TTI介质PS波小角度AVO分析
摘要
AVO分析和反演一直以来是地震勘探领域中的一个重要内容。随着勘探难度的不断加大和勘探精度要求的日益提高,AVO的相关理论也已从最初的地下介质的各向同性假设拓展到各向异性的领域中,以便得到越来越广泛的实际应用。
本文介绍了各向异性介质AVO的基本理论,系统分析了近些年来针对各向异性介质中PP波、PS波反射-透射系数表达式,并特别针对TTI介质研究了PS波的反射系数、AVO梯度等量与介质各向异性参数的关系。最后,本文将遗传算法引入到AVO的反演过程中,对模拟数据进行各向异性参数的反演,结果具有一定的可信度。总之,无论是AVO的定性分析还是定量反演都可以不同程度的获得地下储层的裂隙倾角和方位等有效的地层信息。
In seismic exploration , amplitude variation with offset (AVO) and amplitude variation with azimuth (AVAZ) analyses are frequently-used and perfect useful methords for recognizing the lithology and inversing the stratum parameters . The traditional AVO theory is on the assumption that the underground medium is isotropic, but along with the more and more higher exploration precision, all the seismic exploration works should comsider the fact that the underground media is anisotropic . The AVO analysis in anisotropic media a very rapidness improving.
In this articale , first , we introduced the the basic theory of anistropic media especially the TI (transversely isotropic) media which containing elasticity coefficients, anisotropic Thomsen parameters and the phase velocity and group velocity in anisotropic media.All of these parameters are the necessarily condition of getting the reflection coefficients in anisotropic media. Recently, the methords of getting the reflection and transmission coefficients are based on the first order perturbation theory in the approximately of weak contrast and weak anisotropic. In this article ,this theory is introduced briefly.
Based on, we analysis and summarize the reflection coefficients of PP wave and PS wave in anisotropic media. First, the VTI ( transversely isotropic with a vertical symmetry ) media and HTI(transversely isotropic with a horizontal symmetry) media are the special cases of orthorhombic anisotropic media, then the existing reflection coefficients expressions of orthorhombic anisotropic media can be applicable in VTI and HTI media. There is a corresponding relationship between the anisotropic parameters in orthorhombic anisotropic media and in the VTI or HTI media. From this on we can get new reflection coefficients expressions which are suitable for VTI and HTI media.For the orthorhombic anisotropic, VTI and HTI media ,we can get the reflection coefficients on the interface which comparting any two medias we talked about before. At the same time,because the incidence angle are normaly minum or commonly in the AVO analysis of factly seismic data, so in the reflection coefficients expressions the third order terms of the incidence angle’s sine value are be close to zero.At this moment the eave out of these terms should not take too much errors of reflection coefficients.On the other hand this predigestion makes the work of AVO anylysis and inverse more practicality and easely.
In the former reflection coefficients expressions of PP wave in anisotropic media, we can not find a direct relationship between the reflection coefficients and the Thomsen anisotropic parameters. In this article ,we first get the VTI media’s elasticity coefficients matrix through the relationship of Thomsen anisotropin patameters and elasticity coefficients. When we have confirm azimuth and dip angles of the symmetry in TTI media the elasticity coefficients in TTI meida can be confirmed by the rotating of reference frame.Finally we get the reflection coefficients in TTI media through the common expressions of reflection coefficients in weak anisotropic media.
When one of the two medias around the interface is TTI media, a very complex phenomena appears for the PS wave. In the first order perturbation we can get a conclusion that a PS reflection wave appearing by a vertical incidence P wave when the A34 and A35 in the elasticity coefficients matrix are nonzero. We know that in the isotropic,VTI or HTI media,all the two elasticity coefficients are zero, but if one of the two medias is TTI, the vertical incidence P wave makes a reflection PS wave.The reflection coefficients can even be as high as 0.1 although the media is a moderate anisotropic media. In this article we summarize the express of the phase velocity previously, this exact phase velocity make it possible to get the exact reflection coefficients of the PS wave which appearance because of the P wave’s normal incidence on the ISO/TTI or a TTI/TTI interface. Finally, systematical analysis the PS wave’s ormal incidence reflection coefficients and the AVO gradient varing with the wave velocity in the urper and lower layer,the density and the anisotropic parameters.
Finally,the nonlinear inverse methords are introduced into the process of the inverse from the AVO information to anisotropic parameters in anisotropic media. In this article, there’s a inverse processing from synthetic seismic recoder to anisotropic parameters in anistropic media using genetic algorithm. It is well know that the genetic algorithm is a heuristics monte-carlo inverse algorithm, it simulates the process of life evolution in nature, so lots of large scal and multivariable nonlinear inverse problem can be resolverd through the genetic algorithm. In this article, we get the exactly PP and PS wave reflection coefficients, build a objective fuction, make a optimization inverse, the finally result is close to the theoretical value. In a word we get the target that inverse the anisotropic parameters using the reflection coefficients.
We can get a conclusion that the inverse result from PP wave reflection is a little worse than the result from PS wave although they’re all using the genetic algorithm. Through a careful observation we can get a reasonable explaination. In the results of PS wave we can find that the result of dip angle is more accurately than the azimuth angle of the symmetry in TTI media. By analysising the forward data we find the reason why the phenomenon occur.
From the wave equation semic record getted by pseudo-spectral methord we met a terrible problem to get the exact reflection coefficients. Because the anisotropic parameters are very sensitiveble to the varing of reflection coefficients, even a less erros can make the inverse processing failed. However, the error of reflection would not effect the qualitative analysis. The line consisted by the plots of relative amplitude and the sine of incidence angle is correlated with the AVO gradient. The slop of the line is proportional to the AVO gradient.
本文介绍了各向异性介质AVO的基本理论,系统分析了近些年来针对各向异性介质中PP波、PS波反射-透射系数表达式,并特别针对TTI介质研究了PS波的反射系数、AVO梯度等量与介质各向异性参数的关系。最后,本文将遗传算法引入到AVO的反演过程中,对模拟数据进行各向异性参数的反演,结果具有一定的可信度。总之,无论是AVO的定性分析还是定量反演都可以不同程度的获得地下储层的裂隙倾角和方位等有效的地层信息。
In seismic exploration , amplitude variation with offset (AVO) and amplitude variation with azimuth (AVAZ) analyses are frequently-used and perfect useful methords for recognizing the lithology and inversing the stratum parameters . The traditional AVO theory is on the assumption that the underground medium is isotropic, but along with the more and more higher exploration precision, all the seismic exploration works should comsider the fact that the underground media is anisotropic . The AVO analysis in anisotropic media a very rapidness improving.
In this articale , first , we introduced the the basic theory of anistropic media especially the TI (transversely isotropic) media which containing elasticity coefficients, anisotropic Thomsen parameters and the phase velocity and group velocity in anisotropic media.All of these parameters are the necessarily condition of getting the reflection coefficients in anisotropic media. Recently, the methords of getting the reflection and transmission coefficients are based on the first order perturbation theory in the approximately of weak contrast and weak anisotropic. In this article ,this theory is introduced briefly.
Based on, we analysis and summarize the reflection coefficients of PP wave and PS wave in anisotropic media. First, the VTI ( transversely isotropic with a vertical symmetry ) media and HTI(transversely isotropic with a horizontal symmetry) media are the special cases of orthorhombic anisotropic media, then the existing reflection coefficients expressions of orthorhombic anisotropic media can be applicable in VTI and HTI media. There is a corresponding relationship between the anisotropic parameters in orthorhombic anisotropic media and in the VTI or HTI media. From this on we can get new reflection coefficients expressions which are suitable for VTI and HTI media.For the orthorhombic anisotropic, VTI and HTI media ,we can get the reflection coefficients on the interface which comparting any two medias we talked about before. At the same time,because the incidence angle are normaly minum or commonly in the AVO analysis of factly seismic data, so in the reflection coefficients expressions the third order terms of the incidence angle’s sine value are be close to zero.At this moment the eave out of these terms should not take too much errors of reflection coefficients.On the other hand this predigestion makes the work of AVO anylysis and inverse more practicality and easely.
In the former reflection coefficients expressions of PP wave in anisotropic media, we can not find a direct relationship between the reflection coefficients and the Thomsen anisotropic parameters. In this article ,we first get the VTI media’s elasticity coefficients matrix through the relationship of Thomsen anisotropin patameters and elasticity coefficients. When we have confirm azimuth and dip angles of the symmetry in TTI media the elasticity coefficients in TTI meida can be confirmed by the rotating of reference frame.Finally we get the reflection coefficients in TTI media through the common expressions of reflection coefficients in weak anisotropic media.
When one of the two medias around the interface is TTI media, a very complex phenomena appears for the PS wave. In the first order perturbation we can get a conclusion that a PS reflection wave appearing by a vertical incidence P wave when the A34 and A35 in the elasticity coefficients matrix are nonzero. We know that in the isotropic,VTI or HTI media,all the two elasticity coefficients are zero, but if one of the two medias is TTI, the vertical incidence P wave makes a reflection PS wave.The reflection coefficients can even be as high as 0.1 although the media is a moderate anisotropic media. In this article we summarize the express of the phase velocity previously, this exact phase velocity make it possible to get the exact reflection coefficients of the PS wave which appearance because of the P wave’s normal incidence on the ISO/TTI or a TTI/TTI interface. Finally, systematical analysis the PS wave’s ormal incidence reflection coefficients and the AVO gradient varing with the wave velocity in the urper and lower layer,the density and the anisotropic parameters.
Finally,the nonlinear inverse methords are introduced into the process of the inverse from the AVO information to anisotropic parameters in anisotropic media. In this article, there’s a inverse processing from synthetic seismic recoder to anisotropic parameters in anistropic media using genetic algorithm. It is well know that the genetic algorithm is a heuristics monte-carlo inverse algorithm, it simulates the process of life evolution in nature, so lots of large scal and multivariable nonlinear inverse problem can be resolverd through the genetic algorithm. In this article, we get the exactly PP and PS wave reflection coefficients, build a objective fuction, make a optimization inverse, the finally result is close to the theoretical value. In a word we get the target that inverse the anisotropic parameters using the reflection coefficients.
We can get a conclusion that the inverse result from PP wave reflection is a little worse than the result from PS wave although they’re all using the genetic algorithm. Through a careful observation we can get a reasonable explaination. In the results of PS wave we can find that the result of dip angle is more accurately than the azimuth angle of the symmetry in TTI media. By analysising the forward data we find the reason why the phenomenon occur.
From the wave equation semic record getted by pseudo-spectral methord we met a terrible problem to get the exact reflection coefficients. Because the anisotropic parameters are very sensitiveble to the varing of reflection coefficients, even a less erros can make the inverse processing failed. However, the error of reflection would not effect the qualitative analysis. The line consisted by the plots of relative amplitude and the sine of incidence angle is correlated with the AVO gradient. The slop of the line is proportional to the AVO gradient.
引文
[1]蒋鸿亮,陈湛文,陈小宏.高分辨率AVO反演技术研究[J].地球物理学进展,2006,21(2):478-482.
[2]殷八斤,曾灏.AVO技术的理论与实践[M].北京.石油工业出版社,1995.
[3]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].长春:吉林大学出版社,1996.
[4] Thomsen, L. Weak elastic anisotropy[J]. Geophysics, 1986, 51(10): 1954–1966.
[5]何樵登.地震勘探原理和方法[M].北京:地质出版社,1986.
[6]何樵登,陶春晖.用遗传算法反演裂隙各向异性介质[J].石油物探1995,34(3):46-50.
[7]张文生,何樵登.用遗传算法反演各向异性介质弹性参数[J].物探化探计算技术1998,20(4):293-299.
[8]周辉,何樵登.横向各向同性介质走时反演[J].石油物探1995,34(3):63-68.
[9]傅旦丹,何樵登.遗传算法的改进及其在各向异性介质参数反演中的应用[J].石油物探2002,41(3):293-298.
[10]轩义华.倾斜横向各向同性介质(TT1)参数反演方法研究[D].长春:吉林大学,2007.
[11]王晓欢.TTI介质中地震波传播特性研究[D].长春:吉林大学,2006.
[12]郝奇.三维TTI介质地震波场正演模拟[D].长春:吉林大学,2007.
[13] I. P?en?ík,Vavry?uk,V.Weak Contrast PP Wave Displacement R/T Coefficients in Weakly Anisotropic Elastic Media[J]. Pure appl. Geophys, 1998, 151: 699–718.
[14] Petr Jilek. Converted PS-wave Reflection Coefficients in Weakly Anisotropic Media[J]. Pure appl.geophys, 2002, 159: 1527- 1562.
[15] Jyoti Behura, Ilya Tsvankin. Small-angle AVO response of PS-waves in tilted TImedia[J]. Geophysics, 2006, 71(5): 69- 79.
[16] Donati, M. S, Martin, N W. Making AVO analysis for converted waves a practical issue[C], 68th Ann. Internat. Mtg: Soc. of Expl. Geophys. 1998, 2060-2063.
[17] Dumitrescu, C, Gray, D, Bellman, L. 2003, Converted-wave P-S-AVO and PP-AVO analysis, Expanded Abstracts of the 2003 CSPG/CSEG Convention.
[18] Ramos, A C B, Castagna, J P. Useful approximations for converted-wave AVO: Geophysics, 2001, 66, 1721-1734.
[19] Xiangyang Li, Jianxin Yuan. Converted-wave Seismology in Anisotropic Media Revisited, Part I: Basic Theory[J]. APPLIED GEOPHYSICS, 2005, 2(1): 26-40.
[20] Xiangyang Li, Jianxin Yuan. Converted-wave Seismology in Anisotropic Media Revisited, Part II: Application to Parameter Estimation[J]. APPLIED GEOPHYSICS, 2005, 2(3): 153-167.
[21] Jiri Je?h, Ivan P?en?ík.First-order perturbation method for anisotropic media[J].Geophys, 1989, 99: 367-376.
[22] Hongbo Zhang, R James Brown. A review of AVO analysis CREWES Research Report [R]. 2001, 13: 357-380.
[23]郝重涛,姚陈,王迅.任意空间取向TI介质中速度随方位变化特征[J].地球物理学进展,2006,21(2):524-530.
[24] Luc T Ikelle, Lasse Amundsen. AVO-A response of an anisotropic half-space bounded by adipping surface for PP,PSV and PSH data[J].Journal of Applied Geophysics, 2001, 46: 1–29.
[25] Crampin, S. A review of wave motion in a anisotropic and cracked elastic media[J]: Wave Motion, 1981,3, 343–391.
[26] Ilya Tsvankin, Vladimir Grechka.3D description and inversion of reflection moveout of PS–waves in anisotrpic media. Geophysical Prospecting, 2002, 50: 301-316.
[27] Vavry?uk,V. I. P?en?ík, PP-wave reflection coefficients in weakly elastic media[J]: Geophysics,1998, 63: 2129–2141.
[28] Vavry?uk, V. Weak-contrast reflection/transmission coefficients in weakly anisotropic elastic media, P-wave incidence[J]: Geophysical Journal International, 1999,138: 553–562.
[29]周竹生.P-SV波和SH波的AVO分析[J].石油地球物理勘探1993,28(4):430–438.
[30]徐亦鸣,黄中玉.转换波AVO分析技术的实现[C] .中国地球物理学会第22届年会论文集.2006.
[31]孙鹏远,孙建国,卢秀丽,P-SV波AVO分析[J]:石油地球物理勘探,2003,38(2),131-135
[32] Pawan Dewangan, Ilya Tsvankin Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part I - Horizontal TTI layer[J]. Geophysics, 2006, 71(4): 107–121.
[33] Pawan Dewangan, Ilya Tsvankin, Mike Batzle, etal. PS-wave moveout inversion for tilted TI media: A physical-modeling study[J]. Geophysics, 2006, 71(4 ):135–143.
[34] Fredy A.V. Artola, Ricardo Leiderman, Sergio A.B. Fontoura, Mercia B.C. Silva. P–S converted wave: conversion point and zero-offset energy in anisotropic media[J] . Journal of Applied Geophysics 2004, 56: 155– 163.
[35] Aki,K. and Richards,P.G., Quantitative seismology-theory and methods[M] , W.H. Freeman and Company, 1980.
[36]张中杰.地震各向异性研究进展[J].地球物理学进展,2002,17(2):281-293.
[37]孙鹏远.多属性AVO分析及弹性参数反演方法研究[D].长春:吉林大学,2004.
[38]孙月成.多相介质多波AVO正演模拟对比研究[D].长春:吉林大学,2006.
[39]张世俊,杨慧珠.遗传算法反演HTI介质各向异性参数[J].石油地球物理勘探,2002,37(1): 24- 28.
[40]卢明辉,彭立才,杨慧珠等.小生境遗传算法AVOA反演[J].石油地球物理勘探,2006,41 (4): 447-450.
[41]胡龙胜,王家林,吴键生.遗传算法在地球物理中的应用进展[J].地球物理学进展,2002,17 (4):598-604.
[42]阎贫.横向各向同性介质中的地震波正反演初探[D].长春:长春地质学院,1992.
[43]周辉.各向异性介质波动方程正演及其非线性反演方法研究[D].长春:长春地质学院,1995.
[44] Rüger, A., Reflection coefficients and azimuthal AVO analysis in anisotropic media[C]: SEG,2001.
[45]侯伯刚,AVO处理解释技术研究及应用[D].北京:中国地质大学,2005.
[46]罗小明,王世瑞.纵波VTI介质各向异性参数的求取[J].物探与化探,2006, 30(3): 233- 235.
[47] Psencík, I.,and J. L. Martins, Properties of weak contrast PP reflection/ transmission coefficients for weakly anisotropic elastic media[J]. Studia Geophysica et Geodaetica, 2001, 45: 176– 199.
[48]胡中平.AVO反演技术[J].勘探地球物理进展,2003,26(5):382– 386.
[49] Antonio, C. B. R, P. C. John,Useful approximations for converted-wave AVO[J]: Geophysics, 2001,66(6): 1721- 1734.
[2]殷八斤,曾灏.AVO技术的理论与实践[M].北京.石油工业出版社,1995.
[3]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].长春:吉林大学出版社,1996.
[4] Thomsen, L. Weak elastic anisotropy[J]. Geophysics, 1986, 51(10): 1954–1966.
[5]何樵登.地震勘探原理和方法[M].北京:地质出版社,1986.
[6]何樵登,陶春晖.用遗传算法反演裂隙各向异性介质[J].石油物探1995,34(3):46-50.
[7]张文生,何樵登.用遗传算法反演各向异性介质弹性参数[J].物探化探计算技术1998,20(4):293-299.
[8]周辉,何樵登.横向各向同性介质走时反演[J].石油物探1995,34(3):63-68.
[9]傅旦丹,何樵登.遗传算法的改进及其在各向异性介质参数反演中的应用[J].石油物探2002,41(3):293-298.
[10]轩义华.倾斜横向各向同性介质(TT1)参数反演方法研究[D].长春:吉林大学,2007.
[11]王晓欢.TTI介质中地震波传播特性研究[D].长春:吉林大学,2006.
[12]郝奇.三维TTI介质地震波场正演模拟[D].长春:吉林大学,2007.
[13] I. P?en?ík,Vavry?uk,V.Weak Contrast PP Wave Displacement R/T Coefficients in Weakly Anisotropic Elastic Media[J]. Pure appl. Geophys, 1998, 151: 699–718.
[14] Petr Jilek. Converted PS-wave Reflection Coefficients in Weakly Anisotropic Media[J]. Pure appl.geophys, 2002, 159: 1527- 1562.
[15] Jyoti Behura, Ilya Tsvankin. Small-angle AVO response of PS-waves in tilted TImedia[J]. Geophysics, 2006, 71(5): 69- 79.
[16] Donati, M. S, Martin, N W. Making AVO analysis for converted waves a practical issue[C], 68th Ann. Internat. Mtg: Soc. of Expl. Geophys. 1998, 2060-2063.
[17] Dumitrescu, C, Gray, D, Bellman, L. 2003, Converted-wave P-S-AVO and PP-AVO analysis, Expanded Abstracts of the 2003 CSPG/CSEG Convention.
[18] Ramos, A C B, Castagna, J P. Useful approximations for converted-wave AVO: Geophysics, 2001, 66, 1721-1734.
[19] Xiangyang Li, Jianxin Yuan. Converted-wave Seismology in Anisotropic Media Revisited, Part I: Basic Theory[J]. APPLIED GEOPHYSICS, 2005, 2(1): 26-40.
[20] Xiangyang Li, Jianxin Yuan. Converted-wave Seismology in Anisotropic Media Revisited, Part II: Application to Parameter Estimation[J]. APPLIED GEOPHYSICS, 2005, 2(3): 153-167.
[21] Jiri Je?h, Ivan P?en?ík.First-order perturbation method for anisotropic media[J].Geophys, 1989, 99: 367-376.
[22] Hongbo Zhang, R James Brown. A review of AVO analysis CREWES Research Report [R]. 2001, 13: 357-380.
[23]郝重涛,姚陈,王迅.任意空间取向TI介质中速度随方位变化特征[J].地球物理学进展,2006,21(2):524-530.
[24] Luc T Ikelle, Lasse Amundsen. AVO-A response of an anisotropic half-space bounded by adipping surface for PP,PSV and PSH data[J].Journal of Applied Geophysics, 2001, 46: 1–29.
[25] Crampin, S. A review of wave motion in a anisotropic and cracked elastic media[J]: Wave Motion, 1981,3, 343–391.
[26] Ilya Tsvankin, Vladimir Grechka.3D description and inversion of reflection moveout of PS–waves in anisotrpic media. Geophysical Prospecting, 2002, 50: 301-316.
[27] Vavry?uk,V. I. P?en?ík, PP-wave reflection coefficients in weakly elastic media[J]: Geophysics,1998, 63: 2129–2141.
[28] Vavry?uk, V. Weak-contrast reflection/transmission coefficients in weakly anisotropic elastic media, P-wave incidence[J]: Geophysical Journal International, 1999,138: 553–562.
[29]周竹生.P-SV波和SH波的AVO分析[J].石油地球物理勘探1993,28(4):430–438.
[30]徐亦鸣,黄中玉.转换波AVO分析技术的实现[C] .中国地球物理学会第22届年会论文集.2006.
[31]孙鹏远,孙建国,卢秀丽,P-SV波AVO分析[J]:石油地球物理勘探,2003,38(2),131-135
[32] Pawan Dewangan, Ilya Tsvankin Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part I - Horizontal TTI layer[J]. Geophysics, 2006, 71(4): 107–121.
[33] Pawan Dewangan, Ilya Tsvankin, Mike Batzle, etal. PS-wave moveout inversion for tilted TI media: A physical-modeling study[J]. Geophysics, 2006, 71(4 ):135–143.
[34] Fredy A.V. Artola, Ricardo Leiderman, Sergio A.B. Fontoura, Mercia B.C. Silva. P–S converted wave: conversion point and zero-offset energy in anisotropic media[J] . Journal of Applied Geophysics 2004, 56: 155– 163.
[35] Aki,K. and Richards,P.G., Quantitative seismology-theory and methods[M] , W.H. Freeman and Company, 1980.
[36]张中杰.地震各向异性研究进展[J].地球物理学进展,2002,17(2):281-293.
[37]孙鹏远.多属性AVO分析及弹性参数反演方法研究[D].长春:吉林大学,2004.
[38]孙月成.多相介质多波AVO正演模拟对比研究[D].长春:吉林大学,2006.
[39]张世俊,杨慧珠.遗传算法反演HTI介质各向异性参数[J].石油地球物理勘探,2002,37(1): 24- 28.
[40]卢明辉,彭立才,杨慧珠等.小生境遗传算法AVOA反演[J].石油地球物理勘探,2006,41 (4): 447-450.
[41]胡龙胜,王家林,吴键生.遗传算法在地球物理中的应用进展[J].地球物理学进展,2002,17 (4):598-604.
[42]阎贫.横向各向同性介质中的地震波正反演初探[D].长春:长春地质学院,1992.
[43]周辉.各向异性介质波动方程正演及其非线性反演方法研究[D].长春:长春地质学院,1995.
[44] Rüger, A., Reflection coefficients and azimuthal AVO analysis in anisotropic media[C]: SEG,2001.
[45]侯伯刚,AVO处理解释技术研究及应用[D].北京:中国地质大学,2005.
[46]罗小明,王世瑞.纵波VTI介质各向异性参数的求取[J].物探与化探,2006, 30(3): 233- 235.
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