling by oneway equation based on positioning principle,mathematical geophone principle and equal-time stacking principle. Finally,we use elastic and viscoelastic arithmetic to image for viscoelastic forward modeling and comparison. Numerical examples show that viscoelastic medium pre-stack forward decreases the deep reflection wave energy significantly,with the thick axis and narrow band and the lower resolution.Migration with viscoelastic arithmetic has achieved amplitude recovery,and the seismic data resolution also has been enhanced.
Due to absorption of the earth,the seismic data has lower resolution and could not get the precise information.At the same time,one-way wave equation methods have many advantages in seismic forward modeling than full way equation,for example,high calculation efficiency,less memory.In this paper,we combine the quality factor Q with the SSF operator using one-way wave equation to realize wave-field extrapolation arithmetic used for viscoelastic medium.Then,we realize viscoelastic medium nonzero-offset seismic pre-stack forward modeling by oneway equation based on positioning principle,mathematical geophone principle and equal-time stacking principle. Finally,we use elastic and viscoelastic arithmetic to image for viscoelastic forward modeling and comparison. Numerical examples show that viscoelastic medium pre-stack forward decreases the deep reflection wave energy significantly,with the thick axis and narrow band and the lower resolution.Migration with viscoelastic arithmetic has achieved amplitude recovery,and the seismic data resolution also has been enhanced.
引文
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[26] 李子顺.地震波衰减规律及其恢复方法[J].地球物理学进展,2007,22(05) :1545～1551． Li Z S.Seismic wave attenuation and recovering method[J].Progress in Geophysics,2007,22(05) :1545～1551．
[27] 贺振华,胡光眠,黄德济.数学检波器与波动方程地震叠前正演[J].成都理工大学学报(自然科学版),2004,31(6) :675～678． He Z H,Hu G M,Huang D J.Mathematics geophone and preforward of seismic by wave equation[J].Journal of Chengdu University of Technology(Science & Technology Edition),2004,31(6) :675～678．
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[2] 张致付,孟小红,黎咸威.构造单程波算子的优化方法及其在偏移中的应用[J].地球物理学进展,2008,23(4) :1111～1117． Zhang Z F,Meng X H,Li X W.The optimization methods of constructing one way operator and its application in migration[J].Progress in Geophysics,2008,23(4) :1111～1117．
[3] 刘洪,王秀闽,曾锐,等.单程波算子积_分解的象征表示[J].地 球物理学进展,2007,22(02) :463～471 Liu H,Wang X M,Zeng R,et al.Symbol description to integral solution of one-way wave operator[J].Progress in Geophysics,2007,22(02) :463～471
[4] 杨辉,刘洪,李幼铭.单程波方程偏移算子高阶辛格式[J].地球物理学报,2003,46(4) :533～538． Yang H,Liu H,Li Y M.High order symplectic scheme for one-way wave equation operator[J].Chinese J.Geophys.(in Chinese),2003,46(4) :533～538．
[5] 李冰,刘洪,李幼铭.波场延拓短算子构造方法[J].地球物理学报,2003,46(2) :246～251． Li B,Liu H,Li Y M.Method of creating short operator of wave field extrapolating[J].Progress in Geophysics,2003,46(2) : 246～251．
[6] Gazdag J.Wave equation with phase shift method[J].Geophysics.1978,43,1342～1351．
[7] Lai J,Gardner G H.Forward modeling using the PSPI method[J].Seismic acoustic laboratory,Annual progress review,1984 (14) :271～300．
[8] Gazdag J,Sguazzero.Migration of seismic data by phase shift plus interpolation[J].Geophysics,1984．
[9] Stoffa P L.Split step Fourier migration[J].Geophysics,1990．
[10] Huang L J,Fehler M C,Wu R S.Extented local Born Fourier migration[J].Geophysics,1999,64:1524．
[11] 刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报,2007,50(1) :268～276． Liu D J,Yin X Y.A method of Fourier finite-difference preserved amplitude prestack depth migration[J].Chinese J. Geophys.(in Chinese),2007,50(1) :268～276．
[12] RistowD,Ruhl T.Fourier finite-difference migration[J].Geophysics,1994,59,1882～1893
[13] 张金海,王卫民,赵连锋,等.傅里叶有限差分法三维波动方程正演模拟[J].地球物理学报,2007,50(6) :1854～1862． Zhang J H,Wang W M,Zhao L F,et al.Modeling 32D scalar waves using the Fourier finite2difference method[J].Chinese J.Geophys.(inChinese),2007,50(6) :1854～1862．
[14] 熊高君,贺振华,等.改进的正演模拟定位原理[J].石油地球物理勘探,1998,33(6) :742～748． Xiong G J,He Z H,el al.Improved forward simulation Location principle[J].Oil Geophysical Prospecting,1998,33(6) :742～748．
[15] 熊高君,贺振华,等.共炮记录正演模拟检波点下延记录原理[J].石油物探,1999,38(2) :43～49． Xiong G J,He Z H,el al.Geophone downward principle of CSP record forward simulation[J].Geophysical Prospecting for Petroleum.1999,38(2) :43～49．
[16] 熊晓军.单程波动方程地震数值模拟新方法研究[D].成都:成都理工大学博士学位论文,2007． Xiong X J.Method Research of One-way Wav-equation Seismic Numerical Simulation[D].Chendu:Ph.D dessertation,Chendu University of Technology,2007．
[17] HeZ H,Xiong G J,Zhang Y X.Nonzero offset seismic forward modeling by one-way acoustic wave-equation[A]. 68~(th)Annual International Meeting,SEG,Expended Abstracts [C],New Orleans,U.S.A,1998．
[18] 王大兴,辛可锋,李幼铭,等.地层条件下砂岩含水饱和度对波速及衰减影响的实验研究[J].地球物理学报,2006,49(3) :908～914． Wang D X,Xin K F,Li Y M,et al.An experimental study of influence of water saturation on velocity and attenuation in sandstone under stratum conditions[J].Chinese J.Geophys.(in Chinese),2006,49(3) :908～914．
[19] 尹陈,贺振华,黄德济.基于弥散黏滞型波动方程的地震波衰减及延迟分析[J].地球物理学报,2009,52(1) :187～192． Yin C,He Z H,Huang D J.The analysis of seismic attenuation and time delay based on the Diffusivity Viscosity wave equation[J].Chinese J.Geophys.(in Chinese),2009,52(1) :187～192．
[20] 施行觉,李成波,Adnan Aydin,等.地球介质的非定常参数黏弹模型[J].地球物理学报,2009,52(1) :50～56． Shi X J,Li C B,Adnan Aydin,et al.Viscoelastic model with variable paraters for earth medium,J].Chinese J.Geophys.(in Chinese),2009,52(1) :50～56．
[21] 尹军杰,刘学伟,李文慧.地震波散射理论及应用研究综述[J].地球物理学进展,2005,3,20(1) :123～134． Yin J J,Liu X W,Li W H.The view of seismic wave scattering theory and its applications[J].Progress in Geophysics,2005,3,20(1) :123～134．
[22] 王东,张海澜,王秀明.部分饱和孔隙岩石中声波传播数值研究[J].地球物理学报,2006,49(2) :524～532． Wang D,Zhang H L,Wang X M.A numerical study of acoustic wave propagation in partially saturated poroelastic rock[J].Chinese J.Geophys.(in Chinese),2006,49(2) :524～532．
[23] 郭智奇,刘财,杨宝俊,等.粘弹各向异性介质中地震波场模拟与特征[J].地球物理学进展,2007,22(03) :804～810 Guo Z Q,Liu C,Yang B J,et al.Seismic wave fields modeling and feature in viscoelastic anisotropic media[J].Progress in Geophysics,2007,22(03) :804～810．
[24] 郝召兵,秦静欣,伍向阳.地震波品质因子Q研究进展综述[J].地球物理学进展,2009,24(2) :375～381,DOI:10． 3696/j.issn.1004-2903． 2009． 02． 002． Hao Z B,Qin J X,Wu X Y.Overview of research on theseismic wave quality factor(Q)[J].Progress in Geophysics,(in Chinese),2009,24(2) :375～381,DOI:10． 3696/j.issn.1004-2903． 2009． 02． 002．
[25] 李振春,王清振.地震波衰减机理及能量补偿研究综述[J].地球物理学进展.2007,22(4) ,1147～1152． Li Z C,Wang Q Z.A review of research on mechanism of seismic attenuation and energy comopensation[J].Progress in Geophysics,2007,22(4) ,1147～1152．
[26] 李子顺.地震波衰减规律及其恢复方法[J].地球物理学进展,2007,22(05) :1545～1551． Li Z S.Seismic wave attenuation and recovering method[J].Progress in Geophysics,2007,22(05) :1545～1551．
[27] 贺振华,胡光眠,黄德济.数学检波器与波动方程地震叠前正演[J].成都理工大学学报(自然科学版),2004,31(6) :675～678． He Z H,Hu G M,Huang D J.Mathematics geophone and preforward of seismic by wave equation[J].Journal of Chengdu University of Technology(Science & Technology Edition),2004,31(6) :675～678．
[28] 贺振华,熊晓军.等时叠加波动方程正演P1[J].物探化探技术,2005,27(3) :194～198． He Z H,Xiong X J.Equal-time stack forward by wave equation[J].Computing Techniques for Geophysical and Geochemical Exploration,2005,27(3) :194～198．
[29] 丁仁伟,李振春,等.叠前逆时深度偏移中的激发时间成像条件[J].地球物理学进展,2008,23(6) :1859～1865． Ding R W,Li Z C,el al.Prestack reverse-time depth migration and imaging condition[J].Progress in Geophysics,2008,23(6) :1859～1865．
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