共查询到20条相似文献，搜索用时 62 毫秒
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针对地震偏移算法中单程波算子的特征函数近似，采用最优可分表示法将该特征函数展开为空间变量(g)和水平波数(k)的可分表达式，以此可分近似表达式为基础，运用正反Fourier变换重新构造单程波算子. 为了克服特征函数最优可分近似计算在奇点及其领域产生的数值振荡，引入等价黏性技巧以增强算法的数值计算稳定性，并采用分频最优可分及对空间变量(g)线性插值的方法，不仅提高了计算精度，也节约计算机时. 文中具体研究了单程波算子的脉冲响应和二维叠前深度偏移. 结果表明，在不甚大步长情况下，本文构造的算子具有适应横向强变速的能力，运用Marmousi模型验证了本文方法适合复杂构造的成像. 相似文献
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基于扰动理论的混合域波动方程波场外推算子,具有一定介质横向速度变化适应能力,是反射地震学中研究较多的成像方法。此类波场外推算子沿深度层进行波场外推,都存在参考速度选择问题。单参考速度波场外推算子,适应地下介质弱横向变速,而多参考速度波场外推算子可以提高横向变速的适应能力和成像精度,但要以大量计算为代价。本文提出的自适应多参考速度选择策略,根据外推层地质构造的复杂度和给定的速度门槛值自动选择参考速度个数,利用该策略构造混合域SSF、FFD、WXFD和GSP等多参考速度波场外推成像算法。盐丘模型理论数据测试结果表明,自适应多参考速度波场外推算法具有强横向变速适应能力和较高成像精度。 相似文献
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Xu Zhaotao Wang Huazhong 《应用地球物理》2006,3(4):226-233
Based on perturbation theory, the wave equation extrapolation operator with mixed domains has the ability to deal with lateral velocity variations. It is the image method that has undergone much research in seismology. All extrapolation operators face the problem of choosing the reference velocity due to continuation in depth. The wavefield extrapolation operator with a single reference velocity is suitable for media with weak lateral variation. The multi-reference velocity extrapolation operator can cope with severe lateral velocity variations and improve image accuracy. However, the calculation cost is large. We present a self-adaptive approach to automatically determine the number of selected reference velocities according to the complexity of structure and the given velocity threshold value. The approach can be used to construct the SSF, FFD, WXFD, and GSP multi-reference velocity wavefield extrapolation image algorithms. The result of a salt-dome model data test demonstrates that the self-adoptive multi-reference wavefield extrapolation algorithm has the ability to deal with severe lateral velocity variations and can also be used for structure edge detection. The method is flexible and computationally cost-effective. 相似文献
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波场延拓是地震偏移成像的基础. 快速进行目标区波场延拓对石油勘探中急需发展的深部地震勘探和无组合海量地震数据的成像有重要意义. 在目标区成像中，目前已有的波场延拓方法，包括基于走时计算的Dix方法和射线追踪方法，以及基于小步长波场递推的方法，在适应复杂介质、计算精度和计算效率的某一方面还不能完全满足实际需要. 本文提出一种基于“算子相位”李代数积分的快速计算延拓算子的方法，称为大步长波场延拓方法. 在该方法中，指向目标区的波场延拓算子象征的复相位被表示成波数的线性组合. 线性组合的系数是层速度函数及其导数的深度积分，计算和存储较为方便. 波场延拓算子通过相移算子加校正的方法，利用快速Fourier变换在空间域和波数域予以实现. 利用动力学等价关系导出了便于计算的表达式. 本文比较了算子主象征函数用一步法展开和用两步法展开的精度，从而说明大步长方法的精度要高于递推方法. 在横向和纵向线性变化介质中，将大步长方法的脉冲响应与递推法做了比较，说明大步长延拓算子的走时精度主要取决于相移因子中的横向变速校正项；且在各种近似下，大步长算子发生的频散都非常小. 相似文献
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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
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O. HOLBERG 《Geophysical Prospecting》1988,36(2):99-114
Numerical wavefield extrapolation represents the backbone of any algorithm for depth migration pre- or post-stack. For such depth imaging techniques to yield reliable and interpretable results, the underlying wavefield extrapolation algorithm must propagate the waves through inhomogeneous media with a minimum of numerically induced distortion, over a range of frequencies and angles of propagation. A review of finite-difference (FD) approximations to the acoustic one-way wave equation in the space-frequency domain is presented. A straightforward generalization of the conventional FD formulation leads to an algorithm where the wavefield is continued downwards with space-variant symmetric convolutional operators. The operators can be precomputed and made accessible in tables such that the ratio between the temporal frequency and the local velocity is used to determine the correct operator at each grid point during the downward continuation. Convolutional operators are designed to fit the desired dispersion relation over a range of frequencies and angles of propagation such that the resulting numerical distortion is minimized. The optimization is constrained to ensure that evanescent energy and waves propagating at angles higher than the maximum design angle are attenuated in each extrapolation step. The resulting operators may be viewed as optimally truncated and bandlimited spatial versions of the familiar phase shift operator. They are unconditionally stable and can be applied explicitly. This results in a simple wave propagation algorithm, eminently suited for implementation on pipelined computers and on large parallel computing systems. 相似文献
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双程波方程逆时深度偏移是复杂介质高精度成像的有效技术,但其结果中通常包含成像方法引起的噪音和假象,一般的滤波方法会破坏成像剖面上的振幅,其中的假象也会给后续地质解释带来困扰.将波场进行方向分解然后实现入射波与反射波的相关成像能够有效地消除这类成像噪音,并提高逆时偏移成像质量.波传播方向的分解通常在频率波数域实现,它会占用大量的存储和计算资源,不便于在沿时间外推的逆时深度偏移中应用.本文提出解析时间波场外推方法,可以在时间外推的每个时间片上实现波传播方向的显式分解,逆时深度偏移中利用分解后的炮检波场进行对应的相关运算,实现成像噪音和成像信号的分离.在模型和实际数据上的测试表明,相比于常规互相关逆时偏移成像结果,本文方法能够有效地消除低频成像噪音和特殊地质构造导致的成像假象. 相似文献
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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
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G. BLACQUIRE H. W. J. DEBEYE C. P. A. WAPENAAR A. J. BERKHOUT 《Geophysical Prospecting》1989,37(8):925-958
An efficient full 3D wavefield extrapolation technique is presented. The method can be used for any type of subsurface structure and the degree of accuracy and dip-angle performance are user-defined. The extrapolation is performed in the space-frequency domain as a space-dependent spatial convolution with recursive Kirchhoff extrapolation operators. To get a high level of efficiency the operators are optimized such that they have the smallest possible size for a specified accuracy and dip-angle performance. As both accuracy and maximum dip-angle are input parameters for the operator calculation, the method offers the possibility of a trade-off between these quantities and efficiency. The operators are calculated in advance and stored in a table for a range of wavenumbers. Once they have been calculated they can be used many times. At the basis of the operator design is the well-known phase-shift operator. Although this operator is exact for homogeneous media only, it is assumed that it may be applied locally in case of inhomogeneities. Lateral velocity variations can then be handled by choosing the extrapolation operator according to the local value of the velocity. Optionally the operators can be designed such that they act as spatially variant high-cut filters. This means that the evanescent field can be suppressed in one pass with the extrapolation. The extrapolation method can be used both in prestack and post-stack applications. In this paper we use it in zero-offset migration. Tests on 2D and 3D synthetic and 2D real data show the excellent quality of the method. The full 3D result is much better then the result of two-pass migration, which has been applied to the same data. The implementation yields a code that is fully vectorizable, which makes the method very suitable for vector computers. 相似文献
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在频率波数域和频率空间域实现了一种基于拟线性Born近似的叠前深度偏移方法，并在2-D空间进行了Marmousi模型炮集数据的处理.通过与Split-StepFourier、Phase-Screen和稳定的Born近似叠前深度偏移等方法比较，认为基于拟线性Born近似的叠前深度偏移方法不仅在效果上要优于前三者，而且还能更好地处理速度横向变化.在散射波场计算中，使用了一个更稳定的散射波场计算公式，扩大了拟线性Born近似的应用范围，使基于拟线性Born近似的叠前深度偏移方法能够适应更强的横向速度变化. 相似文献
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叠前深度偏移是复杂构造成像的重要手段.本文基于波场分裂理论,首先给出了波场延拓的一般方程,即一个上下行波的耦合方程组.通常所用的波场延拓方程就是该耦合方程组的特例.根据平方根算子的近似,推导了一种新的高精度混合法偏移方法,用分裂法即可进行计算.通过对一个横向强烈变速模型的叠后偏移及Marmousi复杂构造模型的叠前偏移计算,说明了方法的有效性,精度较高.采用MPI并行编程实现并行计算,提高了计算效率.该方法可用于对横向强烈变速的复杂构造的精确成像. 相似文献
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Tariq Alkhalifah 《Geophysical Prospecting》2011,59(4):627-634
The wavefield dependence on a virtual shift in the source location can provide information helpful in velocity estimation and interpolation. However, the second‐order partial differential equation (PDE) that relates changes in the wavefield form (or shape) to lateral perturbations in the source location depends explicitly on lateral derivatives of the velocity field. For velocity models that include lateral velocity discontinuities this is problematic as such derivatives in their classical definition do not exist. As a result, I derive perturbation partial differential wave equations that are independent of direct velocity derivatives and thus, provide possibilities for wavefield shape extrapolation in complex media. These PDEs have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The solutions of the perturbation equations provide the coefficients of a Taylor's series type expansion for the wavefield. The new formulas introduce changes to the background wavefield only in the presence of lateral velocity variation or in general terms velocity variations in the perturbation direction. The accuracy of the representation, as demonstrated on the Marmousi model, is generally good. 相似文献
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叠前深度偏移理论及方法一直是地震数据成像中研究的热点问题.业界对单程波叠前深度偏移方法和逆时深度偏移开展了深入的研究,但对双程波方程波场深度延拓理论及成像方法的研究还鲜有报道.本文以地表记录的波场值为基础,利用单程波传播算子估计波场对深度的偏导数,为在深度域求解双程波方程提供充分的边界条件,并提出利用矩阵分解理论实现双程波方程的波场深度外推.通过对强速度变化介质中传播波场的计算,与传统的单程波偏移方法相比,本文提出的偏移方法计算的波场与常规有限差分技术计算的波场相一致,证明了本方法计算的准确性.通过对SEAM模型的成像,在相同的成像参数下,与传统的单程波偏移算法和逆时深度偏移算法方法相比,本文提出的偏移方法能够提供更少的虚假成像和更清晰的成像结果.本文所提偏移算法具有深度偏移和双程波偏移的双重特色,推动和发展了双程波叠前深度偏移的理论和实践. 相似文献
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本文将常规双平方根（DSR）单程波动方程从深度域变换到双程垂直走时（τ）域，由此推导出可从数学上实现“沉降观测”的单程波DSR传播算子. 其递归波场延拓算法包含波数域针对常速背景的相移处理和空间域针对横向速度扰动的相位校正，可以应对上覆地层速度横向变化对构造成像的影响. 结合零炮检距、零时间成像条件，提出了在τ域进行波场延拓与成像的DSR方程叠前偏移新方法. 为了克服其全三维偏移算法在实际应用中可能面临的困难，本文采用稳相近似，在crossline常炮检距偏移理论基础上推导了实用的共方位角叠前τ偏移方法. 数值试验表明，DSR方程叠前τ偏移在强横向非均匀介质中的成像精度与分辨率优于传统的时间域成像技术. 相似文献
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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
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Extrapolating wavefields and imaging at each depth during three‐dimensional recursive wave‐equation migration is a time‐consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier‐transform‐related wavefield extrapolation method. First, we formulate a three‐dimensional first‐order separation‐of‐variables screen propagator for large‐step wavefield extrapolation, which allows for wide‐angle propagations in highly contrasting media. This propagator significantly improves the performance of the split‐step Fourier method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform in each thick slab. We then extend the two‐dimensional Kirchhoff and Born–Kirchhoff local wavefield interpolators to three‐dimensional cases for each slab. The three‐dimensional Kirchhoff interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, whereas the three‐dimensional Born–Kirchhoff interpolator is derived from the Lippmann–Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the three‐dimensional salt model of the Society of Exploration Geophysicists/European Association of Geoscientists demonstrate that three‐dimensional first‐order separation‐of‐variables screen propagator Born–Kirchhoff depth migration using thick‐slab wavefield extrapolation plus thin‐slab interpolation tolerates a considerable depth‐step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed three‐dimensional interpolators are presented with one‐way Fourier extrapolation methods, they can be extended for applications to general migration methods. 相似文献
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波动方程宽角抛物逼近得到的通常是非常系数的单程波传播算子，其系数是速度横向变化的函数，因此需要利用有限差分(FD)进行数值实施. 通过对Lippmann Schwinger单程波动积分方程的退化核逼近,本文研究了一类宽角退化算子的偏移成像. 这种退化偏移算子只用快速Fourier变换进行波场延拓，将常规的Fourier分裂步地震偏移方法(SSF)推广适应强速度横向变化介质和大角度传播波场. 退化的Fourier偏移算子通过在两个分裂步项之间作波数域线性插值来实现波场延拓，每延拓一层需要比常规的SSF地震偏移方法多一次快速Fourier变换(FFT). 通过SEG/EAGE盐丘模型和实际地震资料的应用表明，退化Fourier偏移算子能很好地对盐下的陡倾角断层和实际地震剖面上的复杂小断块和大断裂地质构造成像. 相似文献