利用矩阵分解理论的双程波方程叠前深度偏移方法

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.     

三维VSP数据高效偏移成像的超道集方法

当前的三维VSP地震数据偏移成像实现都是在共炮点道集或共检波点道集中逐个道集循环进行的,计算效率相对较低.根据三维VSP观测系统中炮点和检波点布置的特殊性和地震波场满足线性叠加的特性,本文提出了一种三维VSP数据的高效偏移成像方法,即首先通过对三维VSP共接收点道集进行地震数据的广义合成得到一种超道集,然后在共接收点道集的波场深度外推过程中逐步应用多震源波场对超道集进行偏移成像,即利用一次波场深度外推循环完成对所有共检波点道集数据的偏移成像.通过三维VSP模型数据与实际地震数据的偏移成像试验验证了这种高效的超道集偏移成像方法可取得与常规共检波点道集相当的偏移成像效果,还具有极高的计算效率,其计算量与单个共检波点道集的偏移成像计算量相当.     

基于波场垂向和水平方向外推的高陡构造偏移

常规的单程波波动方程偏移成像方法对大角度的高陡构造偏移成像存在内在的限制.根据波动方程在各个空间方向的数学特性和高陡构造反射地震波的传播特征,通过把地震波分解为垂向的上下行波、水平方向的前后行波和左右行波,提出基于波场垂向外推和水平方向外推相结合的单程波波动方程高陡构造偏移成像方法,即用波场垂向外推的单程波波动方程偏移成像方法解决中低角度平缓构造的偏移成像,用波场水平方向外推的单程波波动方程偏移成像方法解决中高角度陡倾构造的偏移成像.这种基于波场垂向和水平方向外推相结合的高陡构造偏移成像方法是常规单程波波动方程叠前深度偏移成像方法的补充和改进,它相对基于全波方程的逆时偏移具有计算效率上的优势.     

Diffraction problems of 3D seismic imaging

Migration is essential to seismic imaging. It is carried out by backward extrapolation of the wavefield registered on the observation surface. The quality of images depends on the accuracy of the wavefield reconstruction at interior subsurface points. From the theory based on the exact solution of the scalar wave equation it is known that, for accurate wave extrapolation, data must be obtained from an infinite observation surface. Limiting of migration apertures, which is inevitable in practice, leads to artefacts in extrapolated fields. The distortion they cause in 2D and 3D imaging is different. In 2D migration, the artefacts known as truncation effects are much weaker than the signals being extrapolated and for this reason attract no special attention. In 3D migration, diffractions caused by an aperture edge are stronger and may create serious problems. For a circular aperture, their amplitudes are comparable to the amplitudes of the signals themselves. The study of aperture diffractions is intended to help in the search for ways of either suppressing them efficiently or deliberately utilizing them in order to improve imaging.
In optics, diffractions by an aperture play a constructive role in image making. This research shows that the same may take place in seismic imaging.     

基于时空域自适应高阶有限差分的声波叠前逆时偏移

叠前逆时偏移在理论上是现行偏移方法中最为精确的一种成像方法,其实现过程中的核心步骤之一是波动方程的波场延拓,而波场延拓的本质是求解波动方程,所以精确、快速地求解波动方程对逆时偏移至关重要.本文采用一种基于时空域频散关系的有限差分方法来求解声波方程,分析其频散和稳定性,实现波场数值模拟,并将分析和模拟结果与传统有限差分法进行对比.分析结果和模型数值模拟结果都表明时空域有限差分法模拟精度更高、稳定性更好.将时空域高阶有限差分法应用到叠前逆时偏移波场延拓的方程求解中,然后再利用归一化互相关成像条件成像,理论模型数据偏移处理获得了精度更高的成像.同时,在逆时偏移波场延拓的实现中,采用自适应变长度的空间差分算子求解空间导数的有限差分策略,在不影响数值模拟和成像精度的前提下,有效地提高了计算效率.     

基于起伏地形平化策略的弹性波逆时偏移成像方法

随着能源和资源勘查开采工作的深入,地形强烈起伏的盆山耦合地区的地震资料处理解释技术正日益成为山地地震勘探面临的重要挑战.逆时偏移方法作为精确的地震偏移成像方法之一,能对地下结构进行高精度成像.逆时偏移的核心是地震波场延拓,由于传统的地震波场延拓技术往往基于水平地表条件,相应的方法在直接处理强地形起伏条件下的地震资料时往往存在一定的精度损失.本文引入一种精度无损的处理起伏边界的模型参数化方法：基于贴体网格的地形"平化"策略发展了与地形有关的地震波波动方程数值模拟方法,采用零延迟归一化互相关成像条件实现了起伏地表条件下的弹性波场逆时偏移成像.对工业界的标准Marmousi模型和盐丘模型进行改造,获得了相应起伏地形条件下的复杂几何模型,开展了起伏地表下的地震偏移成像数值试验.结果表明基于贴体网格"平化"策略的逆时偏移成像方法具有较高的灵活性,可适应不同类型起伏地表采集的地震资料,显示出该方法在地震勘探领域的良好应用前景.     

大步长波场深度延拓的理论

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.     

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.     

Visco‐acoustic prestack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method

It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.     

Wavefield interpolation in 3D large‐step Fourier wavefield extrapolation

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.     

基于Gabor-Daubechies小波束叠前深度偏移的角度域共成像道集

传统炮检距域共像集（CIG）在复杂介质中因波传播的多路径而存在反射体位置不确定的问题. 角度域CIG由于克服了这一缺陷而逐步成为速度分析、AVA以及振幅保真偏移成像等研究的主要手段. 以波动理论为基础的地震偏移成像方法的发展为获得高质量的角度域CIG提供了可靠的实现途径. 其中,基于波场局域化分解和传播的小波束域波场延拓和偏移成像方法,因其波场分解基本函数和传播算子在空间和方向上的双重局域特性,而成为角度相关分析研究的有效工具. 本文在采用Gabor Daubechies框架分解的小波束叠前角度域偏移成像基础上,利用不同的叠加方法由局部角度域像矩阵得到了反射角域CIG（CRAIG）和倾角域CIG（CDAIG）. 以SEG EAGE二维盐体模型为例,通过对CRAIG和CDAIG的对比,探讨了这两种角度域CIG的特点及其在地震偏移成像中的潜在应用.     

Utilization of multiple scattering: the next big step forward in seismic imaging

Surface removal and internal multiple removal are explained by recursively separating the primary and multiple responses at each depth level with the aid of wavefield prediction error filtering. This causal removal process is referred to as “data linearization.” The linearized output (primaries only) is suitable for linear migration algorithms. Next, a summary is given on the migration of full wavefields (primaries + multiples) by using the concept of secondary sources in each subsurface gridpoint. These secondary sources are two‐way and contain the gridpoint reflection and the gridpoint transmission properties. In full wavefield migration, a local inversion process replaces the traditional linear imaging conditions. Finally, Marchenko redatuming is explained by iteratively separating the full wavefield response from above a new datum and the full wavefield response from below a new datum. The redatuming output is available for linear migration (Marchenko imaging) or, even better, for full wavefield migration. Linear migration, full wavefield migration, and Marchenko imaging are compared with each other. The principal conclusion of this essay is that multiples should not be removed, but they should be utilized, yielding two major advantages: (i) illumination is enhanced, particularly in the situation of low signal‐to‐noise primaries; and (ii) both the upper side and the lower side of reflectors are imaged. It is also concluded that multiple scattering algorithms are more transparent if they are formulated in a recursive depth manner. In addition to transparency, a recursive depth algorithm has the flexibility to enrich the imaging process by inserting prior geological knowledge or by removing numerical artefacts at each depth level. Finally, it is concluded that nonlinear migration algorithms must have a closed‐loop architecture to allow successful imaging of incomplete seismic data volumes (reality of field data).     

基于解析时间波场外推与波场分解的逆时偏移方法研究

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.     

基于Poynting矢量行波分离的最小二乘逆时偏移

因为在逆时偏移中基于双程波动方程构建震源波场和检波器波场,所以在波场延拓过程中地震波遇到波阻抗界面时,背向发育的反射波会与正常传播的波场互相关产生较强振幅的低频噪声.这一特点使得以逆时偏移为基础的最小二乘偏移方法在梯度计算时同样存在着低频噪声的干扰,从而导致反演收敛的速度减慢.考虑到计算量和存储成本的因素,本文借助Po...     

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.     

稳定的保幅高阶广义屏地震偏移成像方法研究

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.     

Cost-effective 3D one-pass depth migration1

A crucial point in the processing of 3D seismic data is the migration step, both because of its 3D nature and the computational cost involved. The efficiency and accuracy of 3D migration are determined by the wavefield extrapolation technique employed. Wavefield extrapolation based on second-order differential operators of variable-length is very efficient and accurate at the same time. Compared to migration based on the McClellan transform and operator splitting, the use of variable-length second-order differential operators offers significant advantages. The 3D migration operator has an almost perfect circular symmetry. No positioning errors in the 45° azimuth between the in-line and cross-line directions are evident. The method is, in practice, only limited by spatial aliasing and does not require expensive interpolation of data to reduce numerical artifacts. This reduces the computational cost of 3D one-pass depth migration by a large factor.     

DEPTH IMAGING OF OFFSET VERTICAL SEISMIC PROFILE DATA1

Depth migration consists of two different steps: wavefield extrapolation and imaging. The wave propagation is firmly founded on a mathematical frame-work, and is simulated by solving different types of wave equations, dependent on the physical model under investigation. In contrast, the imaging part of migration is usually based on ad hoc‘principles’, rather than on a physical model with an associated mathematical expression. The imaging is usually performed using the U/D concept of Claerbout (1971), which states that reflectors exist at points in the subsurface where the first arrival of the downgoing wave is time-coincident with the upgoing wave. Inversion can, as with migration, be divided into the two steps of wavefield extrapolation and imaging. In contrast to the imaging principle in migration, imaging in inversion follows from the mathematical formulation of the problem. The image with respect to the bulk modulus (or velocity) perturbations is proportional to the correlation between the time derivatives of a forward-propagated field and a backward-propagated residual field (Lailly 1984; Tarantola 1984). We assume a physical model in which the wave propagation is governed by the 2D acoustic wave equation. The wave equation is solved numerically using an efficient finite-difference scheme, making simulations in realistically sized models feasible. The two imaging concepts of migration and inversion are tested and compared in depth imaging from a synthetic offset vertical seismic profile section. In order to test the velocity sensitivity of the algorithms, two erroneous input velocity models are tested. We find that the algorithm founded on inverse theory is less sensitive to velocity errors than depth migration using the more ad hoc U/D imaging principle.