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.     

基于倾角-偏移距域道集的绕射波成像

地震绕射波是地下非连续性地质体的地震响应,绕射波成像对地下断层、尖灭和小尺度绕射体的识别具有重要的意义.在倾角域共成像点道集中,反射波同相轴表现为一条下凸曲线,能量主要集中在菲涅耳带内,绕射波能量则比较发散.由于倾角域菲涅耳带随偏移距变化而存在差异,因此本文提出一种在倾角-偏移距域道集中精确估计菲涅耳带的方法,在各偏移距的倾角域共成像点道集中实现菲涅耳带的精确切除,从而压制反射波.在倾角-偏移距域道集中还可以分别实现绕射波增强,绕射波同相轴相位校正,因此能量弱的绕射波可以清晰地成像.在倾角域共成像点道集中,反射波同相轴的最低点对应于菲涅耳带估计所用的倾角,因此本文提出一种在倾角域共成像点道集中直接自动拾取倾角场的方法.理论与实际资料试算验证了本文绕射波成像方法的有效性.

     

Research Note: Insights into the data dependency on anisotropy: an inversion prospective

While velocity contrasts are responsible for most of the events recorded in our data, the long wavelength behavior of the velocity model is responsible for the geometrical shape of these events. For isotropic acoustic materials, the wave dependency on the long (wave propagation) and short (scattering) wavelength velocity components is stationary with the propagation angle. On the other hand, in representing a transversely isotropic with a vertical symmetry axis medium with the normal moveout velocity, the anellepticity parameter η, the vertical scaling parameter δ, and the sensitivity of waves vary with the polar angle for both the long and short wavelength features of the anisotropic dimensionless medium parameters (δ and η). For horizontal reflectors at reasonable depths, the long wavelength features of the η model is reasonably constrained by the long offsets, whereas the short wavelength features produce very week reflections at even reasonable offsets. Thus, for surface acquired seismic data, we could mainly invert for smooth η responsible for the geometrical shape of reflections. On the other hand, while the δ long wavelength components mildly affects the recorded data, its short wavelength variations can produce reflections at even zero offset, with a behavior pattern synonymous to density. The lack of the long wavelength δ information will mildly effect focusing but will cause misplacement of events in depth. With low enough frequencies (very low), we may be able to recover the long wavelength δ using full waveform inversion. However, unlike velocity, the frequencies needed for that should be ultra‐low to produce long‐wavelength scattering‐based model information as δ perturbations do not exert scattering at large offsets. For a combination given by the horizontal velocity, η, and ε, the diving wave influence of η is absorbed by the horizontal velocity, severely limiting the η influence on the data and full waveform inversion. As a result, with a good smooth η estimation, for example, from tomography, we can focus the full waveform inversion to invert for only the horizontal velocity and maybe ε as a parameter to fit the amplitude. This is possibly the most practical parametrization for inversion of surface seismic data in transversely isotropic with vertical symmetry axis media.     

Anisotropy signature in reverse‐time migration extended images

Reverse‐time migration can accurately image complex geologic structures in anisotropic media. Extended images at selected locations in the Earth, i.e., at common‐image‐point gathers, carry rich information to characterize the angle‐dependent illumination and to provide measurements for migration velocity analysis. However, characterizing the anisotropy influence on such extended images is a challenge. Extended common‐image‐point gathers are cheap to evaluate since they sample the image at sparse locations indicated by the presence of strong reflectors. Such gathers are also sensitive to velocity error that manifests itself through moveout as a function of space and time lags. Furthermore, inaccurate anisotropy leaves a distinctive signature in common‐image‐point gathers, which can be used to evaluate anisotropy through techniques similar to the ones used in conventional wavefield tomography. It specifically admits a V‐shaped residual moveout with the slope of the “V” flanks depending on the anisotropic parameter η regardless of the complexity of the velocity model. It reflects the fourth‐order nature of the anisotropy influence on moveout as it manifests itself in this distinct signature in extended images after handling the velocity properly in the imaging process. Synthetic and real data observations support this assertion.     

What is DMO coverage?

'Coverage' or 'fold' is defined as the multiplicity of common-midpoint (CMP) data. For CMP stacking the coverage is consistent with the number of traces sharing a common reflection point on flat subsurface reflectors. This relationship is not true for dipping reflectors. The deficiencies of CMP stacking with respect to imaging dipping events have long been overcome by the introduction of the dip-moveout (DMO) correction. However, the concept of coverage has not yet satisfactorily been updated to a 'DMO coverage' consistent with DMO stacking. A definition of constant-velocity DMO coverage will be proposed here. A subsurface reflector will be illuminated from a given source and receiver location if the time difference between the reflector zero-offset traveltime and the NMO- and DMO-corrected traveltime of the reflection event is less than half a dominant wavelength. Due to the fact that a subsurface reflector location is determined by its zero-offset traveltime, its strike and its dip, the DMO coverage also depends on these three parameters. For every surface location, the proposed DMO coverage consists of a 3D fold distribution over reflector strike, dip and zero-offset traveltime.     

2D multiscale non-linear velocity inversion

An efficient and robust non-linear inversion method for velocity optimization combining a global random search followed by a simplex technique is presented. The background velocity field is estimated at different spatial scales by analysing image gathers after iterative prestack depth migrations. First, the global random search is used to determine the main features/trends of the velocity model (large-scale component). Then, the simplex technique improves the resolution of the velocity field by estimating smaller-scale features. A measure of the quality of the velocity model (objective function) is based on flattening offset events in depth-migrated image gathers. To help constrain the solution, the algorithm can incorporate a priori information about the model and a smoothness condition. This 2D velocity estimation offers the benefit of being semi-automatic (requiring minimal human intervention) as well as providing a global and objective solution (which is a useful approach to an interpretation-derived velocity-estimation technique). The method is applied to a real data set where AVO analysis is carried out after prestack depth migration, as structural effects are non-negligible. It is demonstrated that the method can successfully estimate a laterally inhomogeneous velocity model at a computational cost modest compared with an interpretation-based iterative prestack depth velocity-analysis technique.     

Poststack diffraction imaging using reverse‐time migration

We propose a method for imaging small‐scale diffraction objects in complex environments in which Kirchhoff‐based approaches may fail. The proposed method is based on a separation between the specular reflection and diffraction components of the total wavefield in the migrated surface angle domain. Reverse‐time migration was utilized to produce the common image gathers. This approach provides stable and robust results in cases of complex velocity models. The separation is based on the fact that, in surface angle common image gathers, reflection events are focused at positions that correspond to the apparent dip angle of the reflectors, whereas diffracted events are distributed over a wide range of angles. The high‐resolution radon‐based procedure is used to efficiently separate the reflection and diffraction wavefields. In this study, we consider poststack diffraction imaging. The advantages of working in the poststack domain are its numerical efficiency and the reduced computational time. The numerical results show that the proposed method is able to image diffraction objects in complex environments. The application of the method to a real seismic dataset illustrates the capability of the approach to extract diffractions.     

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.     

CDP mapping in tilted transversely isotropic (TTI) media. Part II: Velocity analysis by combining CDP mapping with a genetic algorithm

This paper presents a method for velocity analysis in tilted transversely isotropic (TTI) media by combining CDP mapping with a genetic algorithm. CDP mapping is a velocity analysis method for determining anisotropic velocity but has difficulties due to the following factors: (i) it involves a non-linear and multimodal objective function; (ii) it is prohibitively expensive in the evaluation of candidate solutions, which often involves the calculation of images in the depth domain; (iii) there is often a very large parameter space. Recognizing the global and multimodal nature of the problem, a genetic algorithm is employed to search for the optimal velocity model. The efficiency of the method contributes to two critical processes: rapid model evaluation, achieved by generating CDP mapping only in the neighbourhood of specific reflectors, and fast computation, based on Fermat's principle, of the CDP points and traveltimes in TTI media. The method produces subsurface structure images in the depth domain, and can also solve for Thomsen's anisotropic parameters (ɛ and δ), the vertical velocity and the dip of the symmetry axis in the model space, simultaneously.     

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.     

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.     

Image enhancement by multi‐parameter characterization of common image gathers

We present an innovative approach for seismic image enhancement using multi‐parameter angle‐domain characterization of common image gathers. A special subsurface angle‐domain imaging system is used to generate the multi‐parameter common image gathers in a summation‐free image space. The imaged data associated with each common image gathers depth point contain direction‐dependent opening‐angle image contributions from all the available incident and scattered wave‐pairs at this point. Each direction‐dependent opening‐angle data can be differently weighted according to its coherency measure. Once the optimal migration velocity is used, it is assumed that in the actual specular direction, the coherency measure (semblance) along reflection events, from all available opening angles and opening azimuths, is larger than that along non‐specular directions. The computed direction‐dependent semblance attribute is designed to operate as an imaging filter which enhances specular migration contributions and suppresses all others in the final migration image. The ability to analyse the structural properties of the image points by the multi‐parameter common image gather allows us to better handle cases of complicated wave propagation and to improve the image quality at poorly illuminated regions or near complex structures. The proposed method and some of its practical benefits are demonstrated through detailed analysis of synthetic and real data examples.     

Image-domain wavefield tomography for tilted transversely isotropic media

Transversely isotropic models with a tilted symmetry axis have become standard for imaging beneath dipping shale formations and in active tectonic areas. Here, we develop a methodology of wave-equation-based image-domain tomography for acoustic tilted transversely isotropic media. We obtain the gradients of the objective function using an integral wave-equation operator based on a separable dispersion relation that takes the symmetry-axis tilt into account. In contrast to the more conventional differential solutions, the integral operator produces only the P-wavefield without shear-wave artefacts, which facilitates both imaging and velocity analysis. The model is parameterized by the P-wave zero-dip normal-moveout velocity, the Thomsen parameter δ, anellipticity coefficient η and the symmetry-axis tilt θ. Assuming that the symmetry axis is orthogonal to reflectors, we study the influence of parameter errors on energy focusing in extended (space-lag) common-image gathers. Distortions in the anellipticity coefficient η introduce weak linear defocusing regardless of reflector dip, whereas δ influences both the energy focusing and depth scale of the migrated section. These results, which are consistent with the properties of the P-wave time-domain reflection moveout in tilted transversely isotropic media, provide important insights for implementation of velocity model-building in the image-domain. Then the algorithm is tested on a modified anticline section of the BP 2007 benchmark model.     

Velocity model updating using image gathers1

For successful prestack depth migration an accurate velocity model is needed. One method for model updating is based on image gather analysis. In an image gather all reflectors line up horizontally if the correct velocities are used for the depth migration. This is also true for dipping reflectors, as all traces of an image gather belong to the same surface coordinate. The images of the reflector in an image gather curve upwards if the velocity used for the migration is too low, or downwards if the velocity is too high. This deviation can be used for model updating. Curves which depend on depth, offset and a parameter which relates the estimated to the true model are fitted to the image. By calculating the coherence along the deviation curves, this parameter can be estimated and hence an update can be calculated. Formulae are derived for the deviation curves and the update of the velocity depth model for a multilayered model for both shot and common-offset migrated data, with and without gradients. The method is tested on synthetic data with satisfactory results.     

Diffraction imaging by prestack reverse‐time migration in the dip‐angle domain

Prestack image volumes may be decomposed into specular and non‐specular parts by filters defined in the dip‐angle domain. For space‐shift extended image volumes, the dip‐angle decomposition is derived via local Radon transform in depth and midpoint coordinates, followed by an averaging over space‐shifts. We propose to employ prestack space‐shift extended reverse‐time migration and dip‐angle decomposition for imaging small‐scale structural elements, considered as seismic diffractors, in models with arbitrary complexity. A suitable design of a specularity filter in the dip‐angle domain rejects the dominant reflectors and enhances diffractors and other non‐specular image content. The filter exploits a clear discrimination in dip between specular reflections and diffractions. The former are stationary at the specular dip, whereas the latter are non‐stationary without a preferred dip direction. While the filtered image volume features other than the diffractor images (for example, noise and truncation artefacts are also present), synthetic and field data examples suggest that diffractors tend to dominate and are readily recognisable. Averaging over space‐shifts in the filter construction makes the reflectors? rejection robust against migration velocity errors. Another consequence of the space‐shift extension and its angle‐domain transforms is the possibility of exploring the image in a multiple set of common‐image gathers. The filtered diffractions may be analysed simultaneously in space‐shift, scattering‐angle, and dip‐angle image gathers by means of a single migration job. The deliverables of our method obviously enrich the processed material on the interpreter's desk. We expect them to further supplement our understanding of the Earth's interior.     

利用联合反演技术进行反射地震的波速成象

本文介绍了根据反射地震数据进行波速成象的一种方法,其基础为多种反演技术的综合。由于要求的波速图象C（x,z）具有间断性,除利用走时数据T（x,t）外,在地层比较水平的情况下,还利用了均方根速度V（x,t）和统计子波W（t）的数据来成象。计算机层析成象过程分为三步:首先重做速度分析,取得与初次反射走时一致的均方根速度数据;然后用反射走时与均方根速度联合反演对应分析道的层速度和界面深度;最后由联合反演结果和反射面走时求波速图象函数的数字化版。文中还给出了波速成象方法在我国西北某沉积盆地上的应用及验证结果。     

角度域弹性波Kirchhoff叠前深度偏移速度分析方法

为提高地震成像结果的准确性并真实反映实际地震波场在介质中的传播特性,应该充分利用多分量地震数据的矢量特征进行弹性波成像,其中,最为棘手的问题是纵横波偏移速度场的确定,为此,本文提出了直接利用多分量地震数据进行弹性波角度域偏移速度分析的方法.基于空移成像条件的弹性波Kirchhoff偏移方程提取了弹性波局部偏移距域共成像...     

利用联合反演技术进行反射地震的波速成象

本文介绍了根据反射地震数据进行波速成象的一种方法,其基础为多种反演技术的综合。由于要求的波速图象C（x,z）具有间断性,除利用走时数据T（x,t）外,在地层比较水平的情况下,还利用了均方根速度V（x,t）和统计子波W（t）的数据来成象。计算机层析成象过程分为三步:首先重做速度分析,取得与初次反射走时一致的均方根速度数据;然后用反射走时与均方根速度联合反演对应分析道的层速度和界面深度;最后由联合反演结果和反射面走时求波速图象函数的数字化版。文中还给出了波速成象方法在我国西北某沉积盆地上的应用及验证结果。     

ON REVERSE-TIME MIGRATION*

Migration is a process whereby events in ‘image space’ are mapped into their correct positions in ‘object space’. The wave equations associated with this mapping may be defined and solved numerically either in image space or in object space. In the former the CMP section, which represents the initial conditions, is extrapolated toward increasing depths, and the migrated data are recovered at zero time. In the latter, the wave-field extrapolation takes place in the coordinate frame of the depth section, and the CMP data serve as boundary conditions at the surface. Computations begin at the last sample of the record section and continue ‘reverse time’ until time zero. This paper describes a reverse-time migration (RTM) method and compares its performance with that of an image-space method based on the idea of phase shift plus interpolation (PSPI). Synthetic zero-offset sections serve as examples for migration experiments with the RTM and PSPI methods. It is shown that the RTM approach to migration is rather expensive, but its robustness and accuracy are difficult to surpass.