共偏移距道集平面波叠前时间偏移与反偏移

在Dubrulle提出的共偏移距道集频率波数域叠前时间偏移的基础上,提出了共偏移距道集频率波数域叠前时间偏移与反偏移一对共轭算子.讨论了该对算子的变孔径实现过程.并把该对共轭算子串连起来实现了叠前地震数据的规则化处理.指出最小二乘意义下的叠前地震数据规则化会得到更好的效果.v(z)介质模型和Marmousi模型的数值试验结果表明,方法理论正确、有效.     

用于AVO分析的振幅保真平面波叠前时间偏移

To support amplitude variation with offset （AVO） analysis in complex structure areas, we introduce an amplitude-preserving plane-wave prestack time migration approach based on the double-square-root wave equation in media with little lateral velocity variation. In its implementation, a data mapping algorithm is used to obtain offset-plane-wave data sets from the common-midpoint gathers followed by a non-recursive phase-shift solution with amplitude correction to generate common-image gathers in offset-ray-parameter domain and a structural image. Theoretical model tests and a real data example show that our prestack time migration approach is helpful for AVO analysis in complex geological environments.     

一种基于平面波静态编码的最小二乘逆时偏移方法

平面波偏移是一种面炮偏移方法, 相对于常规逐炮偏移, 其具有较高的计算效率.然而常规平面波偏移方法成像精度低, 且成像时会产生串扰噪音.为此, 本文在实现常规平面波偏移算法基础上, 引入反演思想实现了基于静态平面波编码的最小二乘偏移理论方法及处理流程, 在优化算法基础上对平层模型和复杂砂砾断块模型进行了成像测试并与其他成像策略进行对比.研究结果表明:基于时移编码的平面波最小二乘偏移能有效抑制低频成像噪音和串扰噪音, 补偿中深部成像能量, 是一种较为有效的保幅成像策略.     

叠前逆时偏移假象去除方法

叠前逆时偏移(RTM)求解全波动方程进行波场延拓,可以精确描述地震波的传播,在陡倾界面和复杂构造成像方面具有显著优势.但在实际应用中,互相关成像条件会带来低波数高振幅的假象.本文分析了假象产生的原因,实现并比较了Laplace滤波、坡印廷矢量法和上下、左右行波分解这三种假象压制方法,针对不同的计算平台分析其优劣.数值试验表明,坡印廷矢量法当波场简单时较为有效;而上下、左右行波分解法和Laplace滤波可以应对较复杂的波场.就去假象结果而言,使用波场分解成像条件并施加Laplace滤波效果最佳;然而就计算效率而言,CPU平台应用波场分解成像条件只增加少量的计算量,但GPU平台的实现则需要对数据的读写付出较大的代价.因此,综合考虑,对于CPU平台上述两种方案的组合为最佳策略;而基于GPU平台的逆时偏移采用Laplace滤波去噪仍然是目前最经济的选择.Marmousi模型和SEG/HESS VTI模型试验验证了上述结论.     

基于保辛算法的声波叠前逆时偏移

叠前逆时偏移是目前成像精度最高的地震偏移方法之一,其实现过程中的一个重要步骤是数值求解全波方程,所以快速有效求解全波方程的数值算法对逆时偏移至关重要. 四阶近似解析辛可分Runge-Kutta (NSPRK) 方法是近年发展的一种具有高效率、高精度的数值求解波动方程的保辛差分方法, 能在粗网格条件下有效压制数值频散, 从而提高计算效率, 节省计算机内存需求量. 本文利用四阶NSPRK方法构造的基本思想,发展了具有六阶空间精度的NSPRK方法,并对新的六阶NSPRK方法进行了详细的稳定性和数值频散分析,以及计算效率比较和波场模拟. 同时将该方法用于声波叠前逆时偏移中, 得到一种时间上保辛、空间具有六阶精度、低数值频散、可应用大步长进行波场延拓并能长时计算的叠前逆时偏移方法,对Sigsbee2B模型进行了偏移成像, 并和四阶NSPRK方法、传统的六阶差分方法、四阶Lax-Wendroff correction (LWC) 方法进行了对比. 数值结果表明, 基于六阶NSPRK方法的叠前逆时偏移能得到更好的成像结果, 是一种优于四阶NSPRK方法、传统的六阶差分方法、四阶LWC叠前逆时偏移的方法, 尤其是在粗网格情况下具有更明显的优越性.     

基于平面波加速的VTI介质最小二乘逆时偏移

地震各向异性集中表现为速度各向异性,势必影响地震波运动学特征.传统声波逆时偏移(RTM)和最小二乘逆时偏移(LSRTM)没有考虑介质各向异性特征,导致反射波不能正确归位、同相轴出现扭曲及寻优速度慢或不收敛等,VTI介质逆时偏移(VTI-RTM)矫正了声波成像的不足,但仍存在低频干扰严重、中深部成像不佳、振幅保持差等缺陷.为此,本文首先实现了VTI介质最小二乘逆时偏移(VTI-LSRTM)方法,为了节省I/O及内存需求并提高效率,进一步引入平面波编码技术,提出了一种基于平面波加速的VTI介质最小二乘逆时偏移(VTI-PLSRTM)策略.在此基础上开展了简单模型及复杂Marmousi模型成像试验,并与标准逆时偏移剖面对比表明:本方法能够校正各向异性造成的相位畸变,且在迭代中自动压制串扰及低频噪声、补偿中深部能量,是一种兼具质量与效率的保幅成像策略;对速度误差的敏感性测试说明该方法需要相对正确的偏移速度及Thomsen参数模型.     

The issues of prestack reverse time migration and solutions with Graphic Processing Unit implementation

Prestack reverse time migration (RTM) is a very useful tool for seismic imaging but has mainly three bottlenecks: highly intensive computation cost, low‐frequency band imaging noise and massive memory demand. Traditionally, PC‐clusters with thousands of computation nodes are used to perform RTM but it is too expensive for small companies and oilfields. In this article, we use Graphic Processing Unit (GPU) architecture, which is cheaper and faster to implement RTM and we obtain an order of magnitude higher speedup ratio to solve the problem of intensive computation cost. Aiming at the massive memory demand, we adopt the pseudo random boundary condition that sacrifices the computation cost but reduces the memory demand. For rugged topography RTM, it is difficult to deal with the rugged free boundary condition with the finite difference method. We employ a simplified boundary condition that avoids the abundant logical judgment to make the GPU implementation possible and does not induce any sacrifice on efficiency. Besides, we have also done some tests on multi‐GPU implementation for wide azimuth geometries using the latest GPU cards and drivers. Finally, we discuss the challenges of anisotropy RTM and GPU solutions. All the jobs stated above are based on GPU and the synthetic data examples will show the efficiency of the algorithm and solutions.     

基于插值原理的检查点技术波场重构与叠前逆时偏移

叠前逆时偏移等基于波场互相关原理的地球物理方法存在极大的计算与存储需求,因此采用合适的波场重构方法显得尤为重要.常规的随机边界法容易产生成像噪声,而有效边界法在三维情况仍难以实现,检查点技术具有内存要求小的特点,但存在较高的重算率,因此本文提出了插值原理的检查点技术波场重构方法.在满足Nyquist采样定理的前提下对相邻检查点间的波场进行规则抽样,将抽样波场作为插值节点,运用多项式插值算法重构任意时刻的波场,从而避免优化检查点技术反复递推造成的计算效率问题.数值实验表明：插值检查点重构算法能有效的恢复波场,其中三次样条插值重构精度最高,而牛顿法插值法计算代价较小适合于快速重构.经Sigsbee模型的叠前逆时偏移证明了插值算法的可行性,并且极大的提高了波场重构的计算效率.三维模型分析得出在增加少量存储的情况下插值重构法的重算率大幅度降低,存储量减少为有效边界法的7.1%,对于三维尺度的叠前逆时偏移有实际意义.

     

Assumptions and goals for least squares migration

Least squares migration uses the assumption that, if we have an operator that can create data from a reflectivity function, the optimal image will predict the actual recorded data with minimum square error. For this assumption to be true, it is also required that: (a) the prediction operator must be error-free, (b) model elements not seen by the operator should be constrained by other means and (c) data weakly predicted by the operator should make limited contribution to the solution. Under these conditions, least squares migration has the advantage over simple migration of being able to remove interference between different model components. Least squares migration does that by de-convolving or inverting the so-called Hessian operator. The Hessian is the cascade of forward modelling and migration; for each image point, it computes the effects of interference from other image points (point-spread function) given the actual recording geometry and the subsurface velocity model. Because the Hessian contains illumination information (along its diagonal), and information about the model cross-correlation produced by non-orthogonality of basis functions, its inversion produces illumination compensation and increases resolution. In addition, sampling deficiencies in the recording geometry map to the Hessian (both diagonal and non-diagonal elements), so least squares migration has the potential to remove sampling artefacts as well. These (illumination compensation, resolution and mitigating recording deficiencies) are the three main goals of least squares migration, although the first one can be achieved by cheaper techniques. To invert the Hessian, least squares migration relies on the residual errors during iterations. Iterative algorithms, like conjugate gradient and others, use the residuals to calculate the direction and amplitudes (gradient and step size) of the necessary corrections to the reflectivity function or model. Failure of conditions (a), (b) or (c) leads the inversion to calculate incorrect model updates, which translate to noise in the final image. In this paper, we will discuss these conditions for Kirchhoff migration and reverse time migration.     

Viscoacoustic prestack reverse time migration based on the optimal time-space domain high-order finite-difference method

Prestack reverse time migration （RTM） is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference （FD） method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.     

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.     

三维偏移距平面波有限差分叠前时间偏移

本文提出了中点-半偏移距域内的三维偏移距平面波(offset plane-wave)方程,并给出了其有限差分解法.偏移距平面波可通过对CMP道集进行平面波分解(倾斜叠加或线性Radon变换)生成,然而这样做会产生严重的噪音干扰.本文提出了局部倾斜叠加方法(local slant-stacking)来消除离散线性Radon变换引入的噪音.针对实际三维数据的不规则性(中点-偏移距域内方位角展布不均匀及偏移距采样不规则),本文还提出了与方位角无关的三维倾斜叠加方法(azimuth-independent 3D slant-stacking),解决了三维平面波分解中存在的问题.使用文中提出的平面波分解方法,可以得到高信噪比的偏移距平面波数据体.同时,三维偏移距平面波偏移可以输出偏移距射线参数域共成像点道集,基于此道集的剩余速度分析方法可以用来更新偏移速度场.偏移距平面波偏移具有很高的计算效率,相较Kirchhoff积分叠前时间偏移有较好的保幅特性,可作为水平地表三维叠前时间偏移的一个很好的解决方案.     

Efficient amplitude encoding least‐squares reverse time migration using cosine basis

Least‐squares reverse time migration provides better imaging result than conventional reverse time migration by reducing the migration artefacts, improving the resolution of the image and balancing the amplitudes of the reflectors. However, it is computationally intensive. To reduce its computational cost, we propose an efficient amplitude encoding least‐squares reverse time migration scheme in the time domain. Although the encoding scheme is effective in increasing the computational efficiency, it also introduces the well‐known crosstalk noise in the gradient that degrades the quality of the imaging result. We analyse the cause of the crosstalk noise using an encoding correlation matrix and then develop two numerical schemes to suppress the crosstalk noise during the inversion process. We test the proposed method with synthetic and field data. Numerical examples show that the proposed scheme can provide better imaging result than reverse time migration, and it also generates images comparable with those from common shot least‐squares reverse time migration but with less computational cost.     

Improving Kirchhoff migration with repeated local plane-wave imaging? A SAR-inspired signal-processing approach in prestack depth imaging

A local plane-wave approach of generalized diffraction tomography in heterogeneous backgrounds, equivalent to Kirchhoff summation techniques when applied in seismic reflection, is re-programmed to act as repeated synthetic aperture radar (SAR) imaging for seismic prestack depth migration. Spotlight-mode SAR imaging quickly provides good images of the electromagnetic reflectivity of the ground via fast Fourier transform (FFT)-based signal processing. By calculating only the Green's functions connecting the aircraft to the centre of the illuminated patch, scattering structures around that centre are also recovered. SAR technology requires us to examine seismic imaging from the local point of view, where the quantity and quality of the available information at each image point are what are important, regardless of the survey geometry. When adapted to seismics, a local image of arbitrary size and sampling is obtained by FFT of seismic energy maps in the scattering wavenumber domain around each node of a pre-calculated grid of Green's functions. These local images can be used to generate a classic prestack depth-migrated section by collecting only their centres. However, the local images also provide valuable information around the centre, as in SAR. They can therefore help to pre-analyse prestack depth migration efficiently, and to perform velocity analysis at a very low cost. The FFT-based signal-processing approach allows local, efficient and automatic control of anti-aliasing, noise and resolution, including optimized Jacobian weights. Repeated local imaging could also be used to speed up migration, with interpolation between local images associated with a coarse grid of Green's functions, as an alternative to interpolation of Green's functions. The local images may, however, show distortions due to the local plane-wave approximation, and the velocity variations across their frame. Such effects, which are not necessarily a problem in SAR, should be controlled and corrected to further enhance seismic imaging. Applications to realistic models and to real data show that, despite the distortion effects, the local images can yield similar information to prestack depth migration, including common-image-point gathers for velocity analyses and AVO/AVA effects, at a much lower cost when a small target is considered.     

起伏地表采集数据的三维直接叠前时间偏移方法

提出一种可对起伏地表采集的三维地震资料直接进行偏移成像的叠前时间偏移方法和流程.它用两个等效速度描述近地表和上覆层对地震波传播的影响,可对炮、检点不在同一水平面的三维地震资料直接进行叠前时间偏移处理.该方法不对近地表地震波传播做垂直出、入射假定,因此可适应高速层出露等不存在明显低、降速带情况.描述近地表和上覆层的两个等效速度参数可依据偏移道集的同相轴是否平直来确定,避免了确定近地表速度的困难;而对已知近地表速度的情况,则可进一步修正近地表速度,获得更好的成像效果.用三维起伏地表的理论数据和中国东部某工区实际数据验证了所发展方法和处理流程的有效性和实用性.     

转换波叠前时间偏移方法综述

本文对各向同性介质和VTI介质中的转换波叠前时间偏移方法进行了总结和归纳,分析了每种方法优缺点和适用条件.认为应在实际应用中根据不同的实际资料选择不同的方法,才能得到较好的成像效果.在转换波叠前时间偏移中,速度模型的建立及各种方法对更复杂构造的适应性仍需加强研究.     

时频域振幅相位联合的最小二乘逆时偏移

最小二乘逆时偏移方法具有复杂地质构造成像精度高、成像振幅准确等优点.但是,当地下存在强散射介质时,最小二乘逆时偏移方法很难透过上覆强散射地质体获得深部构造的高精度成像结果.本文为了提高深部精细构造的成像质量,提出时频域振幅相位联合的最小二乘逆时偏移方法.该方法主要通过构建时频域振幅相位联合目标函数,减弱振幅信息对成像结果的影响,提高深部弱散射地震信号的可成像精度.首先,对地震信号进行时频变换,构建时频域最小二乘偏移目标函数;其次,在目标函数中引入振幅权重因子,调节时频域振幅相位权重;最后,推导时频域振幅相位联合目标函数对模型参数的梯度,并利用L-BFGS局部优化算法对成像结果进行迭代.Marmousi模型和盐丘模型测试结果表明,本文方法能够很好地利用弱散射地震信号的时频域振幅相位信息,实现透过上覆强散射地质体进行深部高精度成像的目标.     

转换波Kirchhoff叠前时间偏移的成像优化方案

叠前时间偏移是转换波数据处理流程中的重要技术环节.由于下行P波和上行S波对应着不同类型的传播速度和传播机理,使得转换波偏移的诸多实施环节和实现技巧均有别于常规的纵波偏移.本文就VTI介质转换波Kirchhoff叠前时间偏移实现过程中的几个关键技术环节进行研究分析,并给出了相应的实施方案.首先,依据常速假设推导了简化的转换波时间偏移振幅加权函数,在保证偏移的高效计算的同时,兼顾了成像振幅的准确性;其次,依据直射线近似假设,推导了转换波偏移的最大无假频频率计算公式,确保了算子假频的有效滤除;接下来,设计使用了依据共转换点对称的偏移孔径,保证了偏移孔径的优化选取.此外,本文还提出利用三次卷积插值进行成像网格上参数值的插值运算,以避免传统线性插值算法的非平滑性对偏移剖面中高频信息的不良影响.多个算例的应用效果证明,本文所给出的关键技术环节的实施方案可以有效的提升转换波叠前时间偏移的成像效果.

     

基于局部倾斜叠加的快速射线束叠前时间偏移

宽方位高密度地震勘探可以有效的提高地震资料的空间分辨率和裂缝预测的精度,但地震道数的增加也大幅度提升了地震数据的处理成本.为提高海量地震数据偏移处理的计算效率,本文发展了一种快速射线束叠前时间偏移方法.该方法首先根据给定的射线束中心间隔将炮记录划分为一系列数据子集,然后利用倾斜叠加将数据子集分解为不同方向的平面波,最后根据射线束中心到地下成像点的双程走时和射线参数拾取相应的平面波振幅累加到成像点上.同Kirchhoff叠前时间偏移相比,本文方法不但保持了一致的成像精度,且由于仅需在稀疏的射线束中心位置进行成像累加运算,计算效率得到了大幅度的提升.文中所给出的模型和实际资料的测试结果验证了本文方法的正确性和有效性.

     

Frequency-domain double-plane-wave least-squares reverse time migration

Least-squares reverse time migration is often formulated as an iterative updating process, where estimating the gradient of the misfit function is necessary. Traditional time domain shot-profile least-squares reverse time migration is computationally expensive because computing the gradient involves solving the two-way wave equation several times in every iteration. To reduce the computational cost of least-squares reverse time migration, we propose a double-plane-wave least-squares reverse time migration method based on a misfit function for frequency-domain double-plane-wave data. In double-plane-wave least-squares reverse time migration, the gradient is computed by multiplying frequency-domain plane-wave Green's functions with the corresponding double-plane-wave data residual. Because the number of plane-wave Green's functions used for migration is relatively small, they can be pre-computed and stored in a computer's discs or memory. We can use the pre-computed plane-wave Green's functions to obtain the gradient without solving the two-way wave equation in each iteration. Therefore, the migration efficiency is significantly improved. In addition, we study the effects of using sparse frequency sampling and sparse plane-wave sampling on the proposed method. We can achieve images with correct reflector amplitudes and reasonable resolution using relatively sparse frequency sampling and plane-wave sampling, which are larger than that determined by the Nyquist theorem. The well-known wrap-around artefacts and linear artefacts generated due to under-sampling frequency and plane wave can be suppressed during iterations in cases where the sampling rates are not excessively large. Moreover, implementing the proposed method with sparse frequency sampling and sparse plane-wave sampling further improves the computational efficiency. We test the proposed double-plane-wave least-squares reverse time migration on synthetic models to show the practicality of the method.