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.     

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.     

Subsurface offset behaviour in velocity analysis with extended reflectivity images

Migration velocity analysis with the constant‐density acoustic wave equation can be accomplished by the focusing of extended migration images, obtained by introducing a subsurface shift in the imaging condition. A reflector in a wrong velocity model will show up as a curve in the extended image. In the correct model, it should collapse to a point. The usual approach to obtain a focused image involves a cost functional that penalizes energy in the extended image at non‐zero shift. Its minimization by a gradient‐based method should then produce the correct velocity model. Here, asymptotic analysis and numerical examples show that this method may be too sensitive to amplitude peaks at large shifts at the wrong depth and to artefacts. A more robust alternative is proposed that can be interpreted as a generalization of stack power and maximizes the energy at zero‐subsurface shift. A real‐data example is included.     

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.     

Anisotropic velocity analysis1

Results from walkaway VSP and shale laboratory experiments show that shale anisotropy can be significantly anelliptic. Heterogeneity and anellipticity both lead to non-hyperbolic moveout curves and the resulting ambiguity in velocity analysis is investigated for the case of a factorizable anisotropic medium with a linear dependence of velocity on depth. More information can be obtained if there are several reflectors. The method of Dellinger et al. for anisotropic velocity analysis in layered transversely isotropic media is examined and is shown to be restricted to media having relatively small anellipticity. A new scheme, based on an expansion of the inverse-squared group velocity in spherical harmonics, is presented. This scheme can be used for larger anellipticity, and is applicable for horizontal layers having monoclinic symmetry with the symmetry plane parallel to the layers. The method is applied to invert the results of anisotropic ray tracing on a model Sand/shale sequence. For transversely isotropic media with small anisotropy, the scheme reduces to the method of Byun et al. and Byun and Corrigan. The expansion in spherical harmonics allows the P-phase slowness surface of each layer to be determined in analytic form from the layer parameters obtained by inversion without the need to assume that the anisotropy is weak.     

Migration velocity analysis using pre‐stack wave fields

Using both image and data domains to perform velocity inversion can help us resolve the long and short wavelength components of the velocity model, usually in that order. This translates to integrating migration velocity analysis into full waveform inversion. The migration velocity analysis part of the inversion often requires computing extended images, which is expensive when using conventional methods. As a result, we use pre‐stack wavefield (the double‐square‐root formulation) extrapolation, which includes the extended information (subsurface offsets) naturally, to make the process far more efficient and stable. The combination of the forward and adjoint pre‐stack wavefields provides us with update options that can be easily conditioned to improve convergence. We specifically use a modified differential semblance operator to split the extended image into a residual part for classic differential semblance operator updates and the image (Born) modelling part, which provides reflections for higher resolution information. In our implementation, we invert for the velocity and the image simultaneously through a dual objective function. Applications to synthetic examples demonstrate the features of the approach.     

Migration velocity analysis by depth image-wave remigration: first results

The image‐wave equation for depth remigration is a partial differential equation that is similar to the acoustic wave equation. In this work, we study its finite‐difference solution and possible applications. The conditions for stability, dispersion and dissipation exhibit a strong wavenumber dependence. Where higher horizontal than vertical wavenumbers are present in the data to be remigrated, stability may be difficult to achieve. Grid dispersion and dissipation can only be reduced to acceptable levels by the choice of very small grid intervals. Numerical tests demonstrate that, upon reaching the true medium velocity, remigrated images of curved reflectors propagate to the correct depth and those of diffractions collapse to single points. The latter property points towards the method's potential for use as a tool for migration velocity analysis. A first application to inhomogeneous media shows that in a horizontally layered medium, the reflector images reach their true depth when the remigration velocity equals the inverse of the mean medium slowness.     

Migration for velocity and attenuation perturbations

Migration maps seismic data to reflectors in the Earth. Reflections are not only caused by small‐scale variations of the velocity and density but also of the quality factor that describes attenuation. We investigated scattering due to velocity and attenuation perturbations by computing the resolution function or point‐spread function in a homogeneous background model. The resolution function is the migration image of seismic reflection data generated by a point scatterer. We found that the resolution function mixes velocity and attenuation parameter perturbations to the extent that they cannot be reconstructed independently. This is true for a typical seismic setting with sources and receivers at the surface and a buried scatterer. As a result, it will be impossible to simultaneously invert for velocity and attenuation perturbations in the scattering approach, also known as the Born approximation. We proceeded to investigate other acquisition geometries that may resolve the ambiguity between velocity and attenuation perturbations. With sources and receivers on a circle around the scatterer, in 2D, the ambiguity disappears. It still shows up in a cross‐well setting, although the mixing of velocity and attenuation parameters is less severe than in the surface‐to‐surface case. We also consider illumination of the target by diving waves in a background model that has velocity increasing linearly with depth. The improvement in illumination is, however, still insufficient to remove the ambiguity.     

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.     

Migration scheme for imaging offset VSP data within local phase space

The imaging of offset VSP data in local phase space can improve the image of the subsurface structure near the well. In this paper, we present a migration scheme for imaging VSP data in a local phase space, which uses the Gabor-Daubechies tight framebased extrapolator (G-D extrapolator) and its high-frequency asymptotic expansion to extrapolate wavefields and also delineates an improved correlation imaging condition in the local angle domain. The results for migrating synthetic and real VSP data demonstrate that the application of the high-frequency G-D extrapolator asymptotic expansion can effectively decrease computational complexity. The local angle domain correlation imaging condition can be used to weaken migration artifacts without increasing computation.     

局域化相空间中的VSP偏移成像方法(英文)

对VSP资料进行偏移成像可提高井附近地下结构的成像分辨率。本文给出了一种基于局域化相空间波场分解的VSP偏移成像方法。此方法采用了基于Gabor-Daubechies紧标架的延拓算子(G-D延拓算子)及其高频渐近形式对相空间波场进行延拓;基于局部平面假设,提出了一种局部角度域相关成像条件。合成和实际VSP资料的偏移成像结果表明,在满足渐近展开的条件下利用G-D延拓算子的高频近似式能够有效的减少计算时间;采用局部角度域相关成像条件能够在不增加计算量的同时,有效减弱VSP成像剖面上的偏移假象。     

地震多次波成像

地震资料含有各种类型多次波,而传统成像方法仅利用地震一次反射波成像,在地震成像前需将多次波去除.然而,多次波携带了丰富的地下结构信息,多次波偏移能够提供除反射波外的额外地下照明.修改传统逆时偏移方法,用包含一次反射波和多次波的原始记录代替震源子波,将SRME方法预测的表面多次波代替一次反射波作为输入数据,可将表面多次波成像.多次波成像的挑战和困难在于大量串扰噪声的产生,针对表面多次波成像中的成像噪声问题,将最小二乘逆时偏移方法与多次波分阶思想结合起来,发展可控阶数的表面多次波反演成像方法,有望初步实现高精度的表面多次波成像.在消除原始记录中的表面多次波后,通过逆散射级数方法预测得到层间多次波,将层间多次波作为逆时偏移方法的输入数据可将其准确归位到地下反射位置.数值实验表明,多次波成像能够有效地为地下提供额外照明,而可控阶表面多次波最小二乘逆时偏移成像方法几乎完全避免成像噪声.

     

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.     

Migration velocity modeling based on common reflection surface gather

The common-reflection-surface (CRS) stacking is a new seismic imaging method, which only depends on seismic three parameters and near-surface velocity instead of macro-velocity model. According to optimized three parameters obtained by CRS stacking, we derived an analytical relationship between three parameters and migration velocity field, and put forward CRS gather migration velocity modeling method, which realize velocity estimation by optimizing three parameters in CRS gather. The test of a sag model proved that this method is more effective and adaptable for velocity modeling of a complex geological body, and the accuracy of velocity analysis depends on the precision of optimized three parameters.     

Velocity analysis from large offset seismic records

One of the most important problems in applied geophysics is to extract velocities of compressional and shear waves, using the observed data collected at the Earth's surface or in boreholes. Unfortunately, in a typical seismic experiment, we do not have enough information to uniquely recover seismic velocities as functions ofx, y, andz. Thus, in the paper, a simplified model of the Earth (a stack of horizontal homogeneous layers) is considered and a critical discussion of modern techniques for processing reflection arrivals is presented.     

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.     

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。

     

南海北部新生界地层的远偏移距折射波速度特征

南海北部为张裂大陆边缘,在新生代时期经历了复杂的地质演化,具有良好油气勘探前景.本文首次利用南海北部某区域长排列地震数据的远偏移距折射波速度计算方法获得南海北部地层层速度,并进行了分析,此外,还提出了非初至折射波的概念.本方法在共偏移距剖面上识别、拾取折射波层位,得到折射波走时的横向连续变化数据,利用不同共偏移距同一折射波层位的到达时差计算该折射层位的速度结构.该方法在南海北部陆坡某区域地震资料的应用,揭示了新生界地层层速度的整体结构,反映了新生代不同时代地层的速度变化特征,为进一步利用折射层速度资料探讨南海新生代地质演化提供了新的视角.研究表明,与常规初至折射波法相比,远偏移距折射波能够提供更多的地质信息;该方法的初步应用能够对远偏移距折射波的研究提供进一步的视角.     

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。     

C#和FORTRAN混合编程在地震速度分析中的应用

本文针对交互式速度分析模块的开发技术进行讨论,融入选择性相关法速度分析理论,增加了对转换波进行速度分析的功能,并充分利用C#提供的强大的图形界面开发平台和FORTRAN语言在科学计算方面的优势,通过混合编程,将两者有机地结合起来,形成了一套精巧和便于移植的交互式地震速度分析软件.软件借助优化算法和速度分析的交互性提高了速度分析的效率和精度,并通过模型分析,将该软件用于浅层及井(巷)隧(道)探测的地质环境中.