单斜介质中方位NMO速度Thomsen参数反演方法研究

采用启发式共轭梯度法,即随机爬山法 + 共轭梯度法,利用单斜介质中P波方位NMO速度椭圆轴向偏转角度接近于零这一特性,简化P波方位NMO速度公式,并利用多方位P波NMO速度,反演出某一初始CMP观测线与自然坐标系之间的夹角,作为进一步进行Thomsen各向异性参数反演的基础. 根据各向异性介质中方位NMO速度与Thomsen参数之间的关系,建立了利用三种波的多方位NMO速度及垂直传播速度反演单层单斜各向异性介质Thomsen各向异性参数的目标函数. 对计算的理论值添加具有一定标准差的正态分布的随机噪声,用以模拟实际观测存在的误差,通过对加噪后的数据进行多次反演的误差分析,表明了所建立的目标函数及选用的反演方法是有效可行的,而且相对稳定.     

裂隙型单斜介质中多方位地面三分量记录模拟

针对裂隙型储集层中更具代表性的各向异性介质模型,即在各向同性背景介质中含有两组斜交的垂直裂隙所构成的单斜各向异性介质模型,利用时间和空间上可达任意阶的高阶交错网格有限差分技术,对具有不同裂隙填充物性质的单斜介质中波的传播快照进行了模拟.结果证实各向异性介质中波的传播速度随传播方向的不同而产生明显的差异;裂隙填充物的性质对于速度各向异性具有很大的影响.另外,利用坐标旋转法,对水平层状各向异性介质中多方位地面三分量记录进行了模拟,结果表明了方位各向异性介质中,波的传播速度不仅随入射角的变化而变化,同时也随观测方位的不同而产生差异.数值模拟结果为进一步利用地面多方位地震属性进行各向异性参数的反演及裂隙参数的描述提供理论基础.     

ulti-azimuth three-component surface seismic modeling for viscoelastic cracked monoclinic media

针对粘弹性裂隙型单斜介质,本文应用高阶交错网格差分法,对其传播快照以及多方位地面三分量记录进行模拟,结果证明了裂隙填充物的性质引起的各向异性与粘弹性性质对单斜介质波场有明显的影响,总结了不同观测方位地震记录呈现出的规律性,这为进一步了解波场在介质中的传播情况,提出更合理的理论模型,提供一种尝试.     

粘弹性裂隙型单斜介质多方位地面三分量记录模拟

针对粘弹性裂隙型单斜介质,本文应用高阶交错网格差分法,对其传播快照以及多方位地面三分量记录进行模拟,结果证明了裂隙填充物的性质引起的各向异性与粘弹性性质对单斜介质波场有明显的影响,总结了不同观测方位地震记录呈现出的规律性,这为进一步了解波场在介质中的传播情况,提出更合理的理论模型,提供一种尝试。     

裂缝型HTI介质的纵波弹性阻抗

裂缝发育导致的地震波场各向异性,是裂缝型油气藏的一个重要特征.然而针对该类油气藏的叠前弹性阻抗技术,一直没有通过各向异性弹性阻抗公式建立与裂缝参数的直接关系.本文在回顾封闭平行硬币状裂缝模型和线性滑动模型的基础上,将裂缝填充物性质、分布密度与围岩的横纵波速度比,引入裂缝型HTI介质弹性阻抗公式,并对相应的归一化弹性阻抗响应特征进行模拟分析.分析表明,弹性阻抗受以上三参数的影响规律存在明显差异,其中含气裂隙介质随裂缝密度的变化要明显高于对应的流体裂隙介质,流体填充裂隙介质随横、纵波速度比的变化幅度要高于对应的含气裂隙介.该结论初步为裂缝型油气藏流体识别工作提供了依据.     

HTI煤层方位AVO响应与裂隙识别

煤层在顶板压实作用下水平裂隙近乎闭合,多垂向裂隙发育,因此将该类煤层等效为HTI介质,研究裂隙密度和填充物类型对方位AVO的影响,可以为预测裂隙提供理论依据,对煤田勘探有重要意义.本文基于Thomsen各向异性理论和模型等效理论建立上层为各向同性介质而下层为垂向裂隙发育的HTI煤层的正演模型,推导出适用于所建模型的更高精度反射系数近似公式对不同裂隙密度、不同填充物类型的模型进行方位AVO数值模拟,并利用反射系数进行地震记录合成;从反射系数空间曲面和地震记录两方面分析不同模型随着入射角、方位角、裂隙密度、裂隙填充物的改变而产生的不同地震响应.结果表明:裂隙密度的增大导致反射系数空间曲面波幅增大,地震记录波振幅增大;裂隙密度相同时,饱和水裂隙模型和干裂隙模型的反射系数空间曲面和合成地震记录存在显著差异;方位角为0°时,饱和水裂隙模型和干裂隙模型的反射系数差值达到0.2,分辨性较强;在方位角为0.时,入射角大于45.时地震记录差异最显著.测试数据中,含饱和水裂隙煤层的反射系数绝对值低于干裂隙煤层,地震记录的振幅也低于干裂隙煤层.     

HTI煤层介质槽波波场与频散特征初步研究

煤层内裂隙较为发育,具有明显的各向异性.目前槽波理论研究以各向同性介质为主,对HTI介质中槽波及其频散性质研究很少.本文以弱各向异性、含垂直裂隙HTI煤层介质为研究对象,研究了HTI煤层介质中的三维槽波波场,采用交错网格高阶有限差分法模拟槽波,推导了三层水平层状HTI煤层介质的Love型槽波理论频散公式和振幅深度分布,分析了HTI各弹性参数对频散曲线的影响.HTI介质和各向同性介质基阶Love槽波频散曲线差异较小,高阶较大;煤厚主要影响Airy相频率,而Airy相速度不变;煤层vs对Airy相速度影响很大;煤层γ对基阶Love槽波影响很小,高阶稍大.各波偏振方向不再与波的传播方向平行或垂直,而是呈一定夹角.利用基阶Love槽波频散曲线推测裂隙发育较为困难,可利用高阶频散曲线.     

垂向裂隙各向异性煤层地震波响应

煤层中存在的裂隙会导致介质表现为各向异性,本文以HTI型煤层为例,结合各向异性介质弹性矩阵和各向异性裂隙理论,推导出不同充填物的垂直裂隙中各向异性参数表达式,将其应用于地震波响应分析;通过改进的交错网格差分法和各向异性Christoffel方程波场分解法,得到地震波合成记录和分解后的P波和SV波记录;将Thomsen群速度与相速度公式,经过坐标轴旋转变换,得到HTI型煤层中不同各向异性参数的地震波速度响应表达式;建立不同类型煤层地质模型,分析了裂隙密度、裂隙充填物以及煤层厚度等参数变化时的地震波响应特征.研究结果为分析垂向裂隙各向异性薄煤层地震波传播规律提供工具,为选用相应地震数据进行地震波各向异性参数反演提供依据.     

裂隙参数对衰减各向异性影响的数值模拟

理论、观测和实验均证实,在地壳和上地幔存在对应力变化敏感的直立裂隙,在整体上呈现方位各向异性.在Hudson裂隙理论基础上,系统全面地数值模拟了裂隙介质几何、物性和弹性波频率等参数对各向异性衰减的影响.结果显示,裂隙密度、裂隙纵横比、泊松比、裂缝填充物、弹性波频率和未破裂岩石母体纵横波速度等对各向异性衰减有着显著影响,...     

SKS波对地壳裂隙各向异性的响应——理论地震图研究

穿透含裂隙、裂缝地壳8s视周期的SV波的理论地震图研究表明,当地壳平均裂隙密度高于0.01即横波各向异性高于1%时,非对称面内不同方位的SKS波均发生分裂;地震图中直接的记录显示是切向T分量上出现SKS波的振动,其振幅随地壳平均裂隙密度的增大而增强,甚至能与径向R分量上的振幅相当.局限于上地壳的强裂缝各向异性同样能引起SKS分裂.长周期SKS波分裂对地壳内裂隙、裂缝的分布缺乏分辨率.直立平行排列裂隙、裂缝使得SKS分裂T分量记录特征具有方位对称性,这来自于HTI介质中快、慢波偏振和到时差随方位变化的对称性;而倾斜裂隙、裂缝使得该方位对称性丧失.对实际观测SKS分裂的偏振解释需要考虑地壳裂隙各向异性,特别是断裂附近的强裂缝各向异性.     

Inversion of normal moveout for monoclinic media1

Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide-azimuth reflection data (combined with known vertical velocity or reflector depth) or multi-azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media. In order to facilitate the inversion procedure, we introduce a Thomsen-style parametrization for monoclinic media that includes the vertical velocities of the P-wave and one of the split S-waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal-moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε^(1,2), δ^(1,2,3) and γ^(1,2)) analogous to those defined by Tsvankin for the higher-symmetry orthorhombic model. The parameters ε^(1,2), δ^(1,2) and γ^(1,2) are primarily responsible for the pure-mode NMO velocities along the coordinate axes x₁ and x₂ (i.e. in the shear-wave polarization directions). The remaining coefficient δ⁽³⁾ is not constrained by conventional-spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ^(1,2,3) which control the rotation of the P-, S₁- and S₂-wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P-wave NMO ellipse and shear-wave polarization directions was recently observed on field data by Pérez et al. Our parameter-estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P-, S₁- and S₂-waves. A Dix-type representation of the NMO velocity of mode-converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS₁- and PS₂-waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.     

Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part II: effective model‡

We use residual moveouts measured along continuous full azimuth reflection angle gathers, in order to obtain effective horizontal transversely isotropic model parameters. The angle gathers are generated through a special angle domain imaging system, for a wide range of reflection angles and full range of phase velocity azimuths. The estimation of the effective model parameters is performed in two stages. First, the background horizontal transversely isotropic (HTI)/vertical transversely isotropic (VTI) layered model is used, along with the values of reflection angles, for converting the measured residual moveouts (or traveltime errors) into azimuthally dependent normal moveout (NMO) velocities. Then we apply a digital Fourier transform to convert the NMO velocities into azimuthal wavenumber domain, in order to obtain the effective HTI model parameters: vertical time, vertical compression velocity, Thomsen parameter delta and the azimuth of the medium axis of symmetry. The method also provides a reliability criterion of the HTI assumption. The criterion shows whether the medium possesses the HTI type of symmetry, or whether the azimuthal dependence of the residual traveltime indicates to a more complex azimuthal anisotropy. The effective model used in this approach is defined for a 1D structure with a set of HTI, VTI and isotropic layers (with at least one HTI layer). We describe and analyse the reduction of a multi‐layer structure into an equivalent effective HTI model. The equivalent model yields the same NMO velocity and the same offset azimuth on the Earth's surface as the original layered structure, for any azimuth of the phase velocity. The effective model approximates the kinematics of an HTI/VTI layered structure using only a few parameters. Under the hyperbolic approximation, the proposed effective model is exact.     

Finite-difference modelling of S-wave splitting in anisotropic media

We have implemented a 3D finite‐difference scheme to simulate wave propagation in arbitrary anisotropic media. The anisotropic media up to orthorhombic symmetry were modelled using a standard staggered grid scheme and beyond (monoclinic and triclinic) using a rotated staggered grid scheme. The rationale of not using rotated staggered grid for all types of anisotropic media is that the rotated staggered grid schemes are more expensive than standard staggered grid schemes. For a 1D azimuthally anistropic medium, we show a comparison between the seismic data generated by our finite‐difference code and by the reflectivity algorithm; they are in excellent agreement. We conducted a study on zero‐offset shear‐wave splitting using the finite‐difference modelling algorithm using the rotated staggered grid scheme. Our S‐wave splitting study is mainly focused on fractured media. On the scale of seismic wavelenghts, small aligned fractures behave as an equivalent anisotropic medium. We computed the equivalent elastic properties of the fractures and the background in which the fractures were embedded, using low‐frequency equivalent media theories. Wave propagation was simulated for both rotationally invariant and corrugated fractures embedded in an isotropic background for one, or more than one, set of fluid‐filled and dry fractures. S‐wave splitting was studied for dipping fractures, two vertical non‐orthogonal fractures and corrugated fractures. Our modelling results confirm that S‐wave splitting can reveal the fracture infill in the case of dipping fractures. S‐wave splitting has the potential to reveal the angle between the two vertical fractures. We also notice that in the case of vertical corrugated fractures, S‐wave splitting is sensitive to the fracture infill.     

基于碳酸盐岩裂缝岩石物理模型的横波速度和各向异性参数预测

高角度缝隙充填的碳酸盐岩储层可以等效为具有水平对称轴的横向各向同性介质.本文提出了适用于裂缝型碳酸盐岩的岩石物理模型构建流程,重点介绍了在碳酸盐岩各向同性背景中,综合利用微小裂隙模型和线性滑动模型添加缝隙系统,并分析了当缝隙充填不同流体时,各向异性参数随纵横波速比的变化特征.同时本文讨论了裂缝密度和缝隙充填流体对地震反射系数的影响,推导了不同类型流体充填时储层反射系数与裂缝密度的近似关系式,阐述了各向异性流体替换理论,最终实现饱含流体碳酸盐岩裂缝储层的纵横波速度和各向异性参数的估测.选取某碳酸盐岩工区A井对该方法进行试算,结果表明基于碳酸盐岩裂缝岩石物理模型估算的纵横波速度值与测井值吻合较好,而且估测所得的各向异性参数值也能够较好地反映出裂缝储层位置.     

Generalized Dix equation and analytic treatment of normal-moveout velocity for anisotropic media*

Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions. Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces. The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy.     

正交各向异性介质P波走时分析及Thomsen参数反演

对于包含有垂向裂缝的横向各向同性地层或含有多组正交裂缝的各向同性地层，正交各向异性介质模型是最简单的与实际地层相符的方位各向异性模型.本文对单层水平反射界面正交各向异性模型采用射线追踪法计算了全方位角变化的P波走时，时距曲线表现出强方位各向异性.采用小生境遗传算法，对三条成一定角度的测线的走时信息进行速度和各向异性参数反演.模型算例表明，此方法可以得到高精度的裂缝方位角、P波垂直速度和较高精度的Thomsen各向异性参数.     

Characterization of dipping fractures in a transverselyisotropic background

Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.     

Reflection moveout inversion in azimuthally anisotropic media: accuracy, limitations and acquisition

Parameter estimation from the elliptical variations in the normal-moveout (NMO) velocity in azimuthally anisotropic media is sensitive to the angular separation between the survey lines in 2D, or equivalently, the source-to-receiver azimuth in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the orientation of an NMO ellipse, in particular the parameter α, is also sensitive to the magnitude of anisotropy. On the other hand, the accuracy in estimating the semi-axes of the NMO-velocity ellipse is about the same for any magnitude of anisotropy.   To invert for the NMO ellipse parameters at least three NMO-velocity measurements along distinct azimuth directions are needed. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to-receiver directions 60° apart. Having more than three distinct source-to-receiver azimuths (e.g. full azimuthal coverage) provides a useful data redundancy that enhances the quality of the estimates.   In order to maximize quality in the inversion process, it is recommended to design the seismic data acquisition such that it contains small sectors (≤10°) with adequate fold and offset distribution.   Using three NMO-velocity measurements, 60° apart, an azimuthally anisotropic layer overlain by an azimuthally isotropic overburden (as might occur for fractured reservoirs) should have a relative thickness (in time) with respect to the total thickness at least equal to the ratio of the error in the NMO (stacking) velocity to the interval anisotropy of the fractured layer. Coverage along more than three azimuths, however, improves this limitation, which is imposed by Dix differentiation, by at most 50%, depending on the number of observations (NMO velocities) that enter the inversion procedure.