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1.
Pure-mode wave propagation is important for applications ranging from imaging to avoiding parameter tradeoff in waveform inversion. Although seismic anisotropy is an elastic phenomenon, pseudo-acoustic approximations are routinely used to avoid the high computational cost and difficulty in decoupling wave modes to obtain interpretable seismic images. However, such approximations may result in inaccuracies in characterizing anisotropic wave propagation. We propose new pure-mode equations for P- and S-waves resulting in an artefact-free solution in transversely isotropic medium with a vertical symmetry axis. Our approximations are more accurate than other known approximations as they are not based on weak anisotropy assumptions. Therefore, the S-wave approximation can reproduce the group velocity triplications in strongly anisotropic media. The proposed approximations can be used for accurate modelling and imaging of pure P- and S-waves in transversely isotropic media. 相似文献
2.
几种弱向异性介质中qSV波速度和偏振异常 总被引：2，自引：2，他引：0
研究了在具有生趣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ｓＳＶ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。 相似文献
3.
On shear-wave triplication in transversely isotropic media 总被引：1，自引：0，他引：1
The exact solution to the problem of qSV triplication in homogenous transversely isotropic media has been long known, but the result is algebraically complex and is seldom applied in practice. We present an appropriate approximation (not assuming weak qSV-anisotropy) that simplifies the conditions for the onset of off-axis triplication as anisotropy is increased, identifying the anisotropy parameter σ as the controlling parameter. It follows that commonly reported surface-seismic P-wave move-out measurements imply that many formations in the earth's sedimentary crust support off-axis qSV triplications. For typical Vp/Vs velocity ratios and a horizontally stratified earth, however, off-axis qSV triplications appear to only occur for shear-wave incidence angles too far from the vertical to be sampled by surface-seismic converted-wave survey geometries. 相似文献
4.
相速度和偏振方向是研究地震波传播规律和描述介质特性的重要参数,在理论研究和实际应用中有重要作用.本文假定倾斜横向各向同性(TTI)介质对称轴位于观测坐标系XOZ面内,在此观测坐标系下直接推导了TTI介质弹性波相速度和偏振方向的解析表达式,再进一步利用Thomsen弱各向异性理论,推导了弱各向异性近似条件下弹性波相速度以及qP波和qSV波偏振方向表达式.理论分析和数值试例表明,在相速度方面,随着各向异性介质参数改变,qP波和qSH波速度变化较为平缓,qSV波速度变化较为剧烈.弹性波相速度近似式误差均较小,能较好地近似精确相速度.在偏振方向方面,SH波偏振方向只是传播方向和对称轴倾角的函数,而与各向异性参数无关,SH波偏振方向既垂直于传播方向,又垂直于TTI介质对称轴方向.除特定方向外,qP波和qSV波的偏振方向与传播方向均成一定角度,并且随TTI介质对称轴倾角的改变而改变;在精确和近似情况下,qP波和qSV波的偏振方向始终垂直;在精度允许范围内,偏振方向的弱各向异性近似式与理论解析式吻合较好. 相似文献
5.
Weak‐anisotropy approximation for P‐wave reflection coefficient at the boundary between two tilted transversely isotropic media 
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下载免费PDF全文 Existing and commonly used in industry nowadays, closed‐form approximations for a P‐wave reflection coefficient in transversely isotropic media are restricted to cases of a vertical and a horizontal transverse isotropy. However, field observations confirm the widespread presence of rock beds and fracture sets tilted with respect to a reflection boundary. These situations can be described by means of the transverse isotropy with an arbitrary orientation of the symmetry axis, known as tilted transversely isotropic media. In order to study the influence of the anisotropy parameters and the orientation of the symmetry axis on P‐wave reflection amplitudes, a linearised 3D P‐wave reflection coefficient at a planar weak‐contrast interface separating two weakly anisotropic tilted tranversely isotropic half‐spaces is derived. The approximation is a function of the incidence phase angle, the anisotropy parameters, and symmetry axes tilt and azimuth angles in both media above and below the interface. The expression takes the form of the well‐known amplitude‐versus‐offset “Shuey‐type” equation and confirms that the influence of the tilt and the azimuth of the symmetry axis on the P‐wave reflection coefficient even for a weakly anisotropic medium is strong and cannot be neglected. There are no assumptions made on the symmetry‐axis orientation angles in both half‐spaces above and below the interface. The proposed approximation can be used for inversion for the model parameters, including the orientation of the symmetry axes. Obtained amplitude‐versus‐offset attributes converge to well‐known approximations for vertical and horizontal transverse isotropic media derived by Rüger in corresponding limits. Comparison with numerical solution demonstrates good accuracy. 相似文献
6.
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. 相似文献
7.
Depth migration of shot records in heterogeneous, transversely isotropic media using optimum explicit operators 总被引：10，自引：0，他引：10
A space–frequency domain 2D depth-migration scheme is generalized for imaging in the presence of anisotropy. The anisotropy model used is that of a transversely isotropic (TI) medium with a symmetry axis that can be either vertical or tilted. In the proposed scheme the anisotropy is described in terms of Thomsen parameters; however, the scheme can accommodate a wide range of anisotropy rather than only weak anisotropy. Short spatial convolution operators are used to extrapolate the wavefields recursively in the space–frequency domain for both qP- and qSV-waves. The weighted least-squares method for designing isotropic optimum operators is extended to asymmetric optimum explicit extrapolation operators in the presence of TI media with a tilted symmetry axis. Additionally, an efficient weighted quadratic-programming design method is developed. The short spatial length of the derived operators makes it possible for the proposed scheme to handle lateral inhomogeneities. The performance of the operators, designed by combining the weighted least-squares and weighted quadratic-programming methods, is demonstrated by migration impulse responses of qP and qSV propagation modes for the weak and strong TI models with both vertical and tilted symmetry axes. Finally, a table-driven shot-record depth-migration scheme is proposed, which is illustrated for finite-difference modelled shot records in TI media. 相似文献
8.
In seismic data processing, serious problems could be caused by the existence of triplication and need to be treated properly for tomography and other inversion methods. The triplication in transversely isotropic medium with a vertical symmetry axis has been well studied and concluded that the triplicated traveltime only occurs for S wave and there is no triplication for P and converted PS waves since the P wave convexity slowness always compensates the S wave slowness concavity. Compared with the vertical symmetry axis model, the research of the triplication in transversely isotropic medium with a tilted symmetry axis is still keeping blank. In order to analyse the triplication for the converted wave in the tilted symmetry axis model, we examine the traveltime of the triplication from the curvature of averaged P and S wave slowness. Three models are defined and tested in the numerical examples to illustrate the behaviour of the tilted symmetry axis model for the triplicated traveltime with the change of the rotation angle. Since the orientation of an interface is related to the orientation of the symmetry axis, the triplicated traveltime is encountered for the converted wave in the tilted symmetry axis model assuming interfaces to be planar and horizontal. The triplicated region is influenced by the place and level of the concave curvature of the P and S wave slowness. 相似文献
9.
Generalized non‐hyperbolic approximation for qP‐wave relative geometrical spreading in a layered transversely isotropic medium with a vertical symmetry axis 下载免费PDF全文
下载免费PDF全文 Compensation for geometrical spreading along the ray‐path is important in amplitude variation with offset analysis especially for not strongly attenuative media since it contributes to the seismic amplitude preservation. The P‐wave geometrical spreading factor is described by a non‐hyperbolic moveout approximation using the traveltime parameters that can be estimated from the velocity analysis. We extend the P‐wave relative geometrical spreading approximation from the rational form to the generalized non‐hyperbolic form in a transversely isotropic medium with a vertical symmetry axis. The acoustic approximation is used to reduce the number of parameters. The proposed generalized non‐hyperbolic approximation is developed with parameters defined by two rays: vertical and a reference rays. For numerical examples, we consider two choices for parameter selection by using two specific orientations for reference ray. We observe from the numerical tests that the proposed generalized non‐hyperbolic approximation gives more accurate results in both homogeneous and multi‐layered models than the rational counterpart. 相似文献
10.
Analysis of different parameterisations of waveform inversion of compressional body waves in an elastic transverse isotropic Earth with a vertical axis of symmetry 下载免费PDF全文
下载免费PDF全文 In a multi‐parameter waveform inversion, the choice of the parameterisation influences the results and their interpretations because leakages and the tradeoff between parameters can cause artefacts. We review the parameterisation selection when the inversion focuses on the recovery of the intermediate‐to‐long wavenumbers of the compressional velocities from the compressional body (P) waves. Assuming a transverse isotropic medium with a vertical axis of symmetry and weak anisotropy, analytical formulas for the radiation patterns are developed to quantify the tradeoff between the shear velocity and the anisotropic parameters and the effects of setting to zero the shear velocity in the acoustic approach. Because, in an anisotropic medium, the radiation patterns depend on the angle of the incident wave with respect to the vertical axis, two particular patterns are discussed: a transmission pattern when the ingoing and outgoing slowness vectors are parallel and a reflection pattern when the ingoing and outgoing slowness vectors satisfy Snell's law. When the inversion aims at recovering the long‐to‐intermediate wavenumbers of the compressional velocities from the P‐waves, we propose to base the parameterisation choice on the transmission patterns. Since the P‐wave events in surface seismic data do not constrain the background (smooth) vertical velocity due to the velocity/depth ambiguity, the preferred parameterisation contains a parameter that has a transmission pattern concentrated along the vertical axis. This parameter can be fixed during the inversion which reduces the size of the model space. The review of several parameterisations shows that the vertical velocity, the Thomsen parameter δ, or the Thomsen parameter ε have a transmission pattern along the vertical axis depending on the parameterisation choice. The review of the reflection patterns of those selected parameterisations should be done in the elastic context. Indeed, when reflection data are also inverted, there are potential leakages of the shear parameter at intermediate angles when we carry out acoustic inversion. 相似文献
11.
由于构造运动等作用,TI介质对称轴往往沿空间任意方向分布,具有任意空间取向对称轴的TI（ATI）介质更符合实际地质情况.VTI介质与ATI介质的相速度在形式上具有一致性,VTI介质中地震波的相角对应ATI介质对称轴与地震波传播方向的夹角.本文基于Tsvankin的VTI介质精确相速度公式,利用TI介质对称轴和地震波传播方向上单位向量的数量积和向量积来计算ATI介质的精确相速度.根据弱各向异性假设,导出qP波和qSV波的近似相速度,分析了近似公式的误差,讨论总结了ATI介质qP波和qSV波的相速度特征.本文中的单位向量采用观测坐标系表示,通过相角关系,可以较为方便地由ATI介质近似相速度导出频散关系,然后借助傅里叶逆变换推导出时间-波数域qP波和qSV波解耦的波动方程.数值算例表明本文的波动方程是qP波和qSV波解耦的,波场计算结果稳定,未出现明显的数值频散,验证了本文方法的有效性. 相似文献
12.
Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI media). This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ε. The finite difference method is used to solve the equation. In addition, a perfectly matched layer (PML) absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium. 相似文献
13.
In an acoustic transversely isotropic medium, there are two waves that propagate. One is the P-wave and another one is the S-wave (also known as S-wave artefact). This paper is devoted to analyse the S-wave in two-dimensional acoustic transversely isotropic media with a tilted symmetry axis. We derive the S-wave slowness surface and traveltime function in a homogeneous acoustic transversely isotropic medium with a tilted symmetry axis. The S-wave traveltime approximations in acoustic transversely isotropic media with a tilted symmetry axis can be mapped from the counterparts for acoustic transversely isotropic media with a vertical symmetry axis. We consider a layered two-dimensional acoustic transversely isotropic medium with a tilted symmetry axis to analyse the S-wave moveout. We also illustrate the behaviour of the moveout for reflected S-wave and converted waves. 相似文献
14.
本文首先利用有限差分法分别对弹性和粘弹性VTI介质进行地震波传播数值模拟，并针对波场快照和波场记录特征，分析不同品质因子组合对波场能量衰减和频率吸收作用的影响.结果表明：对应于膨胀滞弹性形变的品质因子变化主要影响qP波的能量衰减；对应于剪切滞弹性形变的品质因子变化主要影响qSV波的能量衰减；对于qSH波，两个品质因子分别对应于垂直和水平方向的能量衰减；品质因子较小时，qSV波和qSH波的频率向低频方向移动，qP波频率变化不明显. 相似文献
15.
A method for determination of characteristics of quasi-Rayleigh (qR) wave in a transversely isotropic homogeneous half-space with inclined axis of symmetry is outlined. The solution is obtained as a superposition of qP, qSV and qSH waves, and surface wave velocity is determined from the boundary conditions at the free surface and at infinity, as in case of Rayleigh wave in an isotropic half-space. Though the theory is simple enough, a numerical procedure for calculation of surface wave velocity presents some difficulties. The difficulty is caused by necessity to calculate complex roots of a non-linear equation, which in turn contains functions determined as roots of non-linear equations with complex coefficients. Numerical analysis shows that roots of the equation corresponding to the boundary conditions do not exist in the whole domain of azimuths and inclinations of the symmetry axis. The domain of existence of qR wave depends on the ratio of the elastic parameters: for some strongly anisotropic models the wave cannot exist at all. For some angles of inclination qR-wave velocities deviate from those calculated on the basis of the perturbation method valid for weak anisotropy, though they have the same tendency of variation with azimuth. The phase of qR wave varies with depth unlike Rayleigh wave in an isotropic half-space. Unlike Rayleigh wave in an isotropic half-space, qR wave has three components - vertical, radial and transverse. Particle motion in horizontal plane is elliptic. Direction of the major axis of the ellipsis coincides with the direction of propagation only in azimuths 0° (180°) and 90° (270°). 相似文献
16.
Computation of complex-valued traveltimes provides an efficient approach to describe the seismic wave attenuation for applications like attenuation tomography, inverse Q filtering and Kirchhoff migration with absorption compensation. Attenuating acoustic transverse isotropy can be used to describe the directional variation of velocity and attenuation of P-waves in thin-bedding geological structures. We present an approximate method to solve the acoustic eikonal equation for an attenuating transversely isotropic medium with a vertical symmetry axis. We take into account two similar parameterizations of an attenuating vertical symmetry axis medium. The first parameterization uses the normal moveout velocity, whereas the second parameterization uses the horizontal velocity. For each parameterization, we combine perturbation theory and the Shanks transform in different ways to derive analytic solutions. Numerical examples show that the analytic solutions derived from the second parameterization yield better accuracy. The Shanks transform solution with respect to only the anellipticity parameter from the second parameterization is demonstrated numerically to be the most accurate among all the analytic solutions. 相似文献
17.
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. 相似文献
18.
The moveout approximations play an important role in seismic data processing. The standard hyperbolic moveout approximation is based on an elliptical background model with two velocities: vertical and normal moveout. We propose a new set of moveout approximations based on a perturbation series in terms of anellipticity parameters using the alternative elliptical background model defined by vertical and horizontal velocities. We start with a transversely isotropic medium with a vertical symmetry axis. Then, we extend this approach to a homogeneous orthorhombic medium. To define the perturbation coefficients for a new background, we solve the eikonal equation with horizontal velocities in transversely isotropic medium with a vertical symmetry axis and orthorhombic media. To stabilise the perturbation series and improve the accuracy, the Shanks transform is applied for all the cases. We select different parameterisations for both velocities and anellipticity parameters for an orthorhombic model. From the comparison in traveltime error, the new moveout approximations result in better accuracy comparing with the standard perturbation‐based methods and other approximations. 相似文献
19.
Anisotropy is often observed due to the thin layering or aligned micro‐structures, like small fractures. At the scale of cross‐well tomography, the anisotropic effects cannot be neglected. In this paper, we propose a method of full‐wave inversion for transversely isotropic media and we test its robustness against structured noisy data. Optimization inversion techniques based on a least‐square formalism are used. In this framework, analytical expressions of the misfit function gradient, based on the adjoint technique in the time domain, allow one to solve the inverse problem with a high number of parameters and for a completely heterogeneous medium. The wave propagation equation for transversely isotropic media with vertical symmetry axis is solved using the finite difference method on the cylindrical system of coordinates. This system allows one to model the 3D propagation in a 2D medium with a revolution symmetry. In case of approximately horizontal layering, this approximation is sufficient. The full‐wave inversion method is applied to a crosswell synthetic 2‐component (radial and vertical) dataset generated using a 2D model with three different anisotropic regions. Complex noise has been added to these synthetic observed data. This noise is Gaussian and has the same amplitude f?k spectrum as the data. Part of the noise is localized as a coda of arrivals, the other part is not localized. Five parameter fields are estimated, (vertical) P‐wave velocity, (vertical) S‐wave velocity, volumetric mass and the Thomsen anisotropic parameters epsilon and delta. Horizontal exponential correlations have been used. The results show that the full‐wave inversion of cross‐well data is relatively robust for high‐level noise even for second‐order parameters such as Thomsen epsilon and delta anisotropic parameters. 相似文献
20.
In recent years, wave‐equation imaged data are often presented in common‐image angle‐domain gathers as a decomposition in the scattering angle at the reflector, which provide a natural access to analysing migration velocities and amplitudes. In the case of anisotropic media, the importance of angle gathers is enhanced by the need to properly estimate multiple anisotropic parameters for a proper representation of the medium. We extract angle gathers for each downward‐continuation step from converting offset‐frequency planes into angle‐frequency planes simultaneously with applying the imaging condition in a transversely isotropic with a vertical symmetry axis (VTI) medium. The analytic equations, though cumbersome, are exact within the framework of the acoustic approximation. They are also easily programmable and show that angle gather mapping in the case of anisotropic media differs from its isotropic counterpart, with the difference depending mainly on the strength of anisotropy. Synthetic examples demonstrate the importance of including anisotropy in the angle gather generation as mapping of the energy is negatively altered otherwise. In the case of a titled axis of symmetry (TTI), the same VTI formulation is applicable but requires a rotation of the wavenumbers. 相似文献