Anisotropic migration velocity analysis: Application to a data set from West Africa

Although it is widely recognized that anisotropy can have a significant influence on the focusing and positioning of migrated reflection events, conventional depth imaging methods still operate with isotropic velocity fields. Here, we present an application of a 2D migration velocity analysis (MVA) algorithm, designed for factorized v(x, z) VTI (transversely isotropic with a vertical symmetry axis) media, to an offshore data set from West Africa. By approximating the subsurface with factorized VTI blocks, it is possible to decouple the spatial variations in the vertical velocity from the anisotropic parameters with minimal a priori information. Since our method accounts for lateral velocity variation, it produces more accurate estimates of the anisotropic parameters than those previously obtained with time‐domain techniques. The values of the anellipticity parameter η found for the massive shales exceed 0.2, which confirms that ignoring anisotropy in the study area can lead to substantial imaging distortions, such as mis‐stacking and mispositioning of dipping events. While some of these distortions can be removed by using anisotropic time processing, further marked improvement in image quality is achieved by prestack depth migration with the estimated factorized VTI model. In particular, many fault planes, including antithetic faults in the shallow part of the section, are better focused by the anisotropic depth‐migration algorithm and appear more continuous. Anisotropic depth migration facilitates structural interpretation by eliminating false dips at the bottom of the section and improving the images of a number of gently dipping features. One of the main difficulties in anisotropic MVA is the need to use a priori information for constraining the vertical velocity. In this case study, we successfully reconstructed the time–depth curve from reflection data by assuming that the vertical velocity is a continuous function of depth and estimating the vertical and lateral velocity gradients in each factorized block. If the subsurface contains strong boundaries with jumps in velocity, knowledge of the vertical velocity at a single point in a layer is sufficient for our algorithm to determine all relevant layer parameters.     

Migration to multiple offset and velocity analysis1

The stacking velocity best characterizes the normal moveout curves in a common-mid-point gather, while the migration velocity characterizes the diffraction curves in a zero-offset section as well as in a common-midpoint gather. For horizontally layered media, the two velocity types coincide due to the conformance of the normal and the image ray. In the case of dipping subsurface structures, stacking velocities depend on the dip of the reflector and relate to normal rays, but with a dip-dependent lateral smear of the reflection point. After dip-moveout correction, the stacking velocities are reduced while the reflection-point smear vanishes, focusing the rays on the common reflection points. For homogeneous media the dip-moveout correction is independent of the actual velocity and can be applied as a dip-moveout correction to multiple offset before velocity analysis. Migration to multiple offset is a prestack, time-migration technique, which presents data sets which mimic high-fold, bin-centre adjusted, common-midpoint gathers. This method is independent of velocity and can migrate any 2D or 3D data set with arbitrary acquisition geometry. The gathers generated can be analysed for normal-moveout velocities using traditional methods such as the interpretation of multivelocity-function stacks. These stacks, however, are equivalent to multi-velocity-function time migrations and the derived velocities are migration velocities.     

波场延拓速度分析

对常用的静校正方法进行分析,认为把复杂地层速度用其下覆地层介质替换,去掉复杂地层对处理带来的影响,可以提高速度分析的精度,对于CMP道集地震数据,在共中心点一半偏移距中,可以利用波动方程的叠前双平方根算子,实现延拓,进行层层剥离．本文提出层速度替换速度分析方法,用来解决复杂地层速度对地震速度分析的影响,理论模型计算表明,该方法是可行的。     

Use of traveltime skips in refraction analysis to delineate velocity inversion1

First arrival refraction data does not normally provide any indication of the velocity inversion problem. However, under certain favourable circumstances, when the low-velocity layer (LVL) is considerably thicker than the overlying higher-velocity layer (HVL), the velocity inversion can be seen in the form of a traveltime skip. Model Studies show that in such cases the length of the HVL traveltime branch can be used to determine the thickness of the HVL and the magnitude of the traveltime skip in order to determine the thickness of the LVL. This is also applicable in the case of field data.     

基于平均速度分析的近地表纵波速度反演

面波频散曲线对于横波速度、纵波速度、层厚等近地表地球物理参数的敏感度相差较大, 现阶段通过频散曲线可以获得较为精确的近地表横波速度与厚度信息, 但无法直接对纵波速度进行反演.研究表明, 泊松比对于波长(W)-探测深度(D)关系较为敏感.基于这一发现, 本文根据频散曲线与反演获取的横波速度结构计算平均速度, 获取W-D关系曲线.但合成数据测试证明, 因近地表浅层对应的W-D曲线变化较小, 且浅层纵波速度反演不准确会使误差累积, 直接反演W-D曲线无法获取可靠的纵波速度剖面.本文改进了基于平均速度分析的近地表纵波速度反演方法, 在目标函数中加入了对浅层信息较为敏感的W/D-D信息, 同时对W-D曲线与W/D-D曲线进行联合反演.合成数据测试证明可以获取较为准确地浅层与深层纵波速度.将该方法应用于实际地震数据中, 联合反演得到的纵波速度剖面与微测井数据较为吻合, 证明本文提出的方法可以不借助其他信息, 仅通过面波频散信息, 获取更为准确地近地表纵波信息.

     

扩散滤波方法在地震资料处理中的应用研究

在地震勘探中,由于地下结构错综复杂,多尺度非均匀的地质体常会形成包含反射波、散射波等在内的复杂的地震波场。传统的成像方法一般只考虑反射波场,忽略了散射波场,这使得细小结构无法准确成像,从而影响对复杂构造的识别。为了对小尺度构造进行准确的地震成像,要将散射波从地震波场中分离出来。在众多波场分离算法中,基于滤波的波场分离方法可以准确提取散射波,提高成像分辨率。本文调研和归纳多种基于滤波处理的地震散射波分离方法,围绕国内外学者在滤波处理波场分离方面的研究成果,总结各种方法的研究进展,并对比和分析各方法的分离效果,最后结合人工智能深度学习的研究趋势,对未来滤波处理散射波分离的发展方向进行展望。

     

Seismic migration and velocity analysis

Migration using an erroneous velocity gives a curve along which the energy is smeared. Associated with this curve is the caustic enveloped by the normal rays. It is possible to compensate for an erroneous velocity by a simple modification of the imaging principle. Formulae are derived for the general case when the velocity changes laterally, and the position of the caustic suggests how to modify the imaging principle so as to obtain an estimate of the NMO velocity. A synthetic example is used to illustrate the results of the analysis.     

Multicomponent velocity analysis with quaternions

Multicomponent seismic data are acquired by orthogonal geophones that record a vectorial wavefield. Since the single component recordings are not independent, the processing should be performed jointly for all the components. A way to achieve this goal is to exploit quaternions, hyper‐complex numbers that due to their very nature are apt to represent multidimensional data. In fact, quaternion algebra allows us to extend coherence functionals used for scalar observations to multicomponent data. Therefore by means of quaternions we implement semblance and other methods based on matched filtering and on the data covariance properties. As an application we show the results from a quaternion velocity analysis carried out combining information from the geophones and from the hydrophones of an ocean bottom cable (OBC) survey, and thus recognizing the true vectorial nature of the incoming wavefield. This also allows one to relax, at least partially, vector fidelity constraints. We demonstrate that quaternion velocity analysis yields an improved resolution with respect to the single component velocity analysis for any coherence functional chosen and that it simultaneously evidences velocity trends pertaining to different wave modes. This facilitates the interpreter in the estimation of interval Vp/Vs by means of event correlation, and in making use of a priori information from VSP and well logs. It also speeds up the velocity picking that can be performed in a single pass on a multicomponent velocity panel, rather than once for each single component velocity panel.     

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.     

莺东斜坡带速度分析方法研究及速度影响因素分析

莺歌海盆地是一个有勘探潜力的盆地,尤其是莺东斜坡带附近有良好勘探前景.但是由于研究区位于莺东斜坡带附近,因此构造解释具有相当的难度,尤其是由时间解释转化为构造解释有难度,需要有一个准确的速度来进行时深转换.基于此原因,本文首先介绍了速度谱拾取过程中的一些难点及解决方法;其后是速度分析取得的成果,通过DepthTeam形成速度体,从点、面、体三个不同角度证明了速度谱拾取过程中速度的准确性以及速度体的实用性;最后对单井和地层的速度进行了统计分析,总结了本区影响速度变化的主要因素.     

Fast velocity analysis by wave path migration

Iterative migration velocity analysis is computationally expensive, where most of the computation time is used for generating prestack depth images. By using a reduced form of Kirchhoff migration, denoted as wave path migration, we can significantly speed up the depth imaging process and reduce the entire velocity analysis expense accordingly. Our results with 2D synthetic and field data show that wave path migration velocity analysis can efficiently improve the velocity model and the wave path migration velocity analysis updated velocity correlates well with that from the Kirchhoff migration velocity analysis. The central processing unit comparison shows that, for a 2D synthetic and field data set, wave path migration velocity analysis is six times faster than Kirchhoff migration velocity analysis. This efficiency should be even greater for 3D data.     

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.     

时空移动成像条件及偏移速度分析

首先比较了深度聚焦速度分析和剩余曲率速度分析中的成像条件,然后通过时空移动成像条件得到了时移偏移距域共成像点道集和时移角度域共成像点道集.基于时移角度域共成像点道集,统一了偏移速度分析中通常应用的两个偏移速度判断准则：深度聚焦准则和成像道集拉平准则.最后基于时移角度域共成像点道集,推导了速度更新公式,并设计了速度分析流程.合成数据和实际地震资料上的测试证明了方法的可行性和有效性.     

高分辨率P-SV波速度分析

本文在常规转换波速度分析算法基础上,引入两个速度检测因子,提出了两种高分辨率的转换波速度分析方法,称之为转换波协方差速度分析法和转换波ECM（Enhanced Complex Matched Filter Method）速度分析法,同时对转换点计算公式、共转换点道集选排进行了研究,选取了最佳的转换点精确解计算公式,应用到基于时窗的CCP道集分选方法中,并与高分辨率速度分析同时进行,实现了转换波的高分辨率速度分析的算法,理论模型的计算结果表明,二者在时间及速度上都具有较高的分辨率.     

Impact of user parameters in inversion velocity analysis

Migration velocity analysis is a method devoted to the evaluation of both reflectivity and background velocity models, associated with the high and low wavenumber components of the model, respectively. Inversion velocity analysis is one of its improved versions, leading to more stable background velocity updates. Still, the impact of the user parameters should be understood for an optimal update of the background velocity. We show that a sign reversal of the background velocity gradient could occur when the selected surface offset range or the space lag range is too small. We derive the theoretical limits and check their consistency through simulations in a simple model with a single interface. These guidelines determine the necessary ranges of surface offsets and space lags for a proper update of the background velocity model. We discuss their applicability on the Marmousi model. Artefacts in the retrieved background velocity model are observed when the guidelines are not satisfied.     

Refractor velocity analysis: a signal processing procedure

This paper presents a signal processing procedure to perform refractor velocity analysis. The procedure enables one to obtain the seismic velocity from the refracted wavefield without the picking of refracted arrival times. Two processing procedures are derived, one starting from a seismic interferometric approach and another, from the conventional reciprocal method and generalized reciprocal method approaches. The theoretical equivalence of the two approaches is also demonstrated. The proposed processing procedure is applied to synthetic data in order to test the influence of some procedural parameters and its capability to reconstruct a known velocity model starting from refracted signals, without and with perturbations, in arrival times and noise; finally, it is applied to a field data set.     

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.     

Migration velocity analysis for tilted transversely isotropic media

Tilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity V_P0 controlled by the vertical (k_z) and lateral (k_x) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity V_P0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients k_z and k_x and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis. Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and V_P0 is known, the parameters k_z, k_x, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas.     

UK 1-D regional velocity models by analysis of variance of P-wave travel times from local earthquakes

A method is presented for deriving 1-D velocity depth models from earthquake bulletin data. The models can be used as initial models for more advanced modelling techniques such as tomographic inversion. The method is useful when there is little or no refraction and long-range reflection survey data. The bulletin travel times are subjected to an analysis of variance, where they are separated into source, distance, and receiving station terms. The distance terms describe the variation of travel time with distance, and the associated trend lines allow 1-D velocity models for the crustal layers to be determined. The velocity models provide an average crustal model for the region derived from local data. This does not include superficial layers which are necessarily poorly determined. Earthquake bulletin P-wave data from propagation paths across three different regions of the UK are employed to illustrate the use of the technique.