利用qP波慢度和偏振矢量计算弱各向异性介质参数

提出了一种使用慢度矢量分量和偏振矢量计算变井源距垂直地震剖面(walkaway VSP)钻孔中接收点附近介质弱各向异性(WA)参数的方法.假定介质是任意弱各向异性介质,从一般公式中得到了只有一条观测剖面情况下的反演公式.如果知道了慢度矢量的垂直分量和偏振矢量,可以通过反演得到与剖面和钻孔所在平面相关的WA参数,反演过程不用进行射线追踪,与上覆介质无关.用合成数据检验了公式和方法的正确性,并把它们应用于在爪哇海地区得到的一条变井源距垂直地震剖面的弱各向异性参数反演中.     

变井源距垂直地震剖面各向异性参数反演

利用微扰理论推导了弱各向异性(WA)介质参数正反演计算的基本公式;给出了在已知慢度矢量的一个分量和偏振矢量情况下确定WA参数的方法.如果这一方法被用于单一的变井源距垂直地震剖面(walkawayVSP)资料,可以获得9个WA参数.这9个WA参数完全决定了qP波和两个qS波在由剖面和钻井所决定的平面内传播的特性.对单条walkawayVSP观测系统数据的产生和WA参数的反演进行了数值模拟计算,对所能确定的WA参数及其可靠性进行了详细的讨论.     

多测线变偏移距VSP地震各向异性反演

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.      

基于walkaway VSP下行P波的TTI各向异性参数反演

本文基于弱各向异性（WA）介质的正反演公式和qP波的坐标变换,推导了利用qP波反演任意倾斜对称轴的横向各向同性（TTI）介质的各向异性参数和对称轴方向的公式.理论和数值实验表明,利用2个相互正交的变井源距垂直地震剖面（walkaway VSP）可以完全确定钻井中TTI介质qP波的3个WA参数和对称轴的2个方向参数.我们完成了几个由不同数量剖面组成的walkaway VSP模拟实验,使用TTI模型和一般各向异性模型对模拟数据进行了反演,证明了反演公式的正确性和可靠性.使用这些公式,对来自Java Sea的由3条剖面组成的walkaway VSP观测数据进行了各向异性反演,获得了钻井中接收点处介质的WA参数.     

VTI介质中弹性波的波动特征研究

波动特征研究对各向异性介质的弹性参数反演,速度反演、NMO,DMO、时间域的偏移以及地震资料的精确解释有着重要意义.本文由Christoffel方程出发推导出二维VTI介质中XOZ对称平面内弹性波相速度与各向异性参数的关系式以及慢度面的计算式并通过理论模型分析得出以下结论：1)ε值决定了P波的水平相速度的大小,反映了P波水平传播的相速度与垂直传播的相速度的差异;δ值决定了P波垂直方向附近相速度的各向异性程度的大小.2)VTI各向异性介质中纵波偏振方向不再与慢度面是平行而是有一定的夹角,且SV波的慢度面不再完全与偏振方向垂直的.3)准SH 波的波慢度面呈椭圆,准P波与准SV波慢度面为不规则椭圆.     

岩石物理驱动的正交各向异性方位叠前地震反演方法

基于长波长近似假设,周期性薄互层中发育一组平行排列的垂直裂缝则可视为等效的正交各向异性介质.岩石物理是构建裂缝参数与地震响应之间联系的基础,地震散射理论是各向异性介质参数反演的有效途径.文章提出了一种利用方位叠前地震数据实现正交各向异性裂缝储层Thomsen弱各向异性参数与裂缝弱度参数可靠预测的方法.首先,综合考虑矿物基质、孔隙、裂缝及各向异性岩石中流体替换的影响,通过构建正交各向异性裂缝岩石物理等效模型,实现正交各向异性刚度系数的估测,进而预测储层测井数据的弹性参数、Thomsen弱各向异性参数及裂缝弱度参数,为后续地震反演提供初始模型约束;然后,基于地震散射理论,推导了面向Thomsen弱各向异性参数与裂缝弱度参数反演的正交各向异性介质纵波反射系数方程,为后续地震反演奠定了理论基础;最后,发展了贝叶斯框架下的正交各向异性裂缝储层Thomsen弱各向异性参数与裂缝弱度参数AVAZ反演方法,同时考虑柯西稀疏约束正则化和平滑模型约束正则化约束,使用非线性的迭代重加权最小二乘策略实现正交各向异性特征参数的稳定估算.模型和实际资料处理表明,该方法能够稳定可靠地从方位叠前地震资料中获取正交各向异性特征参数,为正交各向异性介质的特征参数预测提供了一种高可靠性的地震反演方法.     

怀来、 延庆及其周边地区地壳 介质各向异性研究

提出了利用人工爆破P波走时反演地壳介质方位各向异性参数的方法. 在假定介质是弱各向异性介质的情况下, 使用扰动理论得到了线性化的反演公式, 其中待反演的弱各向异性参数是P波走时的线性函数. 如果在反演公式中参考走时取相同震中距接收点的P波平均走时, 那么所获得的弱各向异性参数与参考介质速度的选取无关. 反演得到的弱各向异性参数可以看作是不同震中距和不同深度范围内介质的等效弱各向异性参数. 等效弱各向异性参数在一定程度上反映了不同深度范围内水平方向相速度随方位的变化. 这种变化可能是不同时期构造应力作用的结果. 2007年中国地震局在首都圈怀来地区实施了一次大吨位人工爆破实验, 以爆破点为中心, 布设了高密度的地震观测台网和台阵. 台站相对于爆破点具有360°的全方位覆盖, 所得到的地震记录数据为研究怀来、 延庆地区地壳介质P波方位各向异性提供了必要条件. 我们通过走时反演获得了与水平方位相关的弱各向异性参数, 并对弱各向异性参数进行坐标变换, 得到了能够直观描述岩石弱各向异性的具有水平对称轴的横向各向同性介质, 给出了对应的3个独立弱各向异性参数及其对称轴方位, 讨论了介质各向异性与构造应力场的关系. 结果表明该地区地壳介质存在明显的方位各向异性, 其最大值约为4.6%.      

VTI介质多参数联合走时层析成像方法

本文基于球谐展开群速度表达式计算走时关于各向异性参数的Fréchet核函数,利用共轭梯度法对两种参数化方法进行了VTI介质中多参数联合反演方法研究.经过理论分析和数值试验发现,与经典的Thomsen参数化方法相比,垂直慢度、水平慢度与动校正慢度的参数化方式更有利于VTI介质多参数联合走时层析反演.为了克服走时对ε参数的不敏感性,我们采用了两步法进行双参数反演,理论模型试验反演得到了与垂直速度精度相当的ε参数.可以将两步法扩展到三步法以同时反演各向异性介质中的三个参数,数值试验展示了该策略的应用潜力.     

几种弱各向异性介质中qSV波速度和偏振异常

研究了在具有垂直对称轴的横向各向同性介质(TIV 介质)中qSV波群速度及偏振矢量,给出了相应的精确和近似计算公式,进一步讨论了用较简单的近似公式来代替复杂精确公式的可靠性;最后展示了地球内部几种常见各向异性岩石矿物中地震qSV波速度各向异性因子、偏振信息及其与传播方向之间的偏差.     

非均匀正交各向异性特征参数地震散射反演方法研究

在长波长假设条件下,水平层状地层中发育一组垂直排列的裂缝构成了等效正交各向异性介质.各向异性参数与裂缝弱度参数的估算有助于非均匀各向异性介质的各向异性特征描述,而弹性逆散射理论是非均匀介质参数反演的有效途径.基于地震散射理论,我们首先推导了非均匀正交介质中纵波散射系数方程,并通过引入正交各向异性特征参数,提出了一种新颖的正交各向异性方位弹性阻抗参数化方法.为了提高反演的稳定性与横向连续性,我们发展了贝叶斯框架下的正交各向异性方位弹性阻抗反演方法,同时考虑了柯西稀疏约束正则化和平滑模型约束正则化,最终使用非线性的迭代重加权最小二乘策略实现了各向异性特征参数的稳定估算.模型和实际资料处理表明,反演结果与测井解释数据相吻合,证明了该方法能够稳定可靠地从方位叠前地震资料中获取各向异性特征参数,减小参数估算的不确定性,为非均匀正交介质的各向异性预测提供了一种高可靠性的地震反演方法.     

Local Determination of Weak Anisotropy Parameters from qP-wave Slowness and Particle Motion Measurements

— We propose an algorithm for local evaluation of weak anisotropy (WA) parameters from measurements of slowness vector components and/or of particle motions of q P waves at individual receivers in a borehole in a multi-azimuthal multiple-source offset VSP experiment. As a byproduct the algorithm yields approximate angular variation of q P-wave phase velocity. The formulae are derived under assumption of weak but arbitrary anisotropy and lateral inhomogeneity of the medium. The algorithm is thus independent of structural complexities between the source and the receiver. If complete slowness vector is determinable from observed data, then the information about polarization can be used as an independent additional constraint. If only the component of the slowness along the borehole can be determined from observations (which is mostly the case), the inversion without information about polarization is impossible. We present several systems of equations which can be used when different numbers of components of the slowness vector are available. The SVD algorithm is used to solve an overdetermined system of linear equations for WA parameters for two test examples of synthetic multi-azimuthal multiple-source offset VSP data. The system of equations results from approximate first-order perturbation equations for the slowness and polarization vectors of the q P wave. Analysis of singular values and of variances of WA parameters is used for the estimation of chances to recover the sought parameters. Effects of varying number of profiles with sources and of noise added to “observed” data are illustrated. An important observation is that although, due to insufficient data, we often cannot recover all individual WA parameters with sufficient accuracy, angular phase velocity variation can be recovered rather well.     

Local Determination of Weak Anisotropy Parameters from Walkaway VSP qP-Wave Data in the Java Sea Region

We apply the inversion scheme of Zheng and Peník (2002) to the walkaway VSP data of Horne and Leaney (2000) collected in the Java Sea region. The goal is a local determination of parameters of the medium surrounding the borehole receiver array. The inversion scheme is based on linearized equations expressing qP-wave slowness and polarization vectors in terms of weak anisotropy (WA) parameters. It thus represents an alternative approach to Horne and Leaney (2000), who based their procedure on inversion of the Christoffel equation using a global optimization method. The presented inversion scheme is independent of structural complexities in the overburden and of the orientation of the borehole. The inverson formula is local, and has therefore potential to separate effects of anisotropy from effects of inhomogeneity. The data used are components of the slowness vector along the receiver array and polarization vectors. The inversion is performed without any assumptions concerning the remaining components of the slowness vector. The inversion is made (a) assuming arbitrary anisotropy, i.e., without any assumptions about symmetry of the medium, (b) assuming transverse isotropy with a vertical axis of symmetry and (c) assuming isotropy of the medium. Inverted are the raw data as well as data, in which weighting is used to reduce the effect of outliers. It is found that the WA parameters _z, ₁₅ and ₃₅ are considerably more stable than the parameters _x and _x. The latter two parameters are also found to be strongly correlated. Weaker correlation is also found between the mentioned two parameters and _z. The results of inversion show clearly that the studied medium is not isotropic. They also seem to indicate that the studied medium does not possess the VTI symmetry.     

The Use of Wave-field Directivity for Velocity Estimation: Moving Source Profiling (MSP) Experiments at KTB

—Within the "Integrated Seismics Oberpfalz 1989 (ISO89)" a three-component Moving Source Profiling (MSP) experiment, also named walk-away VSP, was carried out at the drilling site of the "Kontinentales Tiefbohrprogramm der Bundesrepublik Deutschland (KTB)" in Germany. Analysis of transmitted waves traveling from the source locations at the surface down to the receiver array in the borehole reveals velocity information about the illuminated part of the subsurface. Complementary to the widely used evaluation of travel-time perturbations to locate velocity inhomogeneities we suggest the use of the directivity of transmitted wave types down in the borehole. To determine the wave-field directivity we focus on transmitted arrivals by employing principles of "Controlled Directional Reception (CDR)." We calculate local slant-stacks for three different depth positions as a function of the source offset, thus obtaining the variation of the vertical slowness (vertical ray parameter) of incident waves along the horizontal source profile and the vertical receiver array. The slowness data combined with travel times are interpreted by forward modeling taking into account geological information of the survey area. Our findings confirm results from gravity measurements which suggest the existence of large amphibolite/metabasite complexes in the vicinity of the borehole. The described method is also used to identify P-to-S converted energy originating from fracture zones above the receiver array and to locate the region in which conversion occurs.     

MIGRATION OF MIXED-MODE VSP WAVEFIELDS1

Two-dimensional VSP surveys are often conducted to provide structural illumination of the subsurface away from the borehole. The illumination is achieved through offsetting the source with respect to the downhole geophone. This inevitably gives rise to mode-conversions in both downgoing and upgoing wavefields. Migration of mixed-mode wavefields is complex because the velocity profile used for wavefield extrapolation is valid only for a particular propagation mode; the other mode always propagates at a different velocity. It is therefore advisable to separate the wave-types (P-wave and SV-wave) prior to migration. This may be achieved through wavemode filtering, a multichannel process which exploits the relation between propagation velocity, slowness of events at the recording array and particle motion. The necessary information about particle motion is available only if the VSP data are acquired with a three-component downhole geophone assembly. The wavemode filter partitions wave-types at the recording array; it provides no information about the various changes of propagation mode experienced by the energy as it travels from source to geophone. For the purpose of migration, the intermediate modes of propagation must be deduced. Much of the energy arriving at the receivers is P-wave which has followed the P-wave velocity profile from the source. It can therefore be imaged by conventional (Kirchhoff) migration. As an example of SV-wave imaging, a common mode-code is P-wave from source to reflector and SV-wave from reflector to geophone. Migration of such data calls for back-propagation of the geophone array wavefield, at SV-wave velocity, to the point in the subsurface where it is time-coincident with the forward propagated downwave, at P-wave velocity.     

基于偶极弯曲波频散的横波慢度径向分布反演

本文针对地层横波慢度径向分层模型,分析了地层横波慢度的径向非均匀性对弯曲波频散的影响.基于径向非均匀与均匀模型之间弯曲波频散的差异,结合微扰法和Backus-Gilbert(BG)理论建立了反演横波慢度径向分布的方程,求取了地层横波慢度的径向分布.在无噪声和参数误差时,反演结果较好地反映了实际地层横波慢度的径向分布,当井孔流体或井外地层纵波慢度的选取误差在10%内变化时,反演结果基本保持不变;存在信噪比(SNR)为20 dB(信号的功率为噪声的100倍)或10 dB(信号的功率为噪声的10倍)噪声时,反演结果没有发生明显的改变,其相对误差基本控制在10%以内,可见噪声对反演结果的影响不大.以上反演结果说明,本文采用的结合微扰法和BG理论的反演方法来估测地层横波慢度的径向分布时,具有很好的鲁棒性,可以被用于现场了解井壁周围的地层性质.     

Seismic characterization of vertical fractures described as general linear-slip interfaces

Fluid flow in many hydrocarbon reservoirs is controlled by aligned fractures which make the medium anisotropic on the scale of seismic wavelength. Applying the linear‐slip theory, we investigate seismic signatures of the effective medium produced by a single set of ‘general’ vertical fractures embedded in a purely isotropic host rock. The generality of our fracture model means the allowance for coupling between the normal (to the fracture plane) stress and the tangential jump in displacement (and vice versa). Despite its low (triclinic) symmetry, the medium is described by just nine independent effective parameters and possesses several distinct features which help to identify the physical model and estimate the fracture compliances and background velocities. For example, the polarization vector of the vertically propagating fast shear wave S₁ and the semi‐major axis of the S₁‐wave normal‐moveout (NMO) ellipse from a horizontal reflector always point in the direction of the fracture strike. Moreover, for the S₁‐wave both the vertical velocity and the NMO velocity along the fractures are equal to the shear‐wave velocity in the host rock. Analysis of seismic signatures in the limit of small fracture weaknesses allows us to select the input data needed for unambiguous fracture characterization. The fracture and background parameters can be estimated using the NMO ellipses from horizontal reflectors and vertical velocities of P‐waves and two split S‐waves, combined with a portion of the P‐wave slowness surface reconstructed from multi‐azimuth walkaway vertical seismic profiling (VSP) data. The stability of the parameter‐estimation procedure is verified by performing non‐linear inversion based on the exact equations.