OFFSET CONTINUATION OF SEISMIC SECTIONS*

Geometrical acoustic and wave theory lead to a second-order partial differential equation that links seismic sections with different offsets. In this equation a time-shift term appears that corresponds to normal moveout; a second term, dependent on offset and time only, corrects the moveout of dipping events. The zero-offset stacked section can thus be obtained by continuing the section with maximum offset towards zero, and stacking along the way the other common-offset sections. Without the correction for dip moveout, the spatial resolution of the section is noticeably impaired, thus limiting the advantages that could be obtained with expensive migration procedures. Trade-offs exist between multiplicity of coverage, spatial resolution, and signal-to-noise; in some cases the spatial resolution on the surface can be doubled and the aliasing noise averaged out. Velocity analyses carried out on data continued to zero offset show a better resolution and improved discrimination against multiples. For instance, sea-floor multiples always appear at water velocity, so that their removal is simplified. This offset continuation can be carried out either in the time-space domain or in the time-wave number domain. The methods are applied both to synthetic and real data.     

一种倾角时差校正和叠前成象方法

本文从测量射线参数出发进行反向射线追踪,导出倾角时差校正（DMO）的公式。经过DMO后,可以从一组等炮检距剖面得出共分角线点道集。用于对这些道集进行叠加的速度值与界面倾角无关。对经过DMO的资料的等时切片进行叠前成象（PSI）,就可以把分布在圆上的绕射能量沿圆弧加起来,并放在圆弧上对应于最大炮检距的位置。经过这两种处理,再应用标准的速度分析和叠加方法,就可得出偏移后的剖面。这两种处理均与速度无关。最后用物理模型试验说明了DMO和PSI的效果是好的。     

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.     

A SIMPLE EFFICIENT METHOD OF DIP-MOVEOUT CORRECTION1

Much of the success of modern seismic data processing derives from the use of the stacking process. Unfortunately, as is well known, conventional normal moveout correction (NMO) introduces mispositioning of data, and hence mis-stacking, when dip is present. Dip moveout correction (DMO) is a technique that converts non-zero-offset seismic data after NMO to true zero-offset locations and reflection times, irrespective of dip. The combination of NMO and DMO followed by post-stack time migration is equivalent to, but can be implemented much more efficiently than, full time migration before stack. In this paper we consider the frequency-wavenumber DMO algorithm developed by Hale. Our analysis centres on the result that, for a given dip, the combination of NMO at migration velocity and DMO is equivalent to NMO at the appropriate, dip-dependent, stacking velocity. This perspective on DMO leads to computationally efficient methods for applying Hale DMO and also provides interesting insights on the nature of both DMO and conventional stacking.     

Offset continuation (OCO) ray tracing using OCO trajectories

Offset continuation (OCO) is a seismic configuration transform designed to simulate a seismic section as if obtained with a certain source-receiver offset using the data measured with another offset. Since OCO is dependent on the velocity model used in the process, comparison of the simulated section to an acquired section allows for the extraction of velocity information. An algorithm for such a horizon-oriented velocity analysis is based on so-called OCO rays. These OCO rays describe the output point of an OCO as a function of the Root Mean Square (RMS) velocity. The intersection point of an OCO ray with the picked traveltime curve in the acquired data corresponding to the output half-offset defines the RMS velocity at that position. We theoretically relate the OCO rays to the kinematic properties of OCO image waves that describe the continuous transformation of the common-offset reflection event from one offset to another. By applying the method of characteristics to the OCO image-wave equation, we obtain a raytracing-like procedure that allows to construct OCO trajectories describing the position of the OCO output point under varying offset. The endpoints of these OCO trajectories for a single input point and different values of the RMS velocity form then the OCO rays. A numerical example demonstrates that the developed ray-tracing procedure leads to reliable OCO rays, which in turn provide high-quality RMS velocities. The proposed procedure can be carried out fully automatically, while conventional velocity analysis needs human intervention. Moreover, since velocities are extracted using offset sections, more redundancy is available or, alternatively, OCO velocities can be studied as a function of offset.     

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.     

MIGRATION OF SEISMIC INTERFACES*

Most interpretation work is still based on stacked and not on migrated sections. In the case of heavy faulting and considerable velocity contrasts between formations, migration of interpreted interfaces poses a problem. In more detail, the problem may be specified as follows: — a given interpretation of a number of interfaces along with a given heterogeneous velocity field may not always have a plausible solution in the form of migrated interfaces in depth; — fault planes, salt boundaries, etc., are, in most cases, not directly interpretable in a section and are plotted by intuition using interface terminations as a guide; — the velocity field in fault zones is, in most cases, hard to determine. The interpreter may arrive at a plausible solution by repeating the migration process with various possible interpretations and various velocity assumptions. The subject of this paper is an algorithm based on ray-theory which allows one: — to handle faults and velocity variations at faults properly; — to perform migration in steps, working a particular geological unit at a time and proceeding to the next unit once the foregoing one has been properly migrated; — to display ray-paths, where necessary, for investigation of interface distortions, e.g., below fault areas. The algorithm is designed and implemented for application in an interactive environment. Inspection of intermediate and final results, investigation of interface distortions and modifications are performed on a graphics screen. Thus, various possible interpretations and velocity assumptions may be investigated within a short time. Interfaces interpreted on migrated sections may be over-migrated because of neglection of the influence of refraction in most section migration programs. This over-migration may also be corrected using the above algorithm in the “image ray” mode.     

OFFSET CONTINUATION FOR SEISMIC STACKING*

Wave equation migration techniques have shown the limits of traditional stacking methods with data from tectonically complicated areas. An improved stack can be obtained utilizing the dip-moveout correction technique based on offset continuation. The properties and the limits of the algorithms used are summarized briefly. Several synthetic and real data examples are shown and compared with the results obtained using conventional processing in order to show the focusing effects and the strong improvement in signal-to-noise ratios, both at the stacked and migrated section level. The possibility of exploiting this technique to transform multiple coverage into increased spatial resolution is illustrated with examples.     

Mapping of moveout attributes using local slopes

Decomposing seismic data in local slopes is the basic idea behind velocity‐independent imaging. Using accurate moveout approximations enables computing moveout attributes such as normal moveout velocity and nonhyperbolic parameters as functions of zero‐offset travel time. Mapping of moveout attributes is performed from the pre‐stack seismic data domain into the time‐migrated image domain. The different moveout attributes have different accuracy for a given moveout approximation that depends on the corresponding order of travel‐time derivative. The most accurate attribute is the zero‐offset travel time, and the nonhyperbolic parameter has the worst accuracy, regardless of the moveout approximation. Typically, the mapping of moveout attributes is performed using a point‐to‐point procedure, whereas the generalized moveout approximation requires two point‐to‐point mappings. Testing the attribute mapping on the different models shows that the accuracy of mapped attributes is model dependent, whereas the generalized moveout approximation gives practically exact results.     

VTI介质长偏移距非双曲动校正公式优化

常规Alkhalifah动校正公式精度低,不能精确描述各向异性介质长偏移距地震反射同相轴的时距关系.本文以提高VTI介质长偏移距地震资料动校正公式的精度为目标,在分析VTI介质常规动校正方程的基础上,根据误差最小原理建立优化校正系数图版,实现对常规动校正公式大偏移距误差的修正,建立最优化校正Alkhalifah动校正方程,实现了对VTI介质长偏移距地震资料常规动校正方程的改进.之后由Fomel群速度公式导出高精度VTI模型长偏移距时距函数,提出了高精度VTI介质长偏移距地震资料动校正方程.将以上的动校正方程用于各向异性参数反演,模型计算表明最优化校正Alkhalifah动校正方程的反演精度是常规长偏移距动校正方程反演精度的2～4倍,高精度动校正方程的反演精度是常规动校正方程反演精度的2～8倍.     

APPLICATION OF THE PARTIAL KARHUNEN-LOÈVE TRANSFORM TO SUPPRESS RANDOM NOISE IN SEISMIC SECTIONS1

The Karhunen-Loève (K–L) transform is an effective technique for suppressing spatially uncorrelated noise, but because of its high computational cost, fast transforms, such as the Fourier transform, have been more favoured. Two techniques that combine to make the K–L transform feasible for seismic data processing are discussed. The first technique filters the data for limited dips. For each dip, linear moveout is applied to the seismic sections so that events with this dip are made flat. By interpolation, we can include dips that are fractions of a sample/trace. After linear moveout, zero-lag K–L filtering is applied followed, by inverse linear moveout; the results from all dips are added to form the final filtered data. The second technique is blocking, in which the seismic section is divided into blocks small enough for each block to be processed using relatively small matrices; the processed blocks are assembled to form the final filtered section. Using a combination of these techniques, seismic sections can be filtered at a reasonable cost using the K-L transform.     

Normal moveout velocity for pure‐mode and converted waves in layered orthorhombic medium

We study the azimuthally dependent hyperbolic moveout approximation for small angles (or offsets) for quasi‐compressional, quasi‐shear, and converted waves in one‐dimensional multi‐layer orthorhombic media. The vertical orthorhombic axis is the same for all layers, but the azimuthal orientation of the horizontal orthorhombic axes at each layer may be different. By starting with the known equation for normal moveout velocity with respect to the surface‐offset azimuth and applying our derived relationship between the surface‐offset azimuth and phase‐velocity azimuth, we obtain the normal moveout velocity versus the phase‐velocity azimuth. As the surface offset/azimuth moveout dependence is required for analysing azimuthally dependent moveout parameters directly from time‐domain rich azimuth gathers, our phase angle/azimuth formulas are required for analysing azimuthally dependent residual moveout along the migrated local‐angle‐domain common image gathers. The angle and azimuth parameters of the local‐angle‐domain gathers represent the opening angle between the incidence and reflection slowness vectors and the azimuth of the phase velocity ψ_phs at the image points in the specular direction. Our derivation of the effective velocity parameters for a multi‐layer structure is based on the fact that, for a one‐dimensional model assumption, the horizontal slowness and the azimuth of the phase velocity ψ_phs remain constant along the entire ray (wave) path. We introduce a special set of auxiliary parameters that allow us to establish equivalent effective model parameters in a simple summation manner. We then transform this set of parameters into three widely used effective parameters: fast and slow normal moveout velocities and azimuth of the slow one. For completeness, we show that these three effective normal moveout velocity parameters can be equivalently obtained in both surface‐offset azimuth and phase‐velocity azimuth domains.     

三维地震资料叠前时间偏移应用研究

本文通过选取合适的叠前时间偏移软件,对两块三维地震资料进行偏移成像试验,验证叠前时间偏移中影响偏移成像效果的几个主要因素.该软件偏移算法的核心技术是弯曲射线偏移处理,这不同于工业界常用的直射线假设.偏移速度是偏移成像好坏的主要因素,通过迭代进行偏移、速度分析,使共成像点道集拉平,从而实现构造的准确成像;偏移孔径也是影响偏移成像的一个关键参数,其选取与成像目标层的倾斜角、深度、速度等有关;反假频参数对偏移成像效果有一定影响,是偏移中需要考虑的因素之一.     

Residual dip moveout in VTI media

Dip‐moveout (DMO) correction is often applied to common‐offset sections of seismic data using a homogeneous isotropic medium assumption, which results in a fast execution. Velocity‐residual DMO is developed to correct for the medium‐treatment limitation of the fast DMO. For reasonable‐sized velocity perturbations, the residual DMO operator is small, and thus is an efficient means of applying a conventional Kirchhoff approach. However, the shape of the residual DMO operator is complicated and may form caustics. We use the Fourier domain for the operator development part of the residual DMO, while performing the convolution with common‐offset data in the space–time domain. Since the application is based on an integral (Kirchhoff) method, this residual DMO preserves all the flexibility features of an integral DMO. An application to synthetic and real data demonstrates effectiveness of the velocity‐residual DMO in data processing and velocity analysis.     

共接收点倾斜叠加波动方程偏移

共接收点倾斜叠加波动方程偏移,本质上是一种叠前偏移方法.每给定一个斜率P,对经过叠前（动校正前）常规处理的地震记录中的各共接收点道集,沿直线t=τ+px进行倾斜叠加,就形成一个共接收点倾斜叠加剖面.对之进行波动方程偏移,该偏移剖面将代表地下真实构造.对一系列的p,我们可以得到一系列这样的偏移剖面.对它们作共接收点叠加,偏移叠加剖面的信噪比将超过水平叠加剖面.本文导出了在均匀、水平层状及非均匀介质条件下的共接收点倾斜叠加波动方程偏移算法.     

Eliminating 3D pre‐stack migration artefacts by 6D filtering

State‐of‐the‐art 3D seismic acquisition geometries have poor sampling along at least one dimension. This results in coherent migration noise that always contaminates pre‐stack migrated data, including high‐fold surveys, if prior‐to‐migration interpolation was not applied. We present a method for effective noise suppression in migrated gathers, competing with data interpolation before pre‐stack migration. The proposed technique is based on a dip decomposition of common‐offset volumes and a semblance‐type measure computation via offset for all constant‐dip gathers. Thus the processing engages six dimensions: offset, inline, crossline, depth, inline dip, and crossline dip. To reduce computational costs, we apply a two‐pass (4D in each pass) noise suppression: inline processing and then crossline processing (or vice versa). Synthetic and real‐data examples verify that the technique preserves signal amplitudes, including amplitude‐versus‐offset dependence, and that faults are not smeared.     

Estimation of geological dip and curvature from time‐migrated zero‐offset reflections in heterogeneous anisotropic media

Starting from a given time‐migrated zero‐offset data volume and time‐migration velocity, recent literature has shown that it is possible to simultaneously trace image rays in depth and reconstruct the depth‐velocity model along them. This, in turn, allows image‐ray migration, namely to map time‐migrated reflections into depth by tracing the image ray until half of the reflection time is consumed. As known since the 1980s, image‐ray migration can be made more complete if, besides reflection time, also estimates of its first and second derivatives with respect to the time‐migration datum coordinates are available. Such information provides, in addition to the location and dip of the reflectors in depth, also an estimation of their curvature. The expressions explicitly relate geological dip and curvature to first and second derivatives of reflection time with respect to time‐migration datum coordinates. Such quantitative relationships can provide useful constraints for improved construction of reflectors at depth in the presence of uncertainty. Furthermore, the results of image‐ray migration can be used to verify and improve time‐migration algorithms and can therefore be considered complementary to those of normal‐ray migration. So far, image‐ray migration algorithms have been restricted to layered models with isotropic smooth velocities within the layers. Using the methodology of surface‐to‐surface paraxial matrices, we obtain a natural extension to smooth or layered anisotropic media.     

输出道方式的共反射面元叠加方法Ⅱ--实践

CRS MZO方法是一种以输出道成像方式合成零偏移距剖面的共反射面元（Common Reflection Surface）叠加算法,它以完全不同的方式实现了CRS叠加.理论I已经对CRS MZO叠加方法的理论进行了详细介绍,本文进一步将CRS MZO方法用于对实际资料的处理.处理结果表明CRS MZO方法有效地改善了零偏移距剖面的成像质量,体现了CRS叠加理论的特点.在结合倾角分解策略消除了倾角歧视现象后,倾角分解CRS MZO方法完全能够用于处理实际数据,为得到高质量的零偏移距剖面提供了一个新的手段.     

Preserved travel‐time smoothing in orthorhombic media

Certain degree of smoothness of velocity models is required for most ray‐based migration and tomography. Applying conventional smoothing in model parameters results in offset‐dependent travel‐time errors for reflected events, which can be large even for small contrasts in model parameters between the layers. This causes the shift in both the depth and residual moveout of the migrated images. To overcome this problem in transversely isotropic medium with a vertical symmetry axis, the preserved travel‐time smoothing method was proposed earlier. We extend this method for orthorhombic media with and without azimuthal variation between the layers. We illustrate this method for a single interface between two orthorhombic layers and show that the smoothing‐driven errors in travel time are very small for practical application.