TTI介质地震波数值模拟
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摘要
在勘探开发深入发展的今天,地球介质的各向异性成为研究的热门问题。近年来勘探开发逐步转向对复杂构造油气藏、岩性油气藏和裂缝油气藏的勘探开发,而这些问题都涉及到各向异性,因此必须将各向异性介质地震波的传播理论加以研究来解决上述问题。TTI介质(具有倾斜对称轴的横向各向同性介质)是常见的地震各向异性介质之一,本论文主要探讨和研究TTI介质中的数值模拟方法及其等效模型的应用。
本文从各向异性介质的基本概念入手,推导了TTI介质的基本弹性波动方程及其弹性参数。并对TTI介质的弹性波方程进行了高阶有限差分求解,实现了地震波数值模拟。本文还对数值模拟中的边界条件进行了研究,对Cerjan提出的衰减边界条件修正了阻尼因子,在同样宽的衰减带内将边界反射压制地更加彻底。同时本文还对数值模拟算法引入了并行化库函数,对高阶有限差分实现了并行化运算,极大的节省正演模拟的计算时间,使算法更加人性化和实用化。
最后,在前人研究的基础上探讨了裂缝的等效理论,并且以碳酸盐岩裂缝储层的概念模型为例,建立了等效模型。本文研究了各向异性模型的波场特征,同时也分析了各向异性介质波场对成像的影响,针对裂缝等效模型进行了试算,并对结果进行了详细的分析和讨论。
The oil exploration and development is developing in-depth recently and the study on the anisotropy of Earth media is becoming popular. The oil exploration and development have gradually shifted to the complex structural hydrocarbon reservoir, lithologic hydrocarbon reservoir and fractured reservoir, which are related to anisotropic media and it is necessary to apply the theory of transmission of seismic waves in anisotropic media for the settling the said issues. TTI (Tilted Transversely Isotropy Media) is one of the common seismic anisotropy media, the application of numerical simulation method and its equivalent model about TTI were mainly researched and studied in this paper.
In this paper, the elastic wave equation and its elastic parameters in TTI media were derived from the basic concept of anisotropic media, with solving the elastic wave equation by the finite difference method of higher order, which achieved the numerical simulation of seismic wave in TTI media. This article also studied the boundary conditions of numerical simulation and revised the damping factor for attenuation boundary conditions proposed by Cerjan, the result proves that new boundary conditions is more effective than the old one and the edge reflection was more thoroughly extinguished at the same width of attenuation zone. This paper also introduces a parallel algorithm library function in the numerical simulation, which help to implement the parallel computing for the higher order finite difference and greatly save the computing time of forward simulation, which made the algorithm more humane and practical.
Finally, the equivalent theory of fissure was researched on the basis of the predecessors, and established the equivalent model with the example of concept model for fractured carbonate reservoir. The wave field characteristic of anisotropic model was researched, meanwhile its effects on imagery was appraised. Then the equivalent model for the fissure was calculated on trial, and the results are analyzed and discussed in detail.
本文从各向异性介质的基本概念入手,推导了TTI介质的基本弹性波动方程及其弹性参数。并对TTI介质的弹性波方程进行了高阶有限差分求解,实现了地震波数值模拟。本文还对数值模拟中的边界条件进行了研究,对Cerjan提出的衰减边界条件修正了阻尼因子,在同样宽的衰减带内将边界反射压制地更加彻底。同时本文还对数值模拟算法引入了并行化库函数,对高阶有限差分实现了并行化运算,极大的节省正演模拟的计算时间,使算法更加人性化和实用化。
最后,在前人研究的基础上探讨了裂缝的等效理论,并且以碳酸盐岩裂缝储层的概念模型为例,建立了等效模型。本文研究了各向异性模型的波场特征,同时也分析了各向异性介质波场对成像的影响,针对裂缝等效模型进行了试算,并对结果进行了详细的分析和讨论。
The oil exploration and development is developing in-depth recently and the study on the anisotropy of Earth media is becoming popular. The oil exploration and development have gradually shifted to the complex structural hydrocarbon reservoir, lithologic hydrocarbon reservoir and fractured reservoir, which are related to anisotropic media and it is necessary to apply the theory of transmission of seismic waves in anisotropic media for the settling the said issues. TTI (Tilted Transversely Isotropy Media) is one of the common seismic anisotropy media, the application of numerical simulation method and its equivalent model about TTI were mainly researched and studied in this paper.
In this paper, the elastic wave equation and its elastic parameters in TTI media were derived from the basic concept of anisotropic media, with solving the elastic wave equation by the finite difference method of higher order, which achieved the numerical simulation of seismic wave in TTI media. This article also studied the boundary conditions of numerical simulation and revised the damping factor for attenuation boundary conditions proposed by Cerjan, the result proves that new boundary conditions is more effective than the old one and the edge reflection was more thoroughly extinguished at the same width of attenuation zone. This paper also introduces a parallel algorithm library function in the numerical simulation, which help to implement the parallel computing for the higher order finite difference and greatly save the computing time of forward simulation, which made the algorithm more humane and practical.
Finally, the equivalent theory of fissure was researched on the basis of the predecessors, and established the equivalent model with the example of concept model for fractured carbonate reservoir. The wave field characteristic of anisotropic model was researched, meanwhile its effects on imagery was appraised. Then the equivalent model for the fissure was calculated on trial, and the results are analyzed and discussed in detail.
引文
[1]何樵登,张中杰.横向各向同性介质中地震波及其数值模拟[M].吉林:吉林大学出版社,1996:130-137
[2]吴国忱.Ti介质qP波地震成像方法研究[D].上海:同济大学,2006
[3]滕吉文,王光杰,杨顶辉.地球各向异性介质中地震波理论、检测与应用研究[J] .地学前缘,1998,5(1-2):83-90
[4]杨顶辉,滕吉文.各向异性介质中三分量地震记录的FCT有限差分模拟[J].石油地球物理勘探,1997,32(2):181-191
[5]刘希强,周蕙兰.地震各向异性研究进展[J] .地震研究,1998,21(2):185-195
[6]刘洋.任意偶数阶精度有限差分数值模拟[J] .石油地球物理勘探,1998,33(1):1-10
[7]催兴福,张关全.地震波方程人工边界的两种处理方法[J].石油物探,2003,42(4):452-455
[8] Postma,G.W.,Wave propagation in a stratified medium[J] .Geophysics,1955,20, 780-806.
[9] Alkhalifah, T.,Larner,K.,Migration error in transversely isotropic media[J] .Geophysics, 1994, 59:1405-1418
[10] Schoenberg, M.,de Hoop, M.V.,Approximate dispersion relations for qP-qSV-waves in transversely isotropic media[J] . Geophysics, 2000, 65:919-933
[11]马在田等.计算地球物理学概论[M].上海:同济大学出版社, 1997:175-188
[12]马在田.地震成像技术—有限差分法偏移[M].北京:石油工业出版社, 1989:201-237
[13]王华忠,徐蔚亚,王建民,马在田.VSP数据波动方程叠前深度偏移成像及立体地震成像[J].石油地球物理勘探,2001,36(5):617-525
[14] Brown, R.J.,Lawton, D.C.,Cheadle, S.P.,Scaled physical modeling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium[J] .Geophys. J. Int., 1991, 107: 693-702
[15] Berenger, J.P.,A perfectly matched layer for absorption of electromagnetic waves[J] .J. Comput Phys., 1994, 114:185-200
[16]宋海滨,马在田,张关泉.层状横向各向同性介质反问题初探[J].地球物理学报,1997,40(1):105-118
[17]程玖兵,王华忠,于富文等.波动方程共炮检距道集叠前深度偏移[J] .石油地球物理勘探,2001,36(5):526-532
[18]陈生昌,曹景忠,马在田.基于拟线性Born近似的叠前深度偏移方法[J] .地球物理学报,2001,44(5):704-709
[19]杨慧珠,张友生,陶果.井眼条件下弹性波传播问题的三维有限差分数值模拟[J].地球物理学进展,2003,12(1):348-352
[20] Tsings, C.,Vafidis, A.,Elastic wave propagation in transversely isotropic media using finite difference[J] .Geophysical Prospecting, 1990, 38:933-949
[21] Igel, H., Mora, P., Riollet, B..Anisotropic wave propagation through finite-difference grids[J] .Geophysics, 1995, 60:1203-1261
[22] Issac, J.H.,Lawton, D.C., Image mispositioning duo to dipping TI media: A physical seismic modeling study[J] . Geophysics, 1999, 64:1230-1238
[23]佘德平.数值模拟技术的发展现状[J].勘探地球物理进展,2003,26(5-6):407-412
[24]张美根.各向异性弹性波正反演问题研究[D] .北京:中国科学院地球物理研究所,2000
[25]贺振华,王才经,李建朝.反射地震资料偏移处理与反演方法重庆[M].重庆:重庆大学出版社,1989:387-499
[26] Jolly, R.N.,Investigation of shear waves[J] . Geophysics, 1956, 21:905-938
[27] Juhlin, C.,Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media[J] . Geophysical Prospecting, 1995, 43:843-858
[28] Meadows, M., Coen, S.,Exact inversion of plane layered isotropic and anisotropic elastic media by the state-space approach[J] . Geophysics, 1986, 52:2031-2050
[29]杨文采.地球物理反演和地震层析成像[M].北京:地质出版社, 1989:331-338
[30]杨文采,李幼铭.应用地震层析成像[M].北京:地质出版社, 1993:557-575
[31]范帧祥,郑仙仲.地震波参数反演与应用技术[M].河南:河南科学技术出版社, 1998:447-465
[32]刘光鼎,李幼铭,吴永刚等.陆相油储地球物理学导论[M].北京:科学出版社, 1998:567-580
[33]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法[J] .地球物理学报,2000,43(3):411-419
[34] Krey, Th.,Helbig, K.,A theorem concerning anisotropy of stratified media and its significance for reflection seismic[J] .Geophysical prospecting, 1956, 4:294-302
[35] Kreys R.G.,Absorbing boundary conditions for acoustic media[J] . Geophysics, 1985, 50:705-708
[36] Dimitri Komatitsch, Christophe Barmes,Jeroen Tromp.Simulation of anisotropic wave propagation based upon a spectral element method: Geophysics, 2000, 65: 1251-1260
[37] Uren, N.F.,Gardner, G. H., McDonald, J. A.,The migrator’s equation for anisotropic media[J] .Geophysics, 1990, 55:1429-1434
[38]张中杰,何樵登.含裂隙介质中地震运动学问题正演模拟[J] .石油地球物理勘探,1989,24(3):290-300
[39]张中杰,滕吉文.各向异性介质中界面上改进型斯奈尔定律[J] .科学通报,1995,40(2):1724-1728
[40]张中杰,滕吉文,贺振华.EDA介质中地震波速度、衰减与品质因子方位异性研究[J].中国科学,1999,29(6):569-574
[41] Uzcategui,O.,2-D depth migration in transversely isotropic media using explicit operators[J] . Geophysics, 1995, 60:1819-1829
[42] Vestrum,R.W.,Lawton,D.C.,Schmid,R.,Imaging structures below dipping TI media[J] .Geophysics, 1999, 64:1239-1246
[43] Williamson, P.R.,On resolution and uniqueness in anisotropic crosshole traveltime tomography[J] .Geophysics, 1998, 63:1184-1189
[44] Wang T.L.,Tang X.M.,Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach[J] .Geophysics, 2003, 68:1749-1755
[45] Zhang, J.,Verschuur, D.J.,Wapenaar, C.P.A.,Depth migration of shot records in heterogeneous transversely isotropic media using optimum explicit operators[J]. Geophysical Prospecting, 49, 2001: 287-299
[46] Juhlin, C.,Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media[J] .Geophysical Prospecting, 1995, 43:843-858
[47]牛滨华,孙春岩.方位界面及其波场数值模拟[J].石油地球物理勘探,1994,29(6): 685-694
[48]牛滨华,何樵登,孙春岩.裂隙各向异性介质波场VSP多分量记录的数值模拟[J].地球物理学报,1995,38(4):519-527
[49]滕吉文,王光杰,杨顶辉.地球各向异性介质中地震波理论、检测与应用研究[J].地学前缘,1998,5(1-2):83-90
[50]邓玉琼,戴霆范,郭宗汾.弹性波叠前有限元反时偏移[J] .石油物探,1990,29(3):22-23
[51]阴可,杨慧珠.各向异性介质中的AVO[J] .地球物理学报,1998,41(3):382-391
[52]朱兆林.倾斜横向各向同性介质中P-S波处理方法研究[D].上海:同济大学,2008
[53]张宝金.地震波参数反演及其可信度分析[D].上海:同济大学,2003
[54]张卫涛,杨慧珠.各向异性介质弹性波传播的三维不规则网格有限差分方法[J].地球物理学报,2004,18(2):332-337
[2]吴国忱.Ti介质qP波地震成像方法研究[D].上海:同济大学,2006
[3]滕吉文,王光杰,杨顶辉.地球各向异性介质中地震波理论、检测与应用研究[J] .地学前缘,1998,5(1-2):83-90
[4]杨顶辉,滕吉文.各向异性介质中三分量地震记录的FCT有限差分模拟[J].石油地球物理勘探,1997,32(2):181-191
[5]刘希强,周蕙兰.地震各向异性研究进展[J] .地震研究,1998,21(2):185-195
[6]刘洋.任意偶数阶精度有限差分数值模拟[J] .石油地球物理勘探,1998,33(1):1-10
[7]催兴福,张关全.地震波方程人工边界的两种处理方法[J].石油物探,2003,42(4):452-455
[8] Postma,G.W.,Wave propagation in a stratified medium[J] .Geophysics,1955,20, 780-806.
[9] Alkhalifah, T.,Larner,K.,Migration error in transversely isotropic media[J] .Geophysics, 1994, 59:1405-1418
[10] Schoenberg, M.,de Hoop, M.V.,Approximate dispersion relations for qP-qSV-waves in transversely isotropic media[J] . Geophysics, 2000, 65:919-933
[11]马在田等.计算地球物理学概论[M].上海:同济大学出版社, 1997:175-188
[12]马在田.地震成像技术—有限差分法偏移[M].北京:石油工业出版社, 1989:201-237
[13]王华忠,徐蔚亚,王建民,马在田.VSP数据波动方程叠前深度偏移成像及立体地震成像[J].石油地球物理勘探,2001,36(5):617-525
[14] Brown, R.J.,Lawton, D.C.,Cheadle, S.P.,Scaled physical modeling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium[J] .Geophys. J. Int., 1991, 107: 693-702
[15] Berenger, J.P.,A perfectly matched layer for absorption of electromagnetic waves[J] .J. Comput Phys., 1994, 114:185-200
[16]宋海滨,马在田,张关泉.层状横向各向同性介质反问题初探[J].地球物理学报,1997,40(1):105-118
[17]程玖兵,王华忠,于富文等.波动方程共炮检距道集叠前深度偏移[J] .石油地球物理勘探,2001,36(5):526-532
[18]陈生昌,曹景忠,马在田.基于拟线性Born近似的叠前深度偏移方法[J] .地球物理学报,2001,44(5):704-709
[19]杨慧珠,张友生,陶果.井眼条件下弹性波传播问题的三维有限差分数值模拟[J].地球物理学进展,2003,12(1):348-352
[20] Tsings, C.,Vafidis, A.,Elastic wave propagation in transversely isotropic media using finite difference[J] .Geophysical Prospecting, 1990, 38:933-949
[21] Igel, H., Mora, P., Riollet, B..Anisotropic wave propagation through finite-difference grids[J] .Geophysics, 1995, 60:1203-1261
[22] Issac, J.H.,Lawton, D.C., Image mispositioning duo to dipping TI media: A physical seismic modeling study[J] . Geophysics, 1999, 64:1230-1238
[23]佘德平.数值模拟技术的发展现状[J].勘探地球物理进展,2003,26(5-6):407-412
[24]张美根.各向异性弹性波正反演问题研究[D] .北京:中国科学院地球物理研究所,2000
[25]贺振华,王才经,李建朝.反射地震资料偏移处理与反演方法重庆[M].重庆:重庆大学出版社,1989:387-499
[26] Jolly, R.N.,Investigation of shear waves[J] . Geophysics, 1956, 21:905-938
[27] Juhlin, C.,Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media[J] . Geophysical Prospecting, 1995, 43:843-858
[28] Meadows, M., Coen, S.,Exact inversion of plane layered isotropic and anisotropic elastic media by the state-space approach[J] . Geophysics, 1986, 52:2031-2050
[29]杨文采.地球物理反演和地震层析成像[M].北京:地质出版社, 1989:331-338
[30]杨文采,李幼铭.应用地震层析成像[M].北京:地质出版社, 1993:557-575
[31]范帧祥,郑仙仲.地震波参数反演与应用技术[M].河南:河南科学技术出版社, 1998:447-465
[32]刘光鼎,李幼铭,吴永刚等.陆相油储地球物理学导论[M].北京:科学出版社, 1998:567-580
[33]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法[J] .地球物理学报,2000,43(3):411-419
[34] Krey, Th.,Helbig, K.,A theorem concerning anisotropy of stratified media and its significance for reflection seismic[J] .Geophysical prospecting, 1956, 4:294-302
[35] Kreys R.G.,Absorbing boundary conditions for acoustic media[J] . Geophysics, 1985, 50:705-708
[36] Dimitri Komatitsch, Christophe Barmes,Jeroen Tromp.Simulation of anisotropic wave propagation based upon a spectral element method: Geophysics, 2000, 65: 1251-1260
[37] Uren, N.F.,Gardner, G. H., McDonald, J. A.,The migrator’s equation for anisotropic media[J] .Geophysics, 1990, 55:1429-1434
[38]张中杰,何樵登.含裂隙介质中地震运动学问题正演模拟[J] .石油地球物理勘探,1989,24(3):290-300
[39]张中杰,滕吉文.各向异性介质中界面上改进型斯奈尔定律[J] .科学通报,1995,40(2):1724-1728
[40]张中杰,滕吉文,贺振华.EDA介质中地震波速度、衰减与品质因子方位异性研究[J].中国科学,1999,29(6):569-574
[41] Uzcategui,O.,2-D depth migration in transversely isotropic media using explicit operators[J] . Geophysics, 1995, 60:1819-1829
[42] Vestrum,R.W.,Lawton,D.C.,Schmid,R.,Imaging structures below dipping TI media[J] .Geophysics, 1999, 64:1239-1246
[43] Williamson, P.R.,On resolution and uniqueness in anisotropic crosshole traveltime tomography[J] .Geophysics, 1998, 63:1184-1189
[44] Wang T.L.,Tang X.M.,Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach[J] .Geophysics, 2003, 68:1749-1755
[45] Zhang, J.,Verschuur, D.J.,Wapenaar, C.P.A.,Depth migration of shot records in heterogeneous transversely isotropic media using optimum explicit operators[J]. Geophysical Prospecting, 49, 2001: 287-299
[46] Juhlin, C.,Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media[J] .Geophysical Prospecting, 1995, 43:843-858
[47]牛滨华,孙春岩.方位界面及其波场数值模拟[J].石油地球物理勘探,1994,29(6): 685-694
[48]牛滨华,何樵登,孙春岩.裂隙各向异性介质波场VSP多分量记录的数值模拟[J].地球物理学报,1995,38(4):519-527
[49]滕吉文,王光杰,杨顶辉.地球各向异性介质中地震波理论、检测与应用研究[J].地学前缘,1998,5(1-2):83-90
[50]邓玉琼,戴霆范,郭宗汾.弹性波叠前有限元反时偏移[J] .石油物探,1990,29(3):22-23
[51]阴可,杨慧珠.各向异性介质中的AVO[J] .地球物理学报,1998,41(3):382-391
[52]朱兆林.倾斜横向各向同性介质中P-S波处理方法研究[D].上海:同济大学,2008
[53]张宝金.地震波参数反演及其可信度分析[D].上海:同济大学,2003
[54]张卫涛,杨慧珠.各向异性介质弹性波传播的三维不规则网格有限差分方法[J].地球物理学报,2004,18(2):332-337