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1.
Double-square-root one-way wave equation prestack tau migration in heterogeneous media 总被引：1，自引：0，他引：1
In this paper, source‐receiver migration based on the double‐square‐root one‐way wave equation is modified to operate in the two‐way vertical traveltime (τ) domain. This tau migration method includes reasonable treatment for media with lateral inhomogeneity. It is implemented by recursive wavefield extrapolation with a frequency‐wavenumber domain phase shift in a constant background medium, followed by a phase correction in the frequency‐space domain, which accommodates moderate lateral velocity variations. More advanced τ‐domain double‐square‐root wave propagators have been conceptually discussed in this paper for migration in media with stronger lateral velocity variations. To address the problems that the full 3D double‐square‐root equation prestack tau migration could meet in practical applications, we present a method for downward continuing common‐azimuth data, which is based on a stationary‐phase approximation of the full 3D migration operator in the theoretical frame of prestack tau migration of cross‐line constant offset data. Migrations of synthetic data sets show that our tau migration approach has good performance in strong contrast media. The real data example demonstrates that common‐azimuth prestack tau migration has improved the delineation of the geological structures and stratigraphic configurations in a complex fault area. Prestack tau migration has some inherent robust characteristics usually associated with prestack time migration. It follows a velocity‐independent anti‐aliasing criterion that generally leads to reduction of the computation cost for typical vertical velocity variations. Moreover, this τ‐domain source‐receiver migration method has features that could be of help to speed up the convergence of the velocity estimation. 相似文献
2.
Tariq Alkhalifah 《Geophysical Prospecting》2014,62(5):1089-1099
Spectral methods provide artefact‐free and generally dispersion‐free wavefield extrapolation in anisotropic media. Their apparent weakness is in accessing the medium‐inhomogeneity information in an efficient manner. This is usually handled through a velocity‐weighted summation (interpolation) of representative constant‐velocity extrapolated wavefields, with the number of these extrapolations controlled by the effective rank of the original mixed‐domain operator or, more specifically, by the complexity of the velocity model. Conversely, with pseudo‐spectral methods, because only the space derivatives are handled in the wavenumber domain, we obtain relatively efficient access to the inhomogeneity in isotropic media, but we often resort to weak approximations to handle the anisotropy efficiently. Utilizing perturbation theory, I isolate the contribution of anisotropy to the wavefield extrapolation process. This allows us to factorize as much of the inhomogeneity in the anisotropic parameters as possible out of the spectral implementation, yielding effectively a pseudo‐spectral formulation. This is particularly true if the inhomogeneity of the dimensionless anisotropic parameters are mild compared with the velocity (i.e., factorized anisotropic media). I improve on the accuracy by using the Shanks transformation to incorporate a denominator in the expansion that predicts the higher‐order omitted terms; thus, we deal with fewer terms for a high level of accuracy. In fact, when we use this new separation‐based implementation, the anisotropy correction to the extrapolation can be applied separately as a residual operation, which provides a tool for anisotropic parameter sensitivity analysis. The accuracy of the approximation is high, as demonstrated in a complex tilted transversely isotropic model. 相似文献
3.
Wavefield extrapolation and prestack depth migration in anelastic inhomogeneous media 总被引：6，自引：0，他引：6
Wavefield depth extrapolation and prestack depth migration in complex anelastic media are studied. Kjartansson's frequency‐independent Q law is used to describe the absorption of seismic energy. The macromodel used is analogous to the macromodel used for current migration schemes except that an additional frequency‐independent Q macromodel needs to be provided. Absorption in the forward one‐way propagator is introduced by assuming a complex phase velocity, and the inverse one‐way propagator is obtained using the reciprocity theorem for one‐way wavefields in dissipative media. The stability of the inverse propagator is achieved by limiting the angle of propagation of wavefields. A table‐driven explicit operator scheme for imaging complex 2D anelastic media is presented. High‐accuracy, short convolution operators are designed by the weighted least‐squares method, and two kinds of imaging conditions are proposed. Numerical examples of depth extrapolation in laterally varying media, the migration of a spatial impulse with dispersion as well as shot record depth migration demonstrate the potential of the proposed explicit forward operator, the explicit inverse operator and the prestack depth migration scheme, respectively. 相似文献
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Wave-equation migration velocity analysis. I. Theory 总被引：2，自引：0，他引：2
We present a migration velocity analysis (MVA) method based on wavefield extrapolation. Similarly to conventional MVA, our method aims at iteratively improving the quality of the migrated image, as measured by the flatness of angle‐domain common‐image gathers (ADCIGs) over the aperture‐angle axis. However, instead of inverting the depth errors measured in ADCIGs using ray‐based tomography, we invert ‘image perturbations’ using a linearized wave‐equation operator. This operator relates perturbations of the migrated image to perturbations of the migration velocity. We use prestack Stolt residual migration to define the image perturbations that maximize the focusing and flatness of ADCIGs. Our linearized operator relates slowness perturbations to image perturbations, based on a truncation of the Born scattering series to the first‐order term. To avoid divergence of the inversion procedure when the velocity perturbations are too large for Born linearization of the wave equation, we do not invert directly the image perturbations obtained by residual migration, but a linearized version of the image perturbations. The linearized image perturbations are computed by a linearized prestack residual migration operator applied to the background image. We use numerical examples to illustrate how the backprojection of the linearized image perturbations, i.e. the gradient of our objective function, is well behaved, even in cases when backprojection of the original image perturbations would mislead the inversion and take it in the wrong direction. We demonstrate with simple synthetic examples that our method converges even when the initial velocity model is far from correct. In a companion paper, we illustrate the full potential of our method for estimating velocity anomalies under complex salt bodies. 相似文献
7.
以先进的波动理论为基础的波动方程保幅地震偏移成像是在给出正确位置的同时也给出真实振幅的一种特殊完善.作者从保幅单程波动方程的非稳态相移公式出发,基于反问题求解中常用的摄动理论,利用单平方根算子的渐进展开,从而推导出保幅叠前深度偏移方程的高阶广义屏形式;针对散射波场计算项对于横向变速介质的不稳定性,通过数学近似提出一个有效提高稳定性的策略,应用到波场递归外推过程中,从而得到一种稳定的保幅高阶广义屏叠前深度偏移算子.理论模型试算和实际资料处理表明,该方法不但可以更精确地使散射能量聚焦、归位,提高成像精度;而且可以输出正确反映地下反射系数的振幅信息,使AVO响应更加清晰,提高了AVO资料的分析精度. 相似文献
8.
Using both image and data domains to perform velocity inversion can help us resolve the long and short wavelength components of the velocity model, usually in that order. This translates to integrating migration velocity analysis into full waveform inversion. The migration velocity analysis part of the inversion often requires computing extended images, which is expensive when using conventional methods. As a result, we use pre‐stack wavefield (the double‐square‐root formulation) extrapolation, which includes the extended information (subsurface offsets) naturally, to make the process far more efficient and stable. The combination of the forward and adjoint pre‐stack wavefields provides us with update options that can be easily conditioned to improve convergence. We specifically use a modified differential semblance operator to split the extended image into a residual part for classic differential semblance operator updates and the image (Born) modelling part, which provides reflections for higher resolution information. In our implementation, we invert for the velocity and the image simultaneously through a dual objective function. Applications to synthetic examples demonstrate the features of the approach. 相似文献
9.
由所建立的三维qP波相速度表示式出发，导出并解析求解各向异性介质中的频散方程，得到三维各向异性介质中的相移算子，进而将以相移算子为基础的对称非平稳相移方法推广到各向异性介质，发展了一个三维各向异性介质的深度偏移方法. 文中使用的各向异性介质的速度模型与现行的各向异性构造的速度估计方法一致，将各向同性、弱各向异性及强各向异性统一在一个模型中. 所建立的各向异性介质对称非平稳相移波场延拓算子可以同时适应速度及各向异性参数横向变化；文中给出的算例虽然是针对二维VTI介质的，但所提出的算法同样适用于三维TI介质. 相似文献
10.
Source–receiver two‐way wave extrapolation for prestack exploding‐reflector modelling and migration 
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下载免费PDF全文 Most modern seismic imaging methods separate input data into parts (shot gathers). We develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield forward or backward in time. This approach has the potential for generating accurate images free of artiefacts associated with conventional approaches. We derive novel high‐order partial differential equations in the source–receiver time domain. The fourth‐order nature of the extrapolation in time leads to four solutions, two of which correspond to the incoming and outgoing P‐waves and reduce to the zero‐offset exploding‐reflector solutions when the source coincides with the receiver. A challenge for implementing two‐way time extrapolation is an essential singularity for horizontally travelling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral‐based extrapolation. Using spectral methods based on the low‐rank approximation of the propagation symbol, we extrapolate only the desired solutions in an accurate and efficient manner with reduced dispersion artiefacts. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach. 相似文献
11.
Václav Bucha 《Studia Geophysica et Geodaetica》2012,56(2):533-552
We use Kirchhoff prestack depth migration to calculate migrated sections in 3-D simple anisotropic homogeneous velocity models in order to demonstrate the impact of anisotropy on migrated images. The recorded wave field is generated in models composed of two homogeneous layers separated by one either non-inclined or inclined curved interface. The anisotropy in the upper layer is triclinic. We apply Kirchhoff prestack depth migration to velocity models with different types of anisotropy: a triclinic anisotropic medium, an isotropic medium, transversely isotropic media with a horizontal (HTI) and vertical (VTI) symmetry axis. We observe asymmetry in migration caused by triclinic anisotropy and we show the errors of the migrated interface caused by inaccurate velocity models used for migration. The study is limited to P-waves. 相似文献
12.
Modeling and RTM for arbitrary-order pure acoustic wave equation in VTI media using normalized pseudo-analytical method 下载免费PDF全文
下载免费PDF全文 The conventional pseudo-acoustic wave equations(PWEs) in vertical transversely isotropic(VTI)media may generate SV-wave artifacts and propagation instabilities when anisotropy parameters cannot satisfy the pseudo-acoustic assumption. One solution to these issues is to use pure acoustic anisotropic wave equations, which can produce stable and pure P-wave responses without any SVwave pollutions. The commonly used pure acoustic wave equations(PAWEs) in VTI media are mainly derived from the decoupled P-SV dispersion relation based on first-order Taylor-series expansion(TE), thus they will suffer from accuracy loss in strongly anisotropic media. In this paper, we adopt arbitrary-order TE to expand the square root term in Alkhalifah's accurate acoustic VTI dispersion relation and solve the corresponding PAWE using the normalized pseudoanalytical method(NPAM) based on optimized pseudodifferential operator. Our analysis of phase velocity errors indicates that the accuracy of our new expression is perfectly acceptable for majority anisotropy parameters. The effectiveness of our proposed scheme also can be demonstrated by several numerical examples and reverse-time migration(RTM) result. 相似文献
13.
虚拟偏移距偏移(POM)是一种新的转换波叠前时间偏移方法,是对等效偏移距偏移(EOM) 的一种改进,它与EOM方法映射方式上虽然不同, 但本质都是相同的,都是将原始输入道集映射成为共转换散射点道集。本文主要介绍了两种偏移方法的原理,通过理论模型来验证两种方法对模型参数的敏感性。在远偏移距情况下,为了能在速度分析中得到更精确的偏移速度,分别用小排列拟合的双曲线公式、三阶近似式、双平方根旅行时公式对映射后的POM道集做动校正,从而验证了三个公式的精度。最后用POM方法对复杂构造进行了叠前时间偏移。 相似文献
14.
We present a new depth‐imaging method for seismic data in heterogeneous anisotropic media. This recursive explicit method uses a non‐stationary extrapolation operator to allow lateral velocity variation, and it uses the relationship between phase angle and the spectral coordinates of seismic data to allow velocity variation with phase angle. A qualitative comparison of migration impulse responses suggests that, for an equivalent cost, the symmetric non‐stationary phase‐shift (SNPS) operator is superior to the phase‐shift plus interpolation (PSPI) operator, for very large depth intervals. To demonstrate the potential of the new method, seismic data from a physical model acquired over a transversely isotropic medium are imaged using a shot‐record migration based on the SNPS operator. 相似文献
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地震波传播算子的计算效率和精度是制约三维叠前深度偏移的关键因素. 广义屏传播算子(GSP, Generalized Screen Propagator)是一种在双域中实现的广角单程波传播算子. 这一方法略去了在非均匀体之间发生的交混回响,但它可以正确处理包括聚焦、衍射、折射和干涉在内的各种多次前向散射现象. 通过背景速度下的相移和扰动速度下的陡倾角校正,广义屏算子能够适应地层速度的强烈横向变化. 这种算子可以直接应用于炮集叠前偏移,通过将广义屏算子作用于双平方根方程,还可以获得一种高效率、高精度的炮检距域叠前深度偏移方法,用于二维共炮检距道集和三维共方位角道集的深度域成像. 本文首先简述了炮检距域广义屏传播算子的理论,进而讨论了共照射角成像(CAI, Common Angle Imaging)条件,由此给出各个不同照射角(炮检距射线参数)下的成像结果,进而得到共照射角像集. 由于照射角和炮检距的对应关系,共照射角像集又为偏移速度分析和AVO(振幅随炮检距变化)分析等提供了有力工具. 相似文献
16.
Conventional two‐way splitting Fourier finite‐difference migration for 3D complex media yields azimuthal anisotropy where an additional phase correction is needed with much increase of computational cost. We incorporate the alternating‐direction‐implicit plus interpolation scheme into the conventional Fourier finite‐difference method to reduce azimuthal anisotropy. This scheme retains the high‐order remnants ignored by the two‐way splitting in the form of a wavefield interpolation in the wavenumber domain. The wavefield interpolation for each step of downward extrapolation is implemented between the wavefields before and after the conventional Fourier finite‐difference extrapolation. As the Fourier finite‐difference migration is implemented in the space and wavenumber dual space, the Fourier transforms between space and wavenumber domain that were needed for the alternating‐direction‐implicit plus interpolation in frequency domain (FD) migration are saved in Fourier finite‐difference migration. Since the azimuth anisotropy in Fourier finite‐difference is much less than that in FD, the application of the alternating‐direction‐implicit plus interpolation scheme in Fourier finite‐difference migration is superior to that in FD migration in handling complex media with large velocity contrasts and steep dips. Impulse responses show that the presented method reduces the azimuthal anisotropy at almost no extra cost. 相似文献
17.
Wavefield computations using the ellipsoidally anisotropic extrapolation operator offer significant cost reduction compared to that for the orthorhombic case, especially when the symmetry planes are tilted and/or rotated. However, ellipsoidal anisotropy does not provide accurate wavefield representation or imaging for media of orthorhombic symmetry. Therefore, we propose the use of ‘effective ellipsoidally anisotropic’ models that correctly capture the kinematic behaviour of wavefields for tilted orthorhombic (TOR) media. We compute effective velocities for the ellipsoidally anisotropic medium using kinematic high-frequency representation of the TOR wavefield, obtained by solving the TOR eikonal equation. The effective model allows us to use the cheaper ellipsoidally anisotropic wave extrapolation operators. Although the effective models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The proposed methodology offers a much better cost versus accuracy trade-off for wavefield computations in TOR media, particularly for media of low to moderate anisotropic strength. Furthermore, the computed wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference based TOR wave extrapolation scheme. We demonstrate applicability and usefulness of our formulation through numerical tests on synthetic TOR models. 相似文献
18.
The offset‐midpoint travel‐time pyramid for P‐wave in 2D transversely isotropic media with a tilted symmetry axis 下载免费PDF全文
下载免费PDF全文 For pre‐stack phase‐shift migration in homogeneous isotropic media, the offset‐midpoint travel time is represented by the double‐square‐root equation. The travel time as a function of offset and midpoint resembles the shape of Cheops’ pyramid. This is also valid for transversely isotropic media with a vertical symmetry axis. In this study, we extend the offset‐midpoint travel‐time pyramid to the case of 2D transversely isotropic media with a tilted symmetry axis. The P‐wave analytical travel‐time pyramid is derived under the assumption of weak anelliptical property of the tilted transverse isotropy media. The travel‐time equation for the dip‐constrained transversely isotropic model is obtained from the depth‐domain travel‐time pyramid. The potential applications of the derived offset‐midpoint travel‐time equation include pre‐stack Kirchhoff migration, anisotropic parameter estimation, and travel‐time calculation in transversely isotropic media with a tilted symmetry axis. 相似文献
19.
从水平叠加成像、叠前时间偏移以及叠前深度偏移三个方面总结了多分量地震成像技术的发展现状.在水平叠加成像方面,分析了转换波与纵波在道集抽取方面的差异,总结了常用的转换点计算公式,着重对比了由炮检坐标映射地下的转换点以及由地表的网格节点映射地下的反射点两种共转换点道集抽取方式各自的优缺点以及应用化程度.概述了各向同性与各向异性叠前时间偏移技术的基本原理,总结了多分量偏移技术发展以及配套软件的工业应用现状,并对最近发展的层匹配多分量偏移技术进行了介绍.最后,从射线理论以及波场延拓理论的角度总结了多分量叠前深度偏移的发展现状与存在的问题,介绍了标量偏移与矢量偏移的差异,并提出了深度域速度建模存在的问题. 相似文献
20.
提出了一套基于平面波分解的波动方程叠前地震数据深度偏移方法. 通过对共炮点道集和共偏移距道集地震数据的平面波分解，分别得到适用于单平方根波场外推方程和双平方根波场外推方程的共ps（炮点坐标平面波参数）平面波道集和共ph（偏移距坐标平面波参数）平面波道集. 在对共炮点道集和共偏移距道集地震数据的平面波分解时，不需要进行通常意义下的τ p变换计算. 通过对共ps平面波道集和共ph平面波道集的偏移效果对比，我们认为在速度弱横向变化介质中，两种平面波道集偏移方法的效果相当，但对于速度强横向变化介质，共ps平面波道集偏移方法的效果要优于共ph平面波道集偏移方法. 在计算效率方面，共ps平面波道集偏移方法与共ph平面波道集偏移方法基本相同. 相似文献