VTI介质中准P波方程叠前逆时深度偏移

根据具有垂直对称轴的横向各向同性（VTI）介质中的一阶准P波方程,导出了该方程在交错网格中逆时延拓的高阶有限差分格式,给出了其稳定性条件,采用完全匹配层吸收边界条件解决边界反射问题,分别应用下行波最大能量法和归一化互相关成像条件, 实现了VTI介质中准P波方程的叠前逆时深度偏移．各向异性Marmousi模型的试算结果表明,VTI介质准P波方程叠前逆时深度偏移算法不受地下构造倾角和介质横向速度变化的限制,对复杂模型具有良好的成像能力;应用归一化互相关成像条件能得到更好的成像效果．对比该模型的各向异性和各向同性逆时偏移剖面表明,在各向异性地区采集的纵波数据用各向异性偏移算法理论上能得到更好的成像结果．      

TTI介质qP波逆时偏移中伪横波噪声压制方法

在对地下复杂构造介质,特别是盐丘侧翼及岩下区域进行成像时,相对于传统的各向同性逆时偏移和VTI逆时偏移,具有倾斜对称轴的TTI逆时偏移成像效果最优.不仅反射同相轴更加的连续,而且能量得到了更好的聚焦.传统的各向异性介质全弹性波RTM的计算量大且计算效率低.由于目前仍以纵波勘探为主,因此TTI逆时偏移qP波波动方程的选取显得尤为重要.为了提高计算效率,采用将沿着对称轴方向的横波速度设为零的方法,简化得到qP波波动方程.然而,这样会引入一种严重影响成像效果的低速度、低振幅的qSV波人为干扰.本文建立了qP波方程的完全匹配层控制方程,而后借助于辅助波场采用一种高效的压制伪横波噪声传播的方法,通过模型测试验证了该方法的有效性.     

多分量联合逆时偏移最佳匹配层吸收边界

有限空间内的波动方程逆时偏移需要利用有效的边界处理技术用以消除人工截断对偏移结果产生的影响。本文以横向各向同性介质弹性波速度-应力方程为基础,依据传统分裂式最佳匹配层（Perfect Matched Layer,PML）吸收边界技术的思想,推导了应用于逆时偏移的完全匹配层波动方程,并给出了其高阶交错网格有限差分格式。针对由边界处向计算区域内传播的＂反射波＂,以及地震记录排列两端地震同相轴突变对计算区域的影响这两方面问题,本文给出了逆时偏移中吸收层的布设方式。模型和实际资料的弹性波叠前多分量联合逆时深度偏移结果表明本文的边界处理方法取得了较好的吸收效果,获得了好的联合偏移成像结果。     

非零偏VSP弹性波叠前逆时深度偏移技术探讨

非零偏VSP地震资料是一种多分量资料,处理非零偏VSP资料,弹性波叠前逆时深度偏移技术无疑是最适合的处理技术.本文从二维各向同性介质的弹性波波动方程出发,研究了对非零偏VSP资料进行叠前逆时深度偏移的偏移算法,讨论了逆时传播过程中的边值问题和数值频散问题及其相应的解决方案;采用求解程函方程计算得到地下各点的地震波初至时间作为成像时间,实现了非零偏VSP资料的叠前逆时深度偏移.最后进行了模型试算和非零偏VSP地震资料的试处理,结果表明该方法不受地层倾角限制,较适用于高陡构造地区或介质横向速度变化较大地区的非零偏VSP地震资料处理.     

叠前逆时深度偏移中的激发时间成像条件

与其他偏移方法相比,逆时偏移基于精确的波动方程而不是对其近似,用时间外推来代替深度外推.因此,它具有良好的精度,不受地下构造倾角和介质横向速度变化的限制.激发时间成像条件的求取是叠前逆时偏移的难点之一,本文采用求解程函方程的方法得到地下各点的初至波走时,以此作为叠前逆时偏移的成像条件.基于任意矩形网格和局部平面波前近似的有限差分初至波走时计算方法精度较高并适用于强纵横向变速的复杂介质.试算结果表明,在复杂介质模型中利用叠前逆时深度偏移收到了很好的成像效果.     

Imaging of offset VSP data acquired in complex areas with modified reverse-time migration

A modified reverse-time migration algorithm for offset vertical seismic profiling data is proposed. This algorithm performs depth imaging of target areas in the borehole vicinity without taking into account the overburden. Originally recorded seismograms are used; reliable results can be obtained using only the velocity profile obtained along the well. The downgoing wavefield emitted from a surface source is approximated in the target area using the transmitted P-wave, recorded by the receivers deployed in the well. This is achieved through a reverse-time extrapolation of the direct transmitted P-wave into the target area after its separation in offset vertical seismic profiling seismograms generated using a finite-difference scheme for the solution of the scalar wave equation.
The proposed approach produces 'kinematically' reliable images from reflected PP- and PS-waves and, furthermore, can be applied as a salt proximity tool for salt body flank imaging based on the transmitted PS-waves. Our experiments on synthetic data demonstrate that the modified reverse-time migration provides reliable depth images based on offset vertical seismic profiling data even if only the velocity profile obtained along the borehole is used.     

横向各向同性介质拟声波方程及其在逆时偏移中的应用

地下岩石的速度各向异性影响地震波的传播与成像.横向各向同性(TI)介质为最普遍的等效各向异性模型.引入TI介质拟声波方程可以避免复杂的弹性波方程求解以及各向异性介质波场分离,以满足对纵波成像的实际需要.本文从垂直横向各向同性(VTI)介质弹性波方程出发,推导出正应力表达的拟声波方程以及相应的纵波分量的表达式,进而分析从频散关系得到的拟声波方程的物理意义,而后将拟声波方程扩展到更一般的倾斜横向各向同性(TTI)介质中.波前快照与群速度平面的对比验证了拟声波方程可以很好地近似描述qP波的运动学特征.在此基础上,将拟声波方程应用在逆时偏移中并与其特例声波近似方程进行对比,讨论了计算效率、稳定性等实际问题.数值试验表明VTI介质情况下采用声波近似方程可以提高计算效率,而TTI介质qP-qSV波方程则在效率相当的情况下可以保证稳定性.SEG/HESS模型和逆冲模型逆时偏移试验验证了本文TI介质拟声波方程的实用性.     

基于三角网格的有限差分法叠后逆时偏移

Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular grids maintains the simplicity of the difference method and the precision of the finite element method. It can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. We apply a finite difference method based on triangular grids for post-stack reverse-time migration for the first time. Tests on model data verify that the combination of the two methods can achieve near-perfect results in application.     

Layer-stripping reverse-time migration1

We present a layer-stripping method of migration for irregularly layered media in which first-order velocity discontinuities separate regions of constant or smoothly varying velocity. We use the reverse-time method to migrate seismic data layer by layer, from the surface downwards. As part of the migration of a given layer, the bottom boundary of the layer is defined based on power in the migrated signal, and a seismic section is collected along it. This new section serves as the boundary condition for migration in the next layer. This procedure is repeated for each layer, with the final image formed from the individual layer images. Layer-stripping migration consists of three steps: (1) layer definition, (2) wavefield extrapolation and imaging, and (3) boundary determination. The migration scheme when used with reverse-time extrapolation is similar to datuming with an imaging condition. The reverse-time method uses an explicit fourth-order time, tenth-order space, finite-difference approximation to the scalar wave equation. The advantages of layer-stripping reverse-time migration are: (1) it preserves the benefits of the reverse-time method by handling strong velocity contrasts between layers and steeply dipping structures; (2) it reduces computer memory and saves computation time in high-velocity layers, and (3) it allows interpretational control of the image. Post-stack layer-stripping reverse-time migration is illustrated with a synthetic CMP data example. Prestack migration is illustrated with a synthetic data set and with a marine seismic reflection profile across the Santa Maria Basin and the Hosgri Fault in central California.     

ON REVERSE-TIME MIGRATION*

Migration is a process whereby events in ‘image space’ are mapped into their correct positions in ‘object space’. The wave equations associated with this mapping may be defined and solved numerically either in image space or in object space. In the former the CMP section, which represents the initial conditions, is extrapolated toward increasing depths, and the migrated data are recovered at zero time. In the latter, the wave-field extrapolation takes place in the coordinate frame of the depth section, and the CMP data serve as boundary conditions at the surface. Computations begin at the last sample of the record section and continue ‘reverse time’ until time zero. This paper describes a reverse-time migration (RTM) method and compares its performance with that of an image-space method based on the idea of phase shift plus interpolation (PSPI). Synthetic zero-offset sections serve as examples for migration experiments with the RTM and PSPI methods. It is shown that the RTM approach to migration is rather expensive, but its robustness and accuracy are difficult to surpass.     

两种类型共炮点域相关型叠前深度偏移方法分析

研究不同偏移方法的成像机理是实现复杂构造高精度成像的前提,研究了两类共炮点域的相关型叠前深度偏移成像方法：基于单程波动方程的叠前深度成像方法和基于双程波动方程的叠前深度成像方法,同时对比了它们在计算效率、数据存储量、成像精度、成像机理、速度敏感性等方面的差异及其共性。以复杂构造模型为例,采用了傅里叶有限差分法（FFD）和逆时成像法（RTM）,这两种方法实现了121个共炮点道集的叠前深度偏移成像处理。计算结果表明,当速度准确时,两种深度域波动方程成像方法均可以恢复出各个地质反射界面,其中逆时偏移对陡倾角成像效果显著,当速度存在百分比误差和随机扰动情况时,逆时成像结果要差于单程波方法,因此,逆时偏移方法对速度的敏感性较大,且低频噪声较为严重。     

等价各向异性介质一阶拟声波 方程正演模拟及其效率分析

为克服各向异性弹性波动方程正演模拟的局限,本文研究了各向异性介质拟声波方程的交错网格有限差分数值解法.首先,从VTI介质胡克定律和qP-qSV波频散关系两种思路出发,通过声假设近似,给出了两种不同形式的VTI介质一阶拟声波方程,并通过引入波场的伪速度分量,推导了一种新的VTI介质一阶应力-速度方程,并通过旋转坐标系将其推广到TTI介质中;其次,构造了一阶拟声波方程的交错网格高阶有限差分格式,并推导了相应的PML边界条件;最后,对本文方法中固有的qSV人为干扰波的产生机制和压制方法进行了简单讨论.数值结果表明:3种一阶拟声波方程在运动学和动力学上是等价的,相对于各向异性弹性波正演模拟,其节省了内存,提高了计算效率;各向异性因素会影响反射波旅行时和振幅等波场特征,在后续的处理、反演和解释中不可忽略;VTI介质HESS模型的逆时偏移结果也验证了本文方法的合理性.      

波动方程有限差分法叠前深度偏移

从地震叠前反射椭圆方程出发,本文导出了基于波动理论的共偏移距地震剖面叠前偏移方程,然后对此方程进行参考速度场中的浮动坐标变换,获得了叠前深度偏移方程．为了解决叠前衍射方程中含有对深度的二阶导数引起波场延拓成像的不适定问题,文中采用低阶偏微分方程组近似描述全上行波的办法,得到了衍射方程的高阶近似方程,并给出了计算衍射方程和折射方程稳定的差分格式,最后用此方法编制的程序对某一碳酸岩地区的地震资料进行了试处理,效果良好．     

井巷工程反射波超前探测逆时偏移成像

探讨了井巷隧道工程反射波法超前地质预报成像问题.从一阶速度－应力弹性波方程出发,推导了二维各向同性介质情况下弹性波逆时传播的高阶差分格式,实现了弹性波在数值空间中的逆时延拓.构建反射波法隧道超前探测中的断层、软弱夹层等介质模型,以反射波探测的正演记录作为初始条件,并从程函方程出发,采用逆时差分格式求取介质模型网格空间中各点的直达波旅行时作为弹性波逆时偏移的成像条件,实现多波多分量资料的逆时偏移.偏移结果表明,逆时偏移能够使隧道壁接收到的波场准确归位,提高隧道反射波超前探测的资料处理的精度.     

Fracture identification based on remote detection acoustic reflection logging

Fracture identification is important for the evaluation of carbonate reservoirs. However, conventional logging equipment has small depth of investigation and cannot detect rock fractures more than three meters away from the borehole. Remote acoustic logging uses phase-controlled array-transmitting and long sound probes that increase the depth of investigation. The interpretation of logging data with respect to fractures is typically guided by practical experience rather than theory and is often ambiguous. We use remote acoustic reflection logging data and high-order finite-difference approximations in the forward modeling and prestack reverse-time migration to image fractures. First, we perform forward modeling of the fracture responses as a function of the fracture–borehole wall distance, aperture, and dip angle. Second, we extract the energy intensity within the imaging area to determine whether the fracture can be identified as the formation velocity is varied. Finally, we evaluate the effect of the fracture–borehole distance, fracture aperture, and dip angle on fracture identification.     

基于吸收衰减补偿的多分量高斯束逆时偏移

高斯束逆时偏移结合了射线类偏移的高计算效率和波动方程逆时偏移的高精度,能很好地处理焦散点、大倾角成像问题,并且具有面向目标成像的能力.多分量地震资料的偏移技术可以对地下复杂构造进行更准确的成像,由于实际地下介质具有黏滞性,研究黏弹性叠前逆时偏移具有一定的现实意义.本文采用高斯束逆时偏移方法对多分量地震数据进行吸收衰减补偿,首先分别给出纵波和转换波共炮域高斯束叠前逆时偏移方法原理,在此基础上推导补偿吸收衰减的表达式,校正Q引起的振幅衰减和相位畸变,实现基于吸收衰减补偿的多分量高斯束叠前逆时偏移.数值模型的测试结果显示,在考虑地下介质的黏滞性时,本文方法具有更高的成像分辨率.     

Viscoacoustic least-squares reverse-time migration of different-order free-surface multiples

Multiples have longer propagation paths and smaller reflection angles than primaries for the same source–receiver combination, so they cover a larger illumination area. Therefore, multiples can be used to image shadow zones of primaries. Least-squares reverse-time migration of multiples can produce high-quality images with fewer artefacts, high resolution and balanced amplitudes. However, viscoelasticity exists widely in the earth, especially in the deep-sea environment, and the influence of Q attenuation on multiples is much more serious than primaries due to multiples have longer paths. To compensate for Q attenuation of multiples, Q-compensated least-squares reverse-time migration of different-order multiples is proposed by deriving viscoacoustic Born modelling operators, adjoint operators and demigration operators for different-order multiples. Based on inversion theory, this method compensates for Q attenuation along all the propagation paths of multiples. Examples of a simple four-layer model, a modified attenuating Sigsbee2B model and a field data set suggest that the proposed method can produce better imaging results than Q-compensated least-squares reverse-time migration of primaries and regular least-squares reverse-time migration of multiples.     

弹性介质中瑞雷面波有限差分法正演模拟

为研究瑞雷面波的形成机理及传播规律，促进瑞雷面波资料处理方法的发展，本文根据弹性波方程，采用交错网格有限差分数值求解算法，对浅层各向同性弹性介质进行了包括瑞雷面波和体波在内的全波场模拟. 提出了变系数吸收边界条件并将之应用于正演模拟，使边界条件的处理简单而高效，同时给出了角点的处理方法. 对工程勘察中常见的连续和层状介质模型进行了模拟，获得了更加接近实际情况的地震记录. 结合模拟记录，探讨了瑞雷面波的形成条件，同时讨论了震源埋深对面波能量的影响.     

Modeling and RTM for arbitrary-order pure acoustic wave equation in VTI media using normalized pseudo-analytical method

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.