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1.
Anisotropy in subsurface geological models is primarily caused by two factors: sedimentation in shale/sand layers and fractures. The sedimentation factor is mainly modelled by vertical transverse isotropy (VTI), whereas the fractures are modelled by a horizontal transversely isotropic medium (HTI). In this paper we study hyperbolic and non‐hyperbolic normal reflection moveout for a package of HTI/VTI layers, considering arbitrary azimuthal orientation of the symmetry axis at each HTI layer. We consider a local 1D medium, whose properties change vertically, with flat interfaces between the layers. In this case, the horizontal slowness is preserved; thus, the azimuth of the phase velocity is the same for all layers of the package. In general, however, the azimuth of the ray velocity differs from the azimuth of the phase velocity. The ray azimuth depends on the layer properties and may be different for each layer. In this case, the use of the Dix equation requires projection of the moveout velocity of each layer on the phase plane. We derive an accurate equation for hyperbolic and high‐order terms of the normal moveout, relating the traveltime to the surface offset, or alternatively, to the subsurface reflection angle. We relate the azimuth of the surface offset to its magnitude (or to the reflection angle), considering short and long offsets. We compare the derived approximations with analytical ray tracing. 相似文献
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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. 相似文献
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We study the azimuthally dependent hyperbolic moveout approximation for small angles (or offsets) for quasi‐compressional, quasi‐shear, and converted waves in one‐dimensional multi‐layer orthorhombic media. The vertical orthorhombic axis is the same for all layers, but the azimuthal orientation of the horizontal orthorhombic axes at each layer may be different. By starting with the known equation for normal moveout velocity with respect to the surface‐offset azimuth and applying our derived relationship between the surface‐offset azimuth and phase‐velocity azimuth, we obtain the normal moveout velocity versus the phase‐velocity azimuth. As the surface offset/azimuth moveout dependence is required for analysing azimuthally dependent moveout parameters directly from time‐domain rich azimuth gathers, our phase angle/azimuth formulas are required for analysing azimuthally dependent residual moveout along the migrated local‐angle‐domain common image gathers. The angle and azimuth parameters of the local‐angle‐domain gathers represent the opening angle between the incidence and reflection slowness vectors and the azimuth of the phase velocity ψphs at the image points in the specular direction. Our derivation of the effective velocity parameters for a multi‐layer structure is based on the fact that, for a one‐dimensional model assumption, the horizontal slowness and the azimuth of the phase velocity ψphs remain constant along the entire ray (wave) path. We introduce a special set of auxiliary parameters that allow us to establish equivalent effective model parameters in a simple summation manner. We then transform this set of parameters into three widely used effective parameters: fast and slow normal moveout velocities and azimuth of the slow one. For completeness, we show that these three effective normal moveout velocity parameters can be equivalently obtained in both surface‐offset azimuth and phase‐velocity azimuth domains. 相似文献
4.
Backus and Crampin derived analytical equations for estimating approximate phase-velocity variations in symmetry planes in weakly anisotropic media, where the coefficients of the equations are linear combinations of the elastic constants. We examine the application of similar equations to group-velocity variations in off-symmetry planes, where the coefficients of the equations are derived numerically. We estimate the accuracy of these equations over a range of anisotropic materials with transverse isotropy with both vertical and horizontal symmetry axes, and with combinations of transverse isotropy yielding orthorhombic symmetry. These modified equations are good approximations for up to 17% shear-wave anisotropy for propagations in symmetry planes for all waves in all symmetry systems examined, but are valid only for lower shear-wave anisotropy (up to 11%) in off-symmetry planes. We also obtain analytical moveout equations for the reflection of qP-, qSH-, and qSV- waves from a single interface for off-symmetry planes in anisotropic symmetry. The moveout equation consists of two terms: a hyperbolic moveout and a residual moveout, where the residual moveout is proportional to the degree of anisotropy and the spread length of the acquisition geometry. Numerical moveout curves are computed for a range of anisotropic materials to verify the analytical moveout equations. 相似文献
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本文通过理论计算、数值模拟与穹窿物理模型三维数据对比分析的方法,对HTI介质中纵波方位各向异性现象进行研究.主要是进行目的层动校正速度以及走时的分析.结果显示,理论数值与实验数值耦合较好,HTI介质会引起动校正速度以及走时随方位角呈现椭圆形的变化;同时发现,观测系统中最大偏移距与目的层深度的比值以及方位角分布对各向异性分析有较大影响. 三维纵波方位各向异性分析对于数据的观测系统设计以及数据质量有较高的要求. 相似文献
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Ilya Tsvankin 《Geophysical Prospecting》1997,45(3):479-512
The transversely isotropic (TI) model with a tilted axis of symmetry may be typical, for instance, for sediments near the flanks of salt domes. This work is devoted to an analysis of reflection moveout from horizontal and dipping reflectors in the symmetry plane of TI media that contains the symmetry axis. While for vertical and horizontal transverse isotropy zero-offset reflections exist for the full range of dips up to 90°, this is no longer the case for intermediate axis orientations. For typical homogeneous models with a symmetry axis tilted towards the reflector, wavefront distortions make it impossible to generate specular zero-offset reflected rays from steep interfaces. The ‘missing’ dipping planes can be imaged only in vertically inhomogeneous media by using turning waves. These unusual phenomena may have serious implications in salt imaging. In non-elliptical TI media, the tilt of the symmetry axis may have a drastic influence on normal-moveout (NMO) velocity from horizontal reflectors, as well as on the dependence of NMO velocity on the ray parameter p (the ‘dip-moveout (DMO) signature’). The DMO signature retains the same character as for vertical transverse isotropy only for near-vertical and near-horizontal orientation of the symmetry axis. The behaviour of NMO velocity rapidly changes if the symmetry axis is tilted away from the vertical, with a tilt of ±20° being almost sufficient to eliminate the influence of the anisotropy on the DMO signature. For larger tilt angles and typical positive values of the difference between the anisotropic parameters ε and δ, the NMO velocity increases with p more slowly than in homogeneous isotropic media; a dependence usually caused by a vertical velocity gradient. Dip-moveout processing for a wide range of tilt angles requires application of anisotropic DMO algorithms. The strong influence of the tilt angle on P-wave moveout can be used to constrain the tilt using P-wave NMO velocity in the plane that includes the symmetry axis. However, if the azimuth of the axis is unknown, the inversion for the axis orientation cannot be performed without a 3D analysis of reflection traveltimes on lines with different azimuthal directions. 相似文献
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In areas of complex geology such as the Canadian Foothills, the effects of anisotropy are apparent in seismic data and estimation of anisotropic parameters for use in seismic imaging is not a trivial task. Here we explore the applicability of common‐focus point (CFP)‐based velocity analysis to estimate anisotropic parameters for the variably tilted shale thrust sheet in the Canadian Foothills model. To avoid the inherent velocity‐depth ambiguity, we assume that the elastic properties of thrust‐sheet with respect to transverse isotropy symmetry axis are homogeneous, the reflector below the thrust‐sheet is flat, and that the anisotropy is weak. In our CFP approach to velocity analysis, for a poorly imaged reflection point, a traveltime residual is obtained as the time difference between the focusing operator for an assumed subsurface velocity model and the corresponding CFP response obtained from the reflection data. We assume that this residual is due to unknown values for anisotropy, and we perform an iterative linear inversion to obtain new model parameters that minimize the residuals. Migration of the data using parameters obtained from our inversion results in a correctly positioned and better focused reflector below the thrust sheet. For traveltime computation we use a brute force mapping scheme that takes into account weakly tilted transverse isotropy media. For inversion, the problem is set up as a generalized Newton's equation where traveltime error (differential time shift) is linearly dependent on the parameter updates. The iterative updates of parameters are obtained by a least‐squares solution of Newton's equations. The significance of this work lies in its applicability to areas where transverse isotropy layers are heterogeneous laterally, and where transverse isotropy layers are overlain by complex structures that preclude a moveout curve fitting. 相似文献
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对Christoffel公式进行Bond变换得到EDA介质的Christoffel方程,并由其非零解推导出EDA介质中视横波(qSV)、横波(SH)、视纵波(qP)的相速度、群速度、偏振向量(质点的振动方向)的三维计算公式.通过模型计算分析了具有水平对称轴的各向异性(HTI)介质和EDA介质中介质对称轴的极角和方位角对相速度、群速度及偏振向量的影响,对其随极角、方位角的变化特征进行了分析,并采用Matlab进行了数值计算,对其特征采用三维显示.通过取极角或方位角为零简化得到HTI介质和具有垂直对称轴的各向异性(VTI)介质中地震波的相速度、群速度,对EDA介质中的三维计算结果进行退化验证. 通过数值计算进一步验证了地震波相速度与EDA介质对称轴的相互关系. 结果表明,通过广角地震勘探可探明地下介质的裂隙走向及密度,从而确定灾害体产状. 相似文献
11.
Bayesian Markov chain Monte Carlo inversion for anisotropy of PP- and PS-wave in weakly anisotropic and heterogeneous media 
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下载免费PDF全文 A single set of vertically aligned cracks embedded in a purely isotropic background may be considered as a long-wavelength effective transversely isotropy (HTI) medium with a horizontal symmetry axis. The crack-induced HTI anisotropy can be characterized by the weakly anisotropic parameters introduced by Thomsen. The seismic scattering theory can be utilized for the inversion for the anisotropic parameters in weakly anisotropic and heterogeneous HTI media. Based on the seismic scattering theory, we first derived the linearized PP- and PS-wave reflection coefficients in terms of P- and S-wave impedances, density as well as three anisotropic parameters in HTI media. Then, we proposed a novel Bayesian Markov chain Monte Carlo inversion method of PP- and PS-wave for six elastic and anisotropic parameters directly. Tests on synthetic azimuthal seismic data contaminated by random errors demonstrated that this method appears more accurate, anti-noise and stable owing to the usage of the constrained PS-wave compared with the standards inversion scheme taking only the PP-wave into account. 相似文献
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Alexey Stovas 《Geophysical Prospecting》2017,65(2):426-452
I derive the kinematic properties of single‐mode P, S1, and S2 waves as well as converted PS1, PS2, and S1S2 waves in elastic orthorhombic media including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross‐term one). I show that the azimuthal dependence of normal moveout velocity and anellipticity is different in phase and group domains. The effects on‐vertical‐axis singularity and on‐vertical‐axis triplication are considered for pure‐mode S1 and S2 waves and converted‐mode S1S2 waves. The conditions and properties of on‐vertical‐axis triplication are defined in terms of kinematic parameters. The results are illustrated in four homogeneous orthorhombic models and one multilayered orthorhombic model with no variation in azimuthal orientation for all the layers. 相似文献
13.
Tariq Alkhalifah 《Geophysical Prospecting》2016,64(2):505-513
While velocity contrasts are responsible for most of the events recorded in our data, the long wavelength behavior of the velocity model is responsible for the geometrical shape of these events. For isotropic acoustic materials, the wave dependency on the long (wave propagation) and short (scattering) wavelength velocity components is stationary with the propagation angle. On the other hand, in representing a transversely isotropic with a vertical symmetry axis medium with the normal moveout velocity, the anellepticity parameter η, the vertical scaling parameter δ, and the sensitivity of waves vary with the polar angle for both the long and short wavelength features of the anisotropic dimensionless medium parameters (δ and η). For horizontal reflectors at reasonable depths, the long wavelength features of the η model is reasonably constrained by the long offsets, whereas the short wavelength features produce very week reflections at even reasonable offsets. Thus, for surface acquired seismic data, we could mainly invert for smooth η responsible for the geometrical shape of reflections. On the other hand, while the δ long wavelength components mildly affects the recorded data, its short wavelength variations can produce reflections at even zero offset, with a behavior pattern synonymous to density. The lack of the long wavelength δ information will mildly effect focusing but will cause misplacement of events in depth. With low enough frequencies (very low), we may be able to recover the long wavelength δ using full waveform inversion. However, unlike velocity, the frequencies needed for that should be ultra‐low to produce long‐wavelength scattering‐based model information as δ perturbations do not exert scattering at large offsets. For a combination given by the horizontal velocity, η, and ε, the diving wave influence of η is absorbed by the horizontal velocity, severely limiting the η influence on the data and full waveform inversion. As a result, with a good smooth η estimation, for example, from tomography, we can focus the full waveform inversion to invert for only the horizontal velocity and maybe ε as a parameter to fit the amplitude. This is possibly the most practical parametrization for inversion of surface seismic data in transversely isotropic with vertical symmetry axis media. 相似文献
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Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t2(x2) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (VP0 and VS0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (VP0, VS0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves. 相似文献
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The azimuthally varying non‐hyperbolic moveout of P‐waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long‐spread, wide‐azimuth P‐wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry‐plane NMO velocities, V(1)nmo and V(2)nmo , and the anellipticity parameters, η(1), η(2) and η(3) . The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah–Tsvankin non‐hyperbolic moveout equation. The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise‐contaminated data for a single orthorhombic layer show that the best‐constrained parameters are the azimuth ? of one of the symmetry planes and the velocities V(1)nmo and V(2)nmo , while the resolution in η(1) and η(2) is somewhat compromised by the trade‐off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter η(3) , which influences only long‐spread moveout in off‐symmetry directions. For stratified orthorhombic models with depth‐dependent symmetry‐plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term. The algorithm was successfully tested on wide‐azimuth P‐wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long‐offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetry‐plane directions are close to the azimuths of the off‐trend fracture sets determined from borehole data and shear‐wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P‐wave time imaging and geometrical‐spreading correction in layered orthorhombic media. 相似文献
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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%. 相似文献
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The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging. 相似文献
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推导了各向异性介质中由弹性系数表示的方位动校NMO速度的具体表达式,表明各向异性介质中方位NMO速度程椭圆形状,并分别对具水平对称轴的横向各向同性介质(HTI)、正交介质和单斜各向异性介质及在不同的裂隙填充物的性质下方位NMO速度进行了计算,结果表明裂隙的存在对NMO速度的影响不仅与裂隙密度有关,还取决于裂隙填充物的性质.同时,研究表明对于裂隙型单斜各向异性介质,其方位NMO速度椭圆轴向并不象HTI介质和正交介质中的那样与自然坐标系的坐标轴一致,而是发生了一定角度的偏离,其大小与裂隙填充物的性质、两组裂隙密度的比值及裂隙间的夹角等因素有关,研究结果为进一步区分裂隙介质的类型及裂隙填充物的性质提供依据. 相似文献
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Certain degree of smoothness of velocity models is required for most ray‐based migration and tomography. Applying conventional smoothing in model parameters results in offset‐dependent travel‐time errors for reflected events, which can be large even for small contrasts in model parameters between the layers. This causes the shift in both the depth and residual moveout of the migrated images. To overcome this problem in transversely isotropic medium with a vertical symmetry axis, the preserved travel‐time smoothing method was proposed earlier. We extend this method for orthorhombic media with and without azimuthal variation between the layers. We illustrate this method for a single interface between two orthorhombic layers and show that the smoothing‐driven errors in travel time are very small for practical application. 相似文献