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1.
Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t2(x2) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (VP0 and VS0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (VP0, VS0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves. 相似文献
2.
提出三维Kirchhoff叠前时间偏移角度域共像点道集的改进算法,克服传统角度求取算法局限,可计算相对倾斜地层法线入射角;与Kirchhoff直射线叠前时间偏移求角度算法相比,本文方法考虑射线弯曲效应,包含层速度,角度范围加大,更接近真实入射角;计算走时采取弯曲射线或者适应线性横向变速介质的非对称走时等算法,角度道集在大角度处得到拉平;采用相对保幅的权因子以及覆盖次数校正技术,有利于叠前AVA反演.模型测试结果表明：叠前时间偏移角度道集,相对CMP、CRP所转化角度道集,更准确反应AVA效应;实际三维数据测试表明本文方法可以提供品质优良的角度道集,适用于AVA分析、反演,提高叠前反演分辨率. 相似文献
3.
R.-G. Ferber 《Geophysical Prospecting》1994,42(2):99-112
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. 相似文献
4.
ZDOAN YILMAZ 《Geophysical Prospecting》1989,37(4):357-382
A conventional velocity-stack gather consists of constant-velocity CMP-stacked traces. It emphasizes the energy associated with the events that follow hyperbolic traveltime trajectories in the CMP gather. Amplitudes along a hyperbola on a CMP gather ideally map onto a point on a velocity-stack gather. Because a CMP gather only includes a cable-length portion of a hyperbolic traveltime trajectory, this mapping is not exact. The finite cable length, discrete sampling along the offset axis and the closeness of hyperbolic summation paths at near-offsets cause smearing of the stacked amplitudes along the velocity axis. Unless this smearing is removed, inverse mapping from velocity space (the plane of stacking velocity versus two-way zero-offset time) back to offset space (the plane of offset versus two-way traveltime) does not reproduce the amplitudes in the original CMP gather. The gather resulting from the inverse mapping can be considered as the model CMP gather that contains only the hyperbolic events from the actual CMP gather. A least-squares minimization of the energy contained in the difference between the actual CMP gather and the model CMP gather removes smearing of amplitudes on the velocity-stack gather and increases velocity resolution. A practical application of this procedure is in separation of multiples from primaries. A method is described to obtain proper velocity-stack gathers with reduced amplitude smearing. The method involves a t2-stretching in the offset space. This stretching maps reflection amplitudes along hyperbolic moveout curves to those along parabolic moveout curves. The CMP gather is Fourier transformed along the stretched axis. Each Fourier component is then used in the least-squares minimization to compute the corresponding Fourier component of the proper velocity-stack gather. Finally, inverse transforming and undoing the stretching yield the proper velocity-stack gather, which can then be inverse mapped back to the offset space. During this inverse mapping, multiples, primaries or all of the hyperbolic events can be modelled. An application of velocity-stack processing to multiple suppression is demonstrated with a field data example. 相似文献
5.
Velocity model updating in prestack Kirchhoff time migration for PS converted waves: Part I – Theory
A velocity model updating approach is developed based on moveout analysis of the diffraction curve of PS converted waves in prestack Kirchhoff time migration. The diffraction curve can be expressed as a product of two factors: one factor depending on the PS converted‐wave velocity only, and the other factor depending on all parameters. The velocity‐dependent factor represents the hyperbolic behaviour of the moveout and the other is a scale factor that represents the non‐hyperbolic behaviour of the moveout. This non‐hyperbolic behaviour of the moveout can be corrected in prestack Kirchhoff time migration to form an inverse normal‐moveout common‐image‐point gather in which only the hyperbolic moveout is retained. This hyperbolic moveout is the moveout that would be obtained in an isotropic equivalent medium. A hyperbolic velocity is then estimated from this gather by applying hyperbolic moveout analysis. Theoretical analysis shows that for any given initial velocity, the estimated hyperbolic velocity converges by an iterative procedure to the optimal velocity if the velocity ratio is optimal or to a value closer to the optimal velocity if the velocity ratio is not optimal. The velocity ratio (VP/VS) has little effect on the estimation of the velocity. Applying this technique to a synthetic seismic data set confirms the theoretical findings. This work provides a practical method to obtain the velocity model for prestack Kirchhoff time migration. 相似文献
6.
7.
Conventional seismic data processing methods based on post‐stack time migration have been playing an important role in coal exploration for decades. However, post‐stack time migration processing often results in low‐quality images in complex geological environments. In order to obtain high‐quality images, we present a strategy that applies the Kirchhoff prestack time migration (PSTM) method to coal seismic data. In this paper, we describe the implementation of Kirchhoff PSTM to a 3D coal seam. Meanwhile we derive the workflow of 3D Kirchhoff PSTM processing based on coal seismic data. The processing sequence of 3D Kirchhoff PSTM includes two major steps: 1) the estimation of the 3D root‐mean‐square (RMS) velocity field; 2) Kirchhoff prestack time migration processing. During the construction of a 3D velocity model, dip moveout velocity is served as an initial migration velocity field. We combine 3D Kirchhoff PSTM with the continuous adjustment of a 3D RMS velocity field by the criteria of flattened common reflection point gathers. In comparison with post‐stack time migration, the application of 3D Kirchhoff PSTM to coal seismic data produces better images of the coal seam reflections. 相似文献
8.
TH. KREY 《Geophysical Prospecting》1976,24(1):91-111
It is well known that interval velocities can be determined from common-reflection-point moveout times. However, the mathematics becomes complicated in the general case of n homogeneous layers with curved interfaces dipping in three dimensions. In this paper the problem is solved by mathematical induction using the second power terms only of the Taylor series which represents the moveout time as a function of the coordinate differences between shot and geophone points. Moreover, the zero-offset reflection times of the nth interface in a certain area surrounding the point of interest have to be known. The n—I upper interfaces and interval velocities are known too on account of the mathematical induction method applied. Thus, the zero-offset reflection raypath of the nth interface can be supposed to be known down to the intersection with the (n—1)th interface. The method applied consists mainly in transforming the second power terms of the moveout time from one interface to the next one. This is accomplished by matrix algebra. Some special cases are discussed as e.g. uniform strike and small curvatures. 相似文献
9.
针对传统Kirchhoff叠前时间偏移方法的一些不足,以及振幅随入射角、方位角变化(AVA/AVAZ)分析的需要,本文提出一种基于射线理论的三维叠前时间偏移角度域成像方法.它通过横向均匀介质中稳健的射线追踪建立单程波走时和传播角度的数值表,然后在此基础上估算反射波双程走时以及在界面处传播的方位角和入射角,最后基于脉冲响应叠加原理获得三维构造图像和方位\|角度域共成像点道集.与传统方法不同之处在于,上述过程均考虑了地震波在垂向变速介质中的射线弯曲效应和三维传播特征,有利于准确提取随入射角和方位角变化的振幅和时差信息.理论模型合成数据和实际地震资料测试结果展示了方法的优越性与实用性. 相似文献
10.
H. JAKUBOWICZ 《Geophysical Prospecting》1990,38(3):221-245
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. 相似文献
11.
Emil Blias 《Geophysical Prospecting》2009,57(3):323-341
Lateral velocity changes (velocity anomalies) in the overburden may cause significant oscillations in normal moveout velocities. Explicit analytical moveout formulas are presented and provide a direct explanation of these lateral fluctuations and other phenomena for a subsurface with gentle deep structures and shallow overburden anomalies. The analytical conditions for this have been derived for a depth-velocity model with gentle structures with dips not exceeding 12°. The influence of lateral interval velocity changes and curvilinear overburden velocity boundaries can be estimated and analysed using these formulas. An analytical approach to normal moveout velocity analysis in a laterally inhomogeneous medium provides an understanding of the connection between lateral interval velocity changes and normal moveout velocities. In the presence of uncorrected shallow velocity anomalies, the difference between root-mean-square and stacking velocity can be arbitrarily large to the extent of reversing the normal moveout function around normal incidence traveltimes. The main reason for anomalous stacking velocity behaviour is non-linear lateral variations in the shallow overburden interval velocities or the velocity boundaries.
A special technique has been developed to determine and remove shallow velocity anomaly effects. This technique includes automatic continuous velocity picking, an inversion method for the determination of shallow velocity anomalies, improving the depth-velocity model by an optimization approach to traveltime inversion (layered reflection tomography) and shallow velocity anomaly replacement. Model and field data examples are used to illustrate this technique. 相似文献
A special technique has been developed to determine and remove shallow velocity anomaly effects. This technique includes automatic continuous velocity picking, an inversion method for the determination of shallow velocity anomalies, improving the depth-velocity model by an optimization approach to traveltime inversion (layered reflection tomography) and shallow velocity anomaly replacement. Model and field data examples are used to illustrate this technique. 相似文献
12.
Stacking velocity V C2, vertical velocity ratio γ 0, effective velocity ratio γ eff, and anisotropic parameter χ eff are correlated in the PS-converted-wave (PS-wave) anisotropic prestack Kirchhoff time migration (PKTM) velocity model and are thus difficult to independently determine. We extended the simplified two-parameter (stacking velocity V C2 and anisotropic parameter k eff) moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter (stacking velocity V C2, vertical velocity ratio γ 0, effective velocity ratio γ eff, and anisotropic parameter k eff) PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified two-parameter moveout equation. In the proposed method, first, the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters; then, the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration. The vertical velocity ratio γ 0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration. The initial effective velocity ratio γ eff is calculated using the Thomsen (1999) equation in combination with the P-wave velocity analysis; ultimately, the final velocity model of the effective velocity ratio γ eff is obtained by percentage scanning migration. This method simplifies the PS-wave parameter estimation in high-quality imaging, reduces the uncertainty of multiparameter estimations, and obtains good imaging results in practice. 相似文献
13.
苏北大陆科学钻探靶区深反射地震的叠前深度偏移 总被引：4，自引：2，他引：2
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。 相似文献
14.
基于共炮偏移的AVO反演 总被引：8，自引：0，他引：8
常规AVO多是利用CMP道集的振幅进行反演。主要有三个方面影响其精度:首先,CMP道集假设地下为水平层状介质,但是实际地下介质多为倾斜地层,地层倾角越大CMP道集的振幅所反映地下介质的位置与实际位置差距就越大。其次,NMO、DMO和反褶积等常规处理流程,都会造成振幅值失真。第三,反演所用的反射系数公式是与入射角有关的量,而欲从CMP道集得到准确的入射角与振幅之间的对应关系,则十分困难。波动方程叠前深度偏移除对复杂介质和陡倾角地层具有较强的成像能力,还可以最大限度的减少常规处理所带来的误差并使振幅归位。本文综合了保幅偏移、角度道集提取以及AVO反演等前人的工作,提出直接从炮集数据反演AVO属性的方法,以期显著减少上述三个因素对AVO反演精度的影响。 相似文献
15.
Investigating a time‐shift extended imaging condition in a Kirchhoff pre‐stack depth migration algorithm 
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下载免费PDF全文 Gareth Shane O'Brien Sean Joseph Delaney Michael Igoe John Doherty Andrew Colhoun 《Geophysical Prospecting》2018,66(4):688-706
Extracting true amplitude versus angle common image gathers is one of the key objectives in seismic processing and imaging. This is achievable to different degrees using different migration techniques (e.g., Kirchhoff, wavefield extrapolation, and reverse time migration techniques) and is a common tool in exploration, but the costs can vary depending on the selected migration algorithm and the desired accuracy. Here, we investigate the possibility of combining the local‐shift imaging condition, specifically the time‐shift extended imaging condition, for angle gathers with a Kirchhoff migration. The aims are not to replace the more accurate full‐wavefield migration but to offer a cheaper alternative where ray‐based methods are applicable and to use Kirchhoff time‐lag common image gathers to help bridge the gap between the traditional offset common image gathers and reverse time migration angle gathers; finally, given the higher level of summation inside the extended imaging migration, we wish to understand the impact on the amplitude versus angle response. The implementation of the time‐shift imaging condition along with the computational cost is discussed, and results of four different datasets are presented. The four example datasets, two synthetic, one land acquisition, and a marine dataset, have been migrated using a Kirchhoff offset method, a Kirchhoff time‐shift method, and, for comparison, a reverse time migration algorithm. The results show that the time‐shift imaging condition at zero time lag is equivalent to the full offset stack as expected. The output gathers are cleaner and more consistent in the time‐lag‐derived angle gathers, but the conversion from time lag to angle can be considered a post‐processing step. The main difference arises in the amplitude versus offset/angle distribution where the responses are different and dramatically so for the land data. The results from the synthetics and real data show that a Kirchhoff migration with an extended imaging condition is capable of generating subsurface angle gathers. The same disadvantages with a ray‐based approach will apply using the extended imaging condition relative to a wave equation angle gather solution. Nevertheless, using this approach allows one to explore the relationship between the velocity model and focusing of the reflected energy, to use the Radon transformation to remove noise and multiples, and to generate consistent products from a ray‐based migration and a full‐wave equation migration, which can then be interchanged depending on the process under study. 相似文献
16.
Tiago A. Coimbra Jorge H. Faccipieri Dany S. Rueda Martin Tygel 《Studia Geophysica et Geodaetica》2016,60(3):500-530
Since the early days of seismic processing, time migration has proven to be a valuable tool for a number of imaging purposes. Main motivations for its widespread use include robustness with respect to velocity errors, as well as fast turnaround and low computation costs. In areas of complex geology, in which it has well-known limitations, time migration can still be of value by providing first images and also attributes, which can be of much help in further, more comprehensive depth migration. Time migration is a very close process to common-midpoint (CMP) stacking and, more recently, to zero-offset commonreflection- surface (CRS) stacking. In fact, Kirchhoff time migration operators can be readily formulated in terms of CRS parameters. In the nineties, several studies have shown advantages in the use of common-reflection-point (CRP) traveltimes to replace conventional CMP traveltimes for a number of stacking and migration purposes. In this paper, we follow that trend and introduce a Kirchhoff-type prestack time migration and velocity analysis algorithm, referred to as CRP time migration. The algorithm is based on a CRP operator together with optimal apertures, both computed with the help of CRS parameters. A field-data example indicates the potential of the proposed technique. 相似文献
17.
Seyyed Ali Fa’al Rastegar Abdolrahim Javaherian Naser Keshavarz Farajkhah Mehrdad Soleimani Monfared Abbas Zarei 《应用地球物理》2016,13(2):353-363
We modified the common-offset–common-reflection-surface (COCRS) method to attenuate ground roll, the coherent noise typically generated by a low-velocity, low-frequency, and high-amplitude Rayleigh wave. The COCRS operator is based on hyperbolas, thus it fits events with hyperbolic traveltimes such as reflection events in prestack data. Conversely, ground roll is linear in the common-midpoint (CMP) and common-shot gathers and can be distinguished and attenuated by the COCRS operator. Thus, we search for the dip and curvature of the reflections in the common-shot gathers prior to the common-offset section. Because it is desirable to minimize the damage to the reflection amplitudes, we only stack the multicoverage data in the ground-roll areas. Searching the CS gathers before the CO section is another modification of the conventional COCRS stacking. We tested the proposed method using synthetic and real data sets from western Iran. The results of the ground-roll attenuation with the proposed method were compared with results of the f–k filtering and conventional COCRS stacking after f–k filtering. The results show that the proposed method attenuates the aliased and nonaliased ground roll better than the f–k filtering and conventional CRS stacking. However, the computation time was higher than other common methods such as f–k filtering. 相似文献
18.
In the western coal-mining area of Ruhrkohle AG, reflection seismic prospecting for the Carboniferous coal measures is severely impaired by structures with halokinetic features. These structures make the interface between Mesozoic and Paleozoic layers, i.e., the top of Zechstein in general, very rugged. Unfortunately the velocity contrast at this interface is very high in that area, the ratio of velocities being 1.5 to 2.0. Therefore, migration and stacking become a problem. Three types of migration are presented:
- 1 (f, x)-time-migration with vertical time-to-depth conversion as a second step.
- 2 Kirchhoff migration down to a level determined approximately by the highest points of the top of Paleozoics, i.e., 0.35 s, and Kirchhoff-downward continuation for all times exceeding 0.35 s. Intermediate static corrections for these latter times with subsequent (f, k)-time-migration and final vertical time-to-depth conversion.
- 3 Direct depth migration in the (f, x)-domain using three interval velocities.
19.
Amplitude versus offset concepts can be used to generate weighted stacking schemes (here called geo-stack) which can be used in an otherwise standard seismic data processing sequence to display information about rock properties. The Zoeppritz equations can be simplified and several different approximations appear in the literature. They describe the variation of P-wave reflection coefficients with the angle of incidence of a P-wave as a function of the P-wave velocities, the S-wave velocities and the densities above and below an interface. Using a smooth, representative interval velocity model (from boreholes or velocity analyses) and assuming no dip, the angle of incidence can be found as a function of time and offset by iterative ray tracing. In particular, the angle of incidence can be computed for each sample in a normal moveout corrected CMP gather. The approximated Zoeppritz equation can then be fitted to the amplitudes of all the traces at each time sample of the gather, and certain rock properties can be estimated. The estimation of the rock properties is achieved by the application of time- and offset-variant weights to the data samples before stacking. The properties which can be displayed by geo-stack are: P-wave reflectivity (or true zero-offset reflectivity), S-wave reflectivity, and the reflectivity of P-wave velocity divided by S-wave velocity (or ‘pseudo-Poisson's ratio reflectivity’). If assumptions are made about the relation between P-wave velocity and S-wave velocity for water-bearing clastic silicate rocks, then it is possible to create a display which highlights the presence of gas. 相似文献
20.
A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P‐wave moveout has to be combined with other information (e.g. borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden creates the dependence of P‐wave reflection data on all three relevant parameters (the vertical velocity VP0 and the Thomsen coefficients ε and δ) and, therefore, may help to determine the depth scale of the velocity field. Here, we propose a tomographic algorithm designed to invert NMO ellipses (obtained from azimuthally varying stacking velocities) and zero‐offset traveltimes of P‐waves for the parameters of homogeneous VTI layers separated by either plane dipping or curved interfaces. For plane non‐intersecting layer boundaries, the interval parameters cannot be recovered from P‐wave moveout in a unique way. Nonetheless, if the reflectors have sufficiently different azimuths, a priori knowledge of any single interval parameter makes it possible to reconstruct the whole model in depth. For example, the parameter estimation becomes unique if the subsurface layer is known to be isotropic. In the case of 2D inversion on the dip line of co‐orientated reflectors, it is necessary to specify one parameter (e.g. the vertical velocity) per layer. Despite the higher complexity of models with curved interfaces, the increased angle coverage of reflected rays helps to resolve the trade‐offs between the medium parameters. Singular value decomposition (SVD) shows that in the presence of sufficient interface curvature all parameters needed for anisotropic depth processing can be obtained solely from conventional‐spread P‐wave moveout. By performing tests on noise‐contaminated data we demonstrate that the tomographic inversion procedure reconstructs both the interfaces and the VTI parameters with high accuracy. Both SVD analysis and moveout inversion are implemented using an efficient modelling technique based on the theory of NMO‐velocity surfaces generalized for wave propagation through curved interfaces. 相似文献