多测线变偏移距VSP地震各向异性反演
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摘要
本文从一般弱各向异性介质参数反演中得到了使用两条相互正交的变偏VSP测线计算弱各向异性(WA)参数的反演公式.如果仅仅使用qP波,则可以确定9个独立的WA参数,这9个WA参数可以完全地描述井中接收点在两个剖面内介质的各向异性性质.通过对走时曲线进行最小二乘条件下的三次样条光滑,可以获得慢度矢量的垂直分量和水平分量.如果介质是横向非均匀介质,则水平分量仅仅被用作反演时的约束条件.为了获得偏振矢量,本文引入质心计算方法,该方法计算简单、稳定,而且不存在解的奇异问题.在寻找与一般各向异性介质最接近的高对称性正交各向异性介质和TTI各向异性介质时,使用qP波各向异性坐标变换方法和最小二乘求解方法,得到了与一般各向异性介质最接近的正交各向异性和TTI各向异性参数及其对称轴方向参数的计算公式.使用这些方法,对瓜哇海地区布设的两条相互正交的变偏VSP测线数据进行各向异性反演,获得了井中10个接收点处介质的WA参数.数值计算和实际资料反演表明,本文所使用的反演方法能够准确地得到VSP井中接收点处介质的WA参数,这是地震勘探中研究地壳介质各向异性性质最直接和最可靠的方法.
Inversion formulae for two orthogonal walkaway VSPs are derived from the general weak anisotropic(WA)inversion formulae.Nine independent WA parameters can be determined if only qP wave is used.These nine WA parameters completely describe the anisotropic property of the medium at or near the receivers in the two profiles.The vertical and horizontal components of slowness vector are obtained by using the cubic spline smoothing function on the condition of least squares.If the medium is laterally inhomogeneous,the horizontal component of the slowness vector can be taken as a constrain condition.A method for calculating mass center is introduced to obtain polarization vector,which is simple,stable and no singular problem.Coordinate transform and least squares method are combined to get the WA parameters for orthorhombic medium and laterally homogeneous isotropic medium with tilted vertical symmetry axis(TTI)which are mostly close to the general anisotropic medium.Two walkaway VSP data from Java Sea are inverted and nine WA parameters at each receiver are obtained.Inversion results from theoretical and real data indicate that the method can be used to determine the anisotropic properties at each receiver in the walkaway VSP measurements.The method is often taken as the most direct and reliable one in the determination of anisotropic parameters in exploration seismology.
Inversion formulae for two orthogonal walkaway VSPs are derived from the general weak anisotropic(WA)inversion formulae.Nine independent WA parameters can be determined if only qP wave is used.These nine WA parameters completely describe the anisotropic property of the medium at or near the receivers in the two profiles.The vertical and horizontal components of slowness vector are obtained by using the cubic spline smoothing function on the condition of least squares.If the medium is laterally inhomogeneous,the horizontal component of the slowness vector can be taken as a constrain condition.A method for calculating mass center is introduced to obtain polarization vector,which is simple,stable and no singular problem.Coordinate transform and least squares method are combined to get the WA parameters for orthorhombic medium and laterally homogeneous isotropic medium with tilted vertical symmetry axis(TTI)which are mostly close to the general anisotropic medium.Two walkaway VSP data from Java Sea are inverted and nine WA parameters at each receiver are obtained.Inversion results from theoretical and real data indicate that the method can be used to determine the anisotropic properties at each receiver in the walkaway VSP measurements.The method is often taken as the most direct and reliable one in the determination of anisotropic parameters in exploration seismology.
引文
刘宪彬,郑需要.2013.利用qP波慢度和偏振矢量计算弱各向异性介质参数[J].地震学报,35(2):184--198.Liu X B,Zheng X Y.2013.Calculation of weakly anisotropic parameters by slowness and polarization vectors of qP wave[J].Acta Seismologica Sinica,35(2):184--198(in Chinese).
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Horne S A,Leaney W S.2000.Polarization and slowness component inversion for TI anisotropy[J].Geophys Prospect,48(4):779--788.
Jech J,Pen cík I.1989.First-order perturbation method for anisotropic media[J].Geophys J Int,99(2):369--376.
Pen cík I,Gajewski D.1998.Polarization,phase velocity and NMO velocity of qP waves in arbitrary weakly anisotropicmedia[J].Geophysics,63(5):1754--1766.
Thomsen L.1986.Weak elastic anisotropy[J].Geophysics,51(10):1954--1966.
Zheng X,Pen cík I.2002.Local determination of weak anisotropy parameters from qP-wave slowness and particle motionmeasurements[J].Pure Appl Geophys,159(7/8):1881--1905.
Zheng X.2004.Inversion for elastic parameters in weakly anisotropic media[J].Geophys J Int,159(3):1077--1089.
Zheng X.2007.Identification of the symmetry planes in weakly anisotropic elastic media[J].Geophys J Int,170(1):468--478.
袭杨.2009.空间直线拟合的一种方法[J].齐齐哈尔大学学报,25(2):64--68.Xi Y.2009.A method for fitting of a space straight line[J].Journal of Qiqihar University,25(2):64--68(in Chinese).
郑需要,董天立,刘一霖.2010.变井源距垂直地震剖面各向异性参数反演[J].地震学报,32(2):157--166.Zheng X Y,Dong T L,Liu Y L.2010.Inversion of seismic anisotropic parameters for walkaway VSP data[J].ActaSeismologica Sinica,32(2):157--166(in Chinese).
CervenV.2001.Seismic Ray Theory[M].Cambridge:Cambridge University Press:189--199.
Horne S A,Leaney W S.2000.Polarization and slowness component inversion for TI anisotropy[J].Geophys Prospect,48(4):779--788.
Jech J,Pen cík I.1989.First-order perturbation method for anisotropic media[J].Geophys J Int,99(2):369--376.
Pen cík I,Gajewski D.1998.Polarization,phase velocity and NMO velocity of qP waves in arbitrary weakly anisotropicmedia[J].Geophysics,63(5):1754--1766.
Thomsen L.1986.Weak elastic anisotropy[J].Geophysics,51(10):1954--1966.
Zheng X,Pen cík I.2002.Local determination of weak anisotropy parameters from qP-wave slowness and particle motionmeasurements[J].Pure Appl Geophys,159(7/8):1881--1905.
Zheng X.2004.Inversion for elastic parameters in weakly anisotropic media[J].Geophys J Int,159(3):1077--1089.
Zheng X.2007.Identification of the symmetry planes in weakly anisotropic elastic media[J].Geophys J Int,170(1):468--478.
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