TTI介质弹性波相速度的一般性近似
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摘要
弹性波速度是弹性波动力学研究的核心内容之一。倾斜横向各向同性(TTI)介质弹性波相速度的理论精确公式比较复杂。由于地球介质弱各向异性的普遍性,在理论研究和实际应用中常常采用弱各向异性假设进行简化,但是面对页岩等中强各向异性介质时,弱各向异性近似不能满足精度要求,甚至不再适用。基于前人的研究成果,从TTI介质弹性波相速度理论精确公式出发,利用近似的配方法将精确公式内的D项近似表示为两项的平方和,从而实现多项式的开方运算。在此基础上,推导了TTI介质qP波和qSV波相速度的一般性近似表达式。理论分析和数值计算结果表明:TTI介质弹性波相速度一般性近似表达式由于在推导过程中没有直接利用弱各向异性的假设,因此不仅适用于弱各向异性,也适用于中强各向异性的情况,即在较大范围内,一般性近似的精度高于弱各向异性近似的精度。并且对于同一种TTI介质,qP波的一般性近似式精度高于qSV波的精度。
Velocity research is one of the core contents of elastic wave dynamics.The exact expression of phase velocity for elastic waves in tilted transversely isotropic(TTI)media is complicated.The assumption of weak anisotropy,due to its universality within the Earth,is often used to simplify seismic media.However,the weak anisotropy approximation is not applicable for moderate to strong anisotropic media such as shale.Based on the exact expression of phase velocity for elastic waves in TTI media,this study approximated the D term in the exact expression of the quadratic sum of two terms,using an approximate method of completing the square,to realize the square-root operation of the polynomial.Thereafter,general approximate expressions of the phase velocity for qP waves and qSV waves in TTI media are derived.Theoretical analysis and numerical calculation show that the general approximate expression of phase velocity for elastic waves in TTI media is applicable to weak,moderate,and strong anisotropic media,because the weak anisotropy assumption is not directly used in the derivation.The accuracy with the general approximation is higher than that with the weak anisotropy approximation.Also,for the same TTI medium,the accuracy with the general approximation expression of the qP wave is higher than that of the qSV wave.
Velocity research is one of the core contents of elastic wave dynamics.The exact expression of phase velocity for elastic waves in tilted transversely isotropic(TTI)media is complicated.The assumption of weak anisotropy,due to its universality within the Earth,is often used to simplify seismic media.However,the weak anisotropy approximation is not applicable for moderate to strong anisotropic media such as shale.Based on the exact expression of phase velocity for elastic waves in TTI media,this study approximated the D term in the exact expression of the quadratic sum of two terms,using an approximate method of completing the square,to realize the square-root operation of the polynomial.Thereafter,general approximate expressions of the phase velocity for qP waves and qSV waves in TTI media are derived.Theoretical analysis and numerical calculation show that the general approximate expression of phase velocity for elastic waves in TTI media is applicable to weak,moderate,and strong anisotropic media,because the weak anisotropy assumption is not directly used in the derivation.The accuracy with the general approximation is higher than that with the weak anisotropy approximation.Also,for the same TTI medium,the accuracy with the general approximation expression of the qP wave is higher than that of the qSV wave.
引文
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[4]万志超,滕吉文,张秉明.各向异性介质中地震波速度分析的研究现状[J].地球物理学进展,1997,12(3):35-44WAN Z C,TENG J W,ZHANG B M.Velocity analysis in anisotropic media[J].Progress in Geophysics,1997,12(3):35-44
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[18]李源,刘伟,刘微,等.各向异性全速度建模技术在山地地震成像中的应用[J].石油物探,2015,54(2):157-164LI Y,LIU W,LIU W,et al.Application of anisotropic full velocity modeling in the mountainous seismic imaging[J].Geophysical Prospecting for Petroleum,2015,54(2):157-164
[19]周进举,王德利,靳松,等.含倾斜裂隙页岩介质地震波场传播特征研究[J].石油物探,2014,53(5):501-508ZHOU J J,WANG D L,JIN S,et al.Research on seismic wavefield propagation characteristics in shale medium containing tilt fracture[J].Geophysical Prospecting for Petroleum,2014,53(5):501-508
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[21]刘喜武,刘宇巍,霍志周,等.页岩油气层地震岩石物理计算方法研究[J].石油物探,2016,55(1):10-17LIU X W,LIU Y W,HUO Z Z,et al.Study on seismic rock physics computational method for shale reservoir[J].Geophysical Prospecting for Petroleum,2016,55(1):10-17
[22]印兴耀,刘欣欣.储层地震岩石物理建模研究现状与进展[J].石油物探,2016,55(3):309-325YIN X Y,LIU X X.Research status and progress of the seismic rock-physics modeling methods[J].Geophysical Prospecting for Petroleum,2016,55(3):309-325
[23]李金磊.涪陵焦石坝页岩气层压力预测技术研究[J].石油物探,2017,56(4):567-574LI J L.Pressure prediction of Jiaoshiba shale gas reservoir in the Fuling Shale Gasfield[J].Geophysical Prospecting for Petroleum,2017,56(4):567-574
[24]张水山,熊晓军,刘阳,等.基于综合信息的三维层速度场建立及其在涪陵页岩气田应用研究[J].石油物探,2018,57(1):122-128ZHANG S S,XIONG X J,LIU Y,et al.Three-dimensional interval velocity building based on comprehensive data analysis and its application in Fuling shale gas field exploration[J].Geophysical Prospecting for Petroleum,2018,57(1):122-128
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[26] TSVANKIN I.Moveout analysis for transversely isotropic media with a tilted symmetry axis[J].Geophysical Prospecting,1997,45(3):479-512
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[31] WAHEED B U,ALKHALIFAH T.A fast sweeping algorithm for accurate solution of the tilted transversely isotropic eikonal equation using factorization[J].Geophysics,2017,82(6):WB1-WB8
[32] XU S G,LIU Y.Pseudoacoustic tilted transversely isotropic modeling with optimal k-space operator-based implicit finite-difference schemes[J].Geophysics,2018,83(3):T139-T157
[33] ZHANG L J,ZHOU B.Calculation of slowness vectors from ray directions for qP-,qSV-,and qSH-waves in tilted transversely isotropic media[J].Geophysics,2018,83(4):C153-C160
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[35]黄金强,李振春,黄建平,等.TTI介质Lebedev网格高阶有限差分正演模拟及波型分离[J].石油地球物理勘探,2017,52(5):915-927HUANG J Q,LI Z C,HUANG J P,et al.Lebedev grid high-order finite-difference modeling and elastic wavemode separation for TTI media[J].Oil Geophysical Prospecting,2017,52(5):915-927
[36] THOMSEN L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-1966
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[2]居兴国,郭恺,刘定进.基于相速度的TTI介质射线追踪方法研究[J].石油物探,2017,56(2):171-178JU X G,GUO K,LIU D J.Research on a ray tracing method for TTI medium based on phase velocity[J].Geophysical Prospecting for Petroleum,2017,56(2):171-178
[3]黄光南,刘洋,李红星,等.TTI介质相速度对弹性模量参数的敏感性研究[J].石油物探,2014,53(3):262-271HUANG G N,LIU Y,LI H X,et al.Research on sensitivity of phase velocity with respect to elastic moduli parameters in TTI media[J].Geophysical Prospecting for Petroleum,2014,53(3):262-271
[4]万志超,滕吉文,张秉明.各向异性介质中地震波速度分析的研究现状[J].地球物理学进展,1997,12(3):35-44WAN Z C,TENG J W,ZHANG B M.Velocity analysis in anisotropic media[J].Progress in Geophysics,1997,12(3):35-44
[5]张衡,刘洪,丁仁伟,等.TTI介质伪解析解耦波动方程[J].地球物理学进展,2016,31(4):1752-1761ZHANG H,LIU H,DING R W,et al.Pseudo-analytical decoupling wave equation for TTI media[J].Progress in Geophysics,2016,31(4):1752-1761
[6] CRAMPIN S.A review of wave motion in anisotropic and cracked elastic-media[J].Wave Motion,1981,3:343-391
[7] TSVANKIN I.P-wave signatures and notation for transversely isotropic media:an overview[J].Geophysics,1996,61(2):467-483
[8] PSENCIK I,GAJEWSKI D.Polarization,phase velocity,and NMO velocity of qP-waves in arbitrary weakly anisotropic media[J].Geophysics,1998,63(5):1754-1766
[9] ALKHALIFAH T.Acoustic approximation for processing in transversely isotropic media[J].Geophysics,1998,63(2):623-631
[10] ALKHALIFAH T.An acoustic wave equation for anisotropic media[J].Geophysics,2000,65(4):1239-1250
[11] SCHOENBERG A M,De HOOP V M,Approximate dispersion relations for qP-qSV-waves in transversely isotropic media[J].Geophysics,2000,65(3):919-933
[12]魏周拓,范宜仁,陈雪莲,等.横波各向异性分析方法及其在复杂储层中的应用[J].石油物探,2011,50(3):275-280WEI Z T,FAN Y R,CHEN X L,et al.S-wave anisotropy analysis method and its application on complex reservoir[J].Geophysical Prospecting for Petroleum,2011,50(3):275-280
[13]贾福宗,李道善,曹孟起,等.宽方位纵波地震资料HTI各向异性校正方法研究与应用[J].石油物探,2013,52(6):650-654JIA F Z,LI D S,CAO M Q,et al.Study and application of HTI anisotropy moveout correction to wide azimuth P-wave seismic data[J].Geophysical Prospecting for Petroleum,2013,52(6):650-654
[14]胡起,陈小宏,李景叶.基于各向异性岩石物理模型的页岩气储层横波速度预测[J].石油物探,2014,53(3):254-261HU Q,CHEN X H,LI J Y.Shear wave velocity prediction for shale gas reservoirs based on anisotropic rock physics model[J].Geophysical Prospecting for Petroleum,2014,53(3):254-261
[15]孙炜,何治亮,李玉凤,等.基于HTI介质各向异性正演的裂缝预测属性优选[J].石油物探,2014,53(2):223-231SUN W,HE Z L,LI Y F,et al.Seismic attributes optimization for fractures prediction based on the anisotropy forwarding of the HTI media[J].Geophysical Prospecting for Petroleum,2014,53(2):223-231
[16]裴云龙,王立歆,邬达理,等.井控各向异性速度建模技术在YKL地区的应用[J].石油物探,2017,56(3):390-399PEI Y L,WANG L X,WU D L,et al.The application of well-controlled anisotropy velocity modeling in YKL region[J].Geophysical Prospecting for Petroleum,2017,56(3):390-399
[17]徐亦鸣,黄中玉,刘路佳.各向异性介质纵波速度分析[J].石油物探,2004,43(5):438-440XU Y M,HUANG Z Y,LIU L J.P-wave velocity analysis in anisotropy medium[J].Geophysical Prospecting for Petroleum,2004,43(5):438-440
[18]李源,刘伟,刘微,等.各向异性全速度建模技术在山地地震成像中的应用[J].石油物探,2015,54(2):157-164LI Y,LIU W,LIU W,et al.Application of anisotropic full velocity modeling in the mountainous seismic imaging[J].Geophysical Prospecting for Petroleum,2015,54(2):157-164
[19]周进举,王德利,靳松,等.含倾斜裂隙页岩介质地震波场传播特征研究[J].石油物探,2014,53(5):501-508ZHOU J J,WANG D L,JIN S,et al.Research on seismic wavefield propagation characteristics in shale medium containing tilt fracture[J].Geophysical Prospecting for Petroleum,2014,53(5):501-508
[20]李金磊,尹正武.四川盆地焦石坝地区页岩气储层地震定量预测方法[J].石油物探,2015,54(3):324-330LI J L,YIN Z W.Seismic quantitative prediction method of shale gas reservoirs in the Jiaoshiba Area,Sichuan Basin[J].Geophysical Prospecting for Petroleum,2015,54(3):324-330
[21]刘喜武,刘宇巍,霍志周,等.页岩油气层地震岩石物理计算方法研究[J].石油物探,2016,55(1):10-17LIU X W,LIU Y W,HUO Z Z,et al.Study on seismic rock physics computational method for shale reservoir[J].Geophysical Prospecting for Petroleum,2016,55(1):10-17
[22]印兴耀,刘欣欣.储层地震岩石物理建模研究现状与进展[J].石油物探,2016,55(3):309-325YIN X Y,LIU X X.Research status and progress of the seismic rock-physics modeling methods[J].Geophysical Prospecting for Petroleum,2016,55(3):309-325
[23]李金磊.涪陵焦石坝页岩气层压力预测技术研究[J].石油物探,2017,56(4):567-574LI J L.Pressure prediction of Jiaoshiba shale gas reservoir in the Fuling Shale Gasfield[J].Geophysical Prospecting for Petroleum,2017,56(4):567-574
[24]张水山,熊晓军,刘阳,等.基于综合信息的三维层速度场建立及其在涪陵页岩气田应用研究[J].石油物探,2018,57(1):122-128ZHANG S S,XIONG X J,LIU Y,et al.Three-dimensional interval velocity building based on comprehensive data analysis and its application in Fuling shale gas field exploration[J].Geophysical Prospecting for Petroleum,2018,57(1):122-128
[25]梁锴,吴国忱,印兴耀,等.三维TTI介质波动方程分解[J].石油地球物理勘探,2009,44(1):19-27LIANG K,WU G C,YIN X Y,et al.Wave equation decomposition in 3-D TTI Medium[J].Oil Geophysical Prospecting,2009,44(1):19-27
[26] TSVANKIN I.Moveout analysis for transversely isotropic media with a tilted symmetry axis[J].Geophysical Prospecting,1997,45(3):479-512
[27] OPERTO S,VIRIEUX J,RIBODETTI A,et al.Finitedifference frequency-domain modeling of visco-acoustic wave propagation in 2D tilted transversely isotropic(TTI)media[J].Geophysics,2009,74(5):T75-T95
[28] OROPEZA E,MCMECHAN G.Common-reflectionpoint migration velocity analysis of 2D P-wave data from TTI media[J].Geophysics,2014,79(3):C65-C79
[29] SHRAGGE J.Acoustic wave propagation in tilted transversely isotropic media:Incorporating topography[J].Geophysics,2016,81(5):C265-C278
[30] WANG H W,PENG S P,DU W F.Azimuthal AVO for tilted TI medium[J].Geophysics,2017,82(1):C21-C33
[31] WAHEED B U,ALKHALIFAH T.A fast sweeping algorithm for accurate solution of the tilted transversely isotropic eikonal equation using factorization[J].Geophysics,2017,82(6):WB1-WB8
[32] XU S G,LIU Y.Pseudoacoustic tilted transversely isotropic modeling with optimal k-space operator-based implicit finite-difference schemes[J].Geophysics,2018,83(3):T139-T157
[33] ZHANG L J,ZHOU B.Calculation of slowness vectors from ray directions for qP-,qSV-,and qSH-waves in tilted transversely isotropic media[J].Geophysics,2018,83(4):C153-C160
[34]姚振岸,孙成禹,谢俊法,等.黏弹TTI介质旋转交错网格微地震波场模拟[J].石油地球物理勘探,2017,52(2):253-263YAO Z A,SUN C Y,XIE J F,et al.Micro-seismic forward modeling in visco-elastic TTI media based on rotated staggered grid finite-difference method[J].Oil Geophysical Prospecting,2017,52(2):253-263
[35]黄金强,李振春,黄建平,等.TTI介质Lebedev网格高阶有限差分正演模拟及波型分离[J].石油地球物理勘探,2017,52(5):915-927HUANG J Q,LI Z C,HUANG J P,et al.Lebedev grid high-order finite-difference modeling and elastic wavemode separation for TTI media[J].Oil Geophysical Prospecting,2017,52(5):915-927
[36] THOMSEN L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-1966
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