垂直对称轴的横向各向同性介质中Thomsen参数对相速度和群速度的影响
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摘要
相速度和群速度对于研究弹性波在各向异性介质中的传播具有重要意义;同时对合理评价地震资料解释成果也具有一定的指导意义。深入研究Thomsen参数与群、相速度的关系有助于研究复杂地层中波的传播规律以及速度的变化趋势,从而使地震资料解释更加准确。首先简要推导了各向同性(VTI)介质中弹性波的群、相速度解析表达式,然后通过编程实现,直观显示了三维速度曲面的变化特征与Thomsen参数的联系;并通过二维及一维速度曲线变化加以验证。实验结果表明:VTI介质中群速度较相速度对Thomsen参数的变化更加敏感;其中随着ε(q P波各向异性强度表征参数)与δ(描述纵横波相速度的过渡性参数)差值的不断增大,各向异性程度明显增强,群速度剧烈变化;尤其是q SV波;随着γ(横波分裂强度表征参数)值的不断增大,SH波群、相速度面的扁率也不断增大。
Phase velocity and group velocity are important for studying the propagation of elastic waves in anisotropic media,and also for guiding the reasonable evaluation of seismic data interpretation results. Further study of the relationship between Thomsen parameters and group velocity and phase velocity is helpful to study the wave propagation and the trend of velocity change in complex strata,so as to make seismic data interpretation more accurate. The analytical expression of group velocity and phase velocity of elastic wave in VTI media were firstly deduced,and then it is realized by programming. The relationship between the change features of the 3 D velocity and surface and the Thomsen parameters are displayed directly,and the change of the two-dimensional and one-dimensional velocity curves is verified. The experimental results show that the group velocity of elastic wave in VTI media is more sensitive to the phase velocity of the Thomsen parameters. With ε( q P anisotropic strength parameters) andδ( description of transitional horizontal parameter wave phase velocity) increasing difference,the degree of anisotropy increased,group velocity changes,especially the q SV wave. With γ( shear wave splitting parameter strength)increases,surface flattening of SH wave phase velocity and group velocity increasing.
Phase velocity and group velocity are important for studying the propagation of elastic waves in anisotropic media,and also for guiding the reasonable evaluation of seismic data interpretation results. Further study of the relationship between Thomsen parameters and group velocity and phase velocity is helpful to study the wave propagation and the trend of velocity change in complex strata,so as to make seismic data interpretation more accurate. The analytical expression of group velocity and phase velocity of elastic wave in VTI media were firstly deduced,and then it is realized by programming. The relationship between the change features of the 3 D velocity and surface and the Thomsen parameters are displayed directly,and the change of the two-dimensional and one-dimensional velocity curves is verified. The experimental results show that the group velocity of elastic wave in VTI media is more sensitive to the phase velocity of the Thomsen parameters. With ε( q P anisotropic strength parameters) andδ( description of transitional horizontal parameter wave phase velocity) increasing difference,the degree of anisotropy increased,group velocity changes,especially the q SV wave. With γ( shear wave splitting parameter strength)increases,surface flattening of SH wave phase velocity and group velocity increasing.
引文
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2李芳,曹思远,姚健.任意各向异性介质相(群)速度的计算.地球物理学报,2012;55(10):3420-3426Li Fang,Cao Siyuan,Yao Jian.Calculation of phase and group velocities in an arbitrary anisotropic medium(AAM).Chinese Journal of Geophysics,2012;55(10):3420-3426
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4牛滨华,孙春岩.地震波理论研究进展---介质模型与地震波传播.地球物理学进展,2004;19(2):255-263Niu Binhua,Sun Chunyan.Developing theory of propagation of seismic waves-medium model and propagation of seismic waves.Progress in Geophysics,2004;19(2):255-263
5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.石油物探,2014;53(3):262-271Huang Guangnan,Liu Yang,Li Hongxing,et al.Research on sensitivity of phase velocity with respect to elastic moduli parameters in TTImedia.Geophysical Prospecting for Petroleum,2014;53(3):262-271
6 Gassmann F.Elastic waves through a packing of spheres.Geophysics,1951;16(4):673-685
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8 Nur A,Simmons G.Stree-induced velocity anisotropy in rock:An experimental study.Journal of Geophysical Research,1969;74(27):6667-6674
9 Daley P F,Hron F.Reflection and transmission coefficients for seismic wave in ellipsoidally anisotropic media.Geophysics,1979;44(1):27-38
10 Byun B S.Seismic parameters for transversely isotropic media.Geophysics,1984;49(11):1908-1914
11 Baan M,Kendall M.Traveltime and conversion-point computations and parameter estimation in layed,anisotropic media by transform.Geophysics,2003;68(1):210-224
12 Bakulin A,Grachka V,Tsvankin I.Seismic inversion for the parameters of two orthogonal fracture sets in a VTI background medium.Geophysics,2002;67(1):292-299
13 Grechka V,Pech A,Tsvankin I.P-wave stacking-velocity tomography for VTI media.Geophysical Prospecting,2002;50(2):151-168
14 Grechka V,Tsvankin I.The joint nonhyperbolic moveout inversion of PP and PS data in VTI media.Geophysics,2002;67(6):1929-1932
15姚振岸,孙成禹,邓小凡,等.任意空间取向TI介质弹性波速度特征分析.石油地球物理勘探,2017;52(4):715-733Yao Zhen'an,Sun Chengyu,Deng Xiaofan,et al.Velocity characteristic analysis of elastic wave for TI media with arbitrary spatial orientation.Oil Geophysical Prospecting,2017;52(4):715-733
16李世凯,文晓涛,阮韵淇,等.基于黏弹各向异性理论的地震波场数值模拟与分析.科学技术与工程,2016;16(26):166-172Li Shikai,Wen Xiaotao,Ruan Yunqi,et al.Analysis of seismic numerical simulation based on theory of viscoelasticity and anisotropy.Science Technology and Engineering,2016;16(26):166-172
17 Anderson D L.Elastic wave propagation in layered anisotropic madia.Journal of Geophysical Research,1961;66(9):2953-2963
18 Thomsen L.Weak elastic anisotropy.Geophysics,1986;51(10):1954-1966
19李磊.TI介质中的相速度和群速度及射线参数.石油物探,2008;47(4):334-337Li Lei.Phase velocity,group velocity,and ray parameters in transversely isotropic media.Geophysical Prospecting for Petroleum,2008;47(4):334-337
20 Berryman J G.Long-wave elastic anisotropy in transversely isotropic media.Geophysics,1979;44(5):896-917
2李芳,曹思远,姚健.任意各向异性介质相(群)速度的计算.地球物理学报,2012;55(10):3420-3426Li Fang,Cao Siyuan,Yao Jian.Calculation of phase and group velocities in an arbitrary anisotropic medium(AAM).Chinese Journal of Geophysics,2012;55(10):3420-3426
3吴国忱,梁锴,戚艳平.三维TTI介质相速度和群速度.地球物理学进展,2009;24(6):2097-2105Wu Guochen,Liang Kai,Qi Yanping.Phase velocity and group velocity in 3D TTI media.Progress in Geophysics,2009;24(6):2097-2105
4牛滨华,孙春岩.地震波理论研究进展---介质模型与地震波传播.地球物理学进展,2004;19(2):255-263Niu Binhua,Sun Chunyan.Developing theory of propagation of seismic waves-medium model and propagation of seismic waves.Progress in Geophysics,2004;19(2):255-263
5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.石油物探,2014;53(3):262-271Huang Guangnan,Liu Yang,Li Hongxing,et al.Research on sensitivity of phase velocity with respect to elastic moduli parameters in TTImedia.Geophysical Prospecting for Petroleum,2014;53(3):262-271
6 Gassmann F.Elastic waves through a packing of spheres.Geophysics,1951;16(4):673-685
7 Postma G W.Wave propagation in a stratified medium.Geophysics,1955;20(4):780-806
8 Nur A,Simmons G.Stree-induced velocity anisotropy in rock:An experimental study.Journal of Geophysical Research,1969;74(27):6667-6674
9 Daley P F,Hron F.Reflection and transmission coefficients for seismic wave in ellipsoidally anisotropic media.Geophysics,1979;44(1):27-38
10 Byun B S.Seismic parameters for transversely isotropic media.Geophysics,1984;49(11):1908-1914
11 Baan M,Kendall M.Traveltime and conversion-point computations and parameter estimation in layed,anisotropic media by transform.Geophysics,2003;68(1):210-224
12 Bakulin A,Grachka V,Tsvankin I.Seismic inversion for the parameters of two orthogonal fracture sets in a VTI background medium.Geophysics,2002;67(1):292-299
13 Grechka V,Pech A,Tsvankin I.P-wave stacking-velocity tomography for VTI media.Geophysical Prospecting,2002;50(2):151-168
14 Grechka V,Tsvankin I.The joint nonhyperbolic moveout inversion of PP and PS data in VTI media.Geophysics,2002;67(6):1929-1932
15姚振岸,孙成禹,邓小凡,等.任意空间取向TI介质弹性波速度特征分析.石油地球物理勘探,2017;52(4):715-733Yao Zhen'an,Sun Chengyu,Deng Xiaofan,et al.Velocity characteristic analysis of elastic wave for TI media with arbitrary spatial orientation.Oil Geophysical Prospecting,2017;52(4):715-733
16李世凯,文晓涛,阮韵淇,等.基于黏弹各向异性理论的地震波场数值模拟与分析.科学技术与工程,2016;16(26):166-172Li Shikai,Wen Xiaotao,Ruan Yunqi,et al.Analysis of seismic numerical simulation based on theory of viscoelasticity and anisotropy.Science Technology and Engineering,2016;16(26):166-172
17 Anderson D L.Elastic wave propagation in layered anisotropic madia.Journal of Geophysical Research,1961;66(9):2953-2963
18 Thomsen L.Weak elastic anisotropy.Geophysics,1986;51(10):1954-1966
19李磊.TI介质中的相速度和群速度及射线参数.石油物探,2008;47(4):334-337Li Lei.Phase velocity,group velocity,and ray parameters in transversely isotropic media.Geophysical Prospecting for Petroleum,2008;47(4):334-337
20 Berryman J G.Long-wave elastic anisotropy in transversely isotropic media.Geophysics,1979;44(5):896-917