Tomographic velocity inversion for ADCIGs in areas with a rugged surface

Pre-stack depth migration velocity analysis is one of the key techniques influencing image quality. As for areas with a rugged surface and complex subsurface, conventional prestack depth migration velocity analysis corrects the rugged surface to a known datum or designed surface velocity model on which to perform migration and update the velocity. We propose a rugged surface tomographic velocity inversion method based on angle-domain common image gathers by which the velocity field can be updated directly from the rugged surface without static correction for pre-stack data and improve inversion precision and efficiency. First, we introduce a method to acquire angle-domain common image gathers (ADCIGs) in rugged surface areas and then perform rugged surface tomographic velocity inversion. Tests with model and field data prove the method to be correct and effective.     

Migration velocity analysis using a genetic algorithm

Migration velocity analysis, a method for determining long wavelength velocity structure, is a critical step in prestack imaging. Solution of this inverse problem is made difficult by a multimodal objective function; a parameter space often vast in extent; and an evaluation procedure for candidate solutions, involving the calculation of depth-migrated image gathers, that can be prohibitively expensive. Recognizing the global nature of the problem, we employ a genetic algorithm (GA) in the search for the optimum velocity model. In order to describe a model efficiently, regions of smooth variation are identified and sparsely parametrized. Region boundaries are obtained via map migration of events picked on the zero-offset time section. Within a region, which may contain several reflectors, separate components describe long and short wavelength variations, eliminating from the parameter space, models with large velocity fluctuations. Vital to the success of the method is rapid model evaluation, achieved by generating image gathers only in the neighbourhood of specific reflectors. Probability of a model, which we seek to maximize, is derived from the flatness of imaged events. Except for an initial interpretation of the zero-offset time section, our method is automatic in that it requires no picking of residual moveout on migrated gathers. Using an example data set from the North Sea, we show that it is feasible to solve for all velocity parameters in the model simultaneously: the method is global in this respect also.     

P-P波及P-SV波叠前深度偏移速度模型建立方法

针对多波叠前深度偏移速度模型的建立问题,提出在CDP道集上利用互换原理组成伪地集作为叠前偏移速度分析的数据道集,先用叠前时间偏移方法求取层间互不影响的等效偏移速度模型,再用餐前深度偏移方法逐层求取层速度模型．对各层的速度质量、整个速度模型层位结构及速度横向变化,采用人机交互方式进行监控,并在速度叠代中引入全局寻优的遗传算法,使整个速度模型建立过程具有稳定、可靠和可视化的优点．经理论和实际资料处理结果证明,本方法是行之有效的．     

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.     

逆时偏移中用Poynting矢量高效地提取角道集

逆时偏移在提高复杂介质的成像质量方面表现出了优越的性能,但逆时偏移对速度精度的要求比较高.共成像点道集是一种非常重要的叠前深度偏移输出,它除了能为深度偏移处理提供速度信息外,还能够提供振幅和相位等信息,为后续的属性解释提供依据.本文提出一种在逆时偏移成像过程中提取角度域共成像点道集的方法,该方法采用矢量波动方程进行波场传播,并用能流密度矢量(Poynting vector)计算反射角,最后应用互相关成像条件输出角度域共成像点道集.该方法简单易于实现,且几乎不需要额外的计算量和存储量,非常适合于进行逆时偏移速度分析,同时提出的角道集也能用于进行AVA等分析.最后通过模型算例和实际数据检验了方法的有效性和优越性.     

3D post‐stack interval velocity analysis with effective use of datuming

Interval velocity analysis using post‐stack data has always been a desire, mainly for 3D data sets. In this study we present a method that uses the unique characteristics of migrated diffractions to enable interval velocity analysis from three‐dimensional zero‐offset time data. The idea is to perform a standard three‐dimensional prestack depth migration on stack cubes and generate three‐dimensional common image gathers that show great sensitivity to velocity errors. An efficient ‘top‐down’ scheme for updating the velocity is used to build the model. The effectiveness of the method is related to the incorporation of wave equation based post‐stack datuming in the model building process. The proposed method relies on the ability to identify diffractions along redatumed zero‐offset data and to analyse their flatness in the migrated local angle domain. The method can be considered as an additional tool for a complete, prestack depth migration based interval velocity analysis.     

Migration velocity analysis and waveform inversion

Least‐squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long‐scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single‐scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey‐sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey‐sinking (depth‐oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning‐based (surface‐oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth‐oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton‐like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model‐based data fitting.     

Image‐domain wavefield tomography with extended common‐image‐point gathers

Waveform inversion is a velocity‐model‐building technique based on full waveforms as the input and seismic wavefields as the information carrier. Conventional waveform inversion is implemented in the data domain. However, similar techniques referred to as image‐domain wavefield tomography can be formulated in the image domain and use a seismic image as the input and seismic wavefields as the information carrier. The objective function for the image‐domain approach is designed to optimize the coherency of reflections in extended common‐image gathers. The function applies a penalty operator to the gathers, thus highlighting image inaccuracies arising from the velocity model error. Minimizing the objective function optimizes the model and improves the image quality. The gradient of the objective function is computed using the adjoint state method in a way similar to that in the analogous data‐domain implementation. We propose an image‐domain velocity‐model building method using extended common‐image‐point space‐ and time‐lag gathers constructed sparsely at reflections in the image. The gathers are effective in reconstructing the velocity model in complex geologic environments and can be used as an economical replacement for conventional common‐image gathers in wave‐equation tomography. A test on the Marmousi model illustrates successful updating of the velocity model using common‐image‐point gathers and resulting improved image quality.     

角度域剩余深度对剩余速度的敏感性分析

本文针对地震勘探深度域偏移速度建模研究,利用角度域共成像点道集(ADCIGS)建立了以剩余速度为自变量,剩余深度为目标函数的关系式,及目标函数的梯度公式.利用导出的两个公式分别对剩余深度与剩余速度的关系进行了定量分析.通过理论分析和模型试算证明初始速度模型的误差具有方向敏感性,即正误差较负误差对速度建模迭代收敛更敏感.利用此结论进行深度域速度建模既可以提高计算效率也可以提高建模精度.     

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.     

RESIDUAL STATICS BY CDP-LOCALIZED STACK OPTIMIZATION1

Many conventional schemes of automated residual statics estimate time lags between prestack traces (sorted as CDP gathers) and a model section, and transform the collected lags into surface-consistent residuals. The method discussed in this paper aims at improving the lag estimator. ‘Externally generated’ reference traces are avoided and a principle of localized stack optimization is introduced whereby application of a multichannel filter to the stack and evaluation of the normalized power of every filtered trace gives a measure of the stack quality. One may consider the power as a function of all variable (inconsistent) shifts applied to the prestack traces. To obtain a set of optimal lag estimates the power function must be maximized. This power function is complex and the number of its variables prohibits a straightforward search for the maximum. Thus an iterative method must be employed, and steepest descent schemes have proved the most satisfactory. In the actual calculation, the repeated evaluation of the objective can be replaced by the computation of certain cross-correlations. At the last iteration (after five to ten coordinate sweeps), the global behaviour of this correlation gives some indications of how well a prestack trace is adapted to the filtered stack. This information is used to compute a weighting factor to be stored with the lag estimate. At this stage simple statistical procedures are run to eliminate the most unlikely estimates. The remaining ones are transformed to surface-consistent residuals by means of a weighted least-squares inversion according to a model which takes into account the fact that the lags have no fixed reference datum. The efficiency of the method is demonstrated by a field data example into which synthetic anomalies were introduced, and the effect of the new process is compared with that of a ‘classical’ production program using field data with genuine static problems.     

频率-空间域有限差分法叠前深度偏移

为了处理横向强变速介质中的深度成像问题,本文提出一种基于共炮道集的优化系数的傍轴近似方程叠前深度偏移算子,并在基于反射系数估算的成像条件下,可实现叠前深度偏移成像.该算子具有方程阶数低且能对陡倾角成像的特征,并采用有限差分法波场延拓,能适应速度场的任意变化.当在频率-空间域进行计算时,相对于纯粹的时间-空间域有限差分算法有计算效率高、成像方便的优点.脉冲响应测试和对Marmousi模型进行的叠前深度偏移结果表明,该偏移方法在强横向变速情况下具有非常好的成像效果.     

Wave-equation migration velocity analysis. I. Theory

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.     

苏北大陆科学钻探靶区深反射地震的叠前深度偏移

由于深反射地震数据具有信噪比低和记录长度长等特点,叠前深度偏移方法的应用有许多困难．为此,我们研究了一种适合于深反射地震的叠前深度偏移方法;包括：用逆风有限差分方法计算程函方程;在常规速度扫描的基础上,用协方差控制提高速度分析精度;用联合反演算法计算层速度,再插值后得到初始速度模型;用Ｋｉｒｃｈｈｏｆｆ法作为偏移速度分析工具,求得最终的速度模型;最终的速度模型作为有限差分深度偏移的输入,求得最终的偏移结果．用该方法对“中国大陆科学深钻工程”东海二维深反射地震数据ＤＨ－４线进行了叠前深度偏移,取得了良好的效果。     

Multiwave velocity analysis based on Gaussian beam prestack depth migration

Prestack depth migration of multicomponent seismic data improves the imaging accuracy of subsurface complex geological structures. An accurate velocity field is critical to accurate imaging. Gaussian beam migration was used to perform multicomponent migration velocity analysis of PP- and PS-waves. First, PP- and PS-wave Gaussian beam prestack depth migration algorithms that operate on common-offset gathers are presented to extract offset-domain common-image gathers of PP- and PS-waves. Second, based on the residual moveout equation, the migration velocity fields of P- and S-waves are updated. Depth matching is used to ensure that the depth of the target layers in the PP- and PS-wave migration profiles are consistent, and high-precision P- and S-wave velocities are obtained. Finally, synthetic and field seismic data suggest that the method can be used effectively in multiwave migration velocity analysis.     

TI介质偏移速度建模研究

经过多年的研究发展,各向异性叠前深度偏移算法已经趋于完善.然而,在地震资料处理过程中导致成像结果不理想的主要原因还是由于建立的地层参数场不够精确.当地层参数接近其真实值时,基于波动方程的剩余曲率建模方法由于不受构造的影响,能够在各向异性和横向变速介质中进行速度分析,所以得到了广泛的研究.本文从偏移结果中抽取共成像道集,然后通过交互运用叠前深度偏移和参数更新实现各向异性偏移速度建模.对理论模型和实际资料进行的试算表明,该方法具有较强的适应性,能极大改善VTI介质反射界面成像效果和分辨率.     

波动方程法共成像点道集偏移速度建模

叠前深度偏移的成像效果对偏移速度场相当敏感，建立正确的偏移速度场是实现高质量叠前深度偏移成像的关键。首先应用成像精度高的波动方程法叠前深度偏移抽取共成像点道集；然后基于摄动法通过参数化速度函数和改进的剩余曲率分析建立偏移速度误差和成像深度误差的定量关系；最后采用单参数／多参数联合迭代反演实现偏移速度建模。对Marmousi模型的试算结果表明：该方法对复杂地质体具有较强的适应性和较好的建模和成像效果，一般只需分析和控制主要反射层，通过3－4次近代就可以满足精度要求。     

Extraction of amplitude-preserving angle gathers based on vector wavefield reverse-time migration

Angle-domain common-image gathers (ADCIGs) transformed from the shotdomain common-offset gathers are input to migration velocity analysis (MVA) and prestack inversion. ADCIGs are non-illusion prestack inversion gathers, and thus, accurate. We studied the extraction of elastic-wave ADCIGs based on amplitude-preserving elastic-wave reversetime migration for calculating the incidence angle of P-and S-waves at each image point and for different source locations. The P-and S-waves share the same incident angle, namely the incident angle of the source P-waves. The angle of incidence of the source P-wavefield was the difference between the source P-wave propagation angle and the reflector dips. The propagation angle of the source P-waves was obtained from the polarization vector of the decomposed P-waves. The reflectors’ normal direction angle was obtained using the complex wavenumber of the stacked reverse-time migration (RTM) images. The ADCIGs of P-and S-waves were obtained by rearranging the common-shot migration gathers based on the incident angle. We used a horizontally layered model, the graben medium model, and part of the Marmousi-II elastic model and field data to test the proposed algorithm. The results suggested that the proposed method can efficiently extract the P-and S-wave ADCIGs of the elastic-wave reverse-time migration, the P-and S-wave incident angle, and the angle-gather amplitude fidelity, and improve the MVA and prestack inversion.     

Wavefield tomography based on local image correlations

The estimation of a velocity model from seismic data is a crucial step for obtaining a high‐quality image of the subsurface. Velocity estimation is usually formulated as an optimization problem where an objective function measures the mismatch between synthetic and recorded wavefields and its gradient is used to update the model. The objective function can be defined in the data‐space (as in full‐waveform inversion) or in the image space (as in migration velocity analysis). In general, the latter leads to smooth objective functions, which are monomodal in a wider basin about the global minimum compared to the objective functions defined in the data‐space. Nonetheless, migration velocity analysis requires construction of common‐image gathers at fixed spatial locations and subsampling of the image in order to assess the consistency between the trial velocity model and the observed data. We present an objective function that extracts the velocity error information directly in the image domain without analysing the information in common‐image gathers. In order to include the full complexity of the wavefield in the velocity estimation algorithm, we consider a two‐way (as opposed to one‐way) wave operator, we do not linearize the imaging operator with respect to the model parameters (as in linearized wave‐equation migration velocity analysis) and compute the gradient of the objective function using the adjoint‐state method. We illustrate our methodology with a few synthetic examples and test it on a real 2D marine streamer data set.     

MODEL-BASED STACK: A METHOD FOR CONSTRUCTING AN ACCURATE ZERO-OFFSET SECTION FOR COMPLEX OVERBURDENS1

The interpretation of stacked time sections can produce a correct geological image of the earth in cases when the stack represents a true zero-offset section. This assumption is not valid in the presence of conflicting dips or strong lateral velocity variations. We present a method for constructing a relatively accurate zero-offset section. We refer to this method as model-based stack (MBS), and it is based on the idea of stacking traces within CMP gathers along actual traveltime curves, and not along hyperbolic trajectories as it is done in a conventional stacking process. These theoretical curves are calculated for each CMP gather by tracing rays through a velocity-depth model. The last can be obtained using one of the methods for macromodel estimation. In this study we use the coherence inversion method for the estimation of the macromodel since it has the advantage of not requiring prestack traveltime picking. The MBS represents an accurate zero-offset section in cases where the estimated macromodel is correct. Using the velocity–depth macromodel, the structural inversion can be completed by post-stack depth migration of the MBS.