VELOCITY-STACK PROCESSING1

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.     

在成像空间中衰减多次波方法研究

在偏移后成像空间中的共成像点道集中可以对多次波进行衰减,对于给定的偏移速度模型,一次波与多次波在叠前偏移后的共成像点道集中具有不同的动校时差,这样我们就可以使用类似于偏移前衰减多次波的方法将一次波和多次波进行分离.本文在成像空间中应用抛物Radon变换分离多次波和有效波,由于每个共成像点道集都包含了复杂三维波场传播效应,所以本文方法具有处理三维数据和复杂地下构造的能力.相比于SRME以及传统Radon变换衰减多次波方法,本文方法能够在保持较小的计算量的同时,保证了衰减多次波的准确性.通过对模型数据试算和对实际数据的处理验证了本文方法在叠前时间偏移后衰减多次波的能力,并取得了很好的成像效果.     

LONG PERIOD SEA-FLOOR MULTIPLES AND THEIR SUPPRESSION*

Multiple sea-floor reflections in deep water often are not effectively suppressed by either CDP stacking nor standard predictive deconvolution methods. These methods fail because the reflection coefficient varies markedly with angle of incidence and also because of the variation of arrival time with offset and because of dip. For a reasonablly flat sea-floor, multiples of various orders and the primary sea-floor reflection which have all been reflected at nearly the same angle lie along a straight line through the origin in time-offset space. This line is called the “radial direction.” The multiples which lie along this line show a systematic relationship because they all experience the same water-bottom reflection effect. In other words, multiples behave in a stationary manner along the radial directions on multi-trace seismic records. A technique of multi-channel predictive deconvolution, called “Radial Multiple Suppression,” utilizes this aspect to design Wiener operators for the prediciton and suppression of water bottom multiples. The effectiveness of the technique is demonstrated by the study of field records, autocorrelations, velocity analyses, and stacked sections before and after Radial Multiple Suppression processing.     

海上多次波的联合衰减法

地震勘探尤其是海上地震勘探中存在着各类多次波,由于多次波的存在严重影响了速度分析、叠加、偏移成像等地震资料处理,海上多次波主要有全程多次波和层间多次两大类,为了压制海上不同类型的多次波,本文首先分析波场外推、预测反褶积和拉东变换衰减不同多次波的理论基础,然后联合采用这些方法,分别衰减全程多次波和层间多次波;即：首先对炮记录或者接收点记录进行波场外推,建立海底多次波模型,预测并减去全程多次波,然后利用预测反褶积衰减掉周期性明显的多次波,最后将数据转换到τ-p域,用拉冬变换根据同一时间多次波和有效波在速度等方面的差异,进一步分离层间多次波和剩余的全程多次波,并在该域中切除分离出的多次波,从而实现联合多次波衰减处理.通过对悉尼海区和里海等实际地震资料的处理证明,文提出的联合多次波衰减方法在海洋地震资料的处理中有着广泛的应用,联合衰减多次波处理流程具有快速、简洁、易于实现的特点,经处理后的地震资料有效信号损失小、保福性好的特点,有利于速度分析、叠加、叠前偏移等的后续处理工作.     

SLOPE DATA WATER-BOTTOM MULTIPLE ATTENUATION1

Methods for predicting and attenuating water-bottom multiples by wavefield extrapolation have been discussed by several investigators. Because these prediction methods operate on shot records, boundary conditions must be specified for every shot record. The approach presented operates in the common-offset plane; a model of expected water-bottom multiples is generated from the observed surface wavefield using a finite-difference wave-equation migration algorithm with an offset term. An accurate water-depth profile is required, but there is no restriction on the shape of the water bottom other than a dip limit of approximately 18–20°. In generating a multiple model, the water-bottom primary and each water-bottom multiple reflection of the observed surface wavefield are extrapolated to a higher order. Thus, the extrapolated water-bottom primary of the model is lined up with a water-bottom multiple in the data and each multiple in the model is lined up with a higher-order (or later) multiple in the data. Prestack multiple attenuation is achieved, for one offset at a time, by first adapting the model of expected multiples to the observed data and then subtracting the predicted multiple energy. An error-constrained adaptation algorithm is proposed in order to control instabilities. No assumptions are made about primary reflections and no subwater-bottom velocities are required. Computational efficiency of modelling and adaptation can be improved by applying this method only to near and intermediate offsets as the stacking process usually provides sufficient multiple attenuation at far offsets. A field data example demonstrates the potential of the proposed method for improving the primary-to-multiple ratio in prestack and post-stack data.     

基于波动方程预测和双曲Radon变换联合压制表面多次波

基于波动方程预测的表面多次波压制方法可处理复杂地下介质的地震资料,但计算成本较高.基于滤波的多次波压制方法计算效率较高,但其成功应用仅局限于一次波和多次波有明显时差差别的地震数据,对来自速度逆转等复杂介质数据则较难获得满意的压制效果.本文将波动方程预测的反馈迭代法和滤波法有效结合,采用GPU(图形处理器)和CPU协同并行加速计算粗略预测表面多次波,随后在双曲Radon域比较分析原始数据和预测的多次波,设计合理有效的Butterworth型自适应滤波器,滤出原始数据Radon域中的多次波能量,进行Radon反变换后,在时空域将多次波从原始数据中减去,得多次波压制结果.文中对理论模拟的单炮数据、复杂的SMAART模型以及实际地震数据进行了计算,结果表明,结合基于波动方程预测和双曲Radon变换的方法有效突破了两种方法各自的局限性,可高效高精度地压制复杂地下介质的表面多次波.     

多方向正交多项式变换压制多次波

提出一种基于Radon 变换和正交多项式变换的多方向正交多项式变换压制多次波方法.抛物Radon变换对不同曲率方向的同相轴叠加,根据速度差异区分一次波和多次波,但Radon反变换会损伤振幅特性,不利于AVO分析.多方向正交多项式变换在Radon变换(某一曲率方向的零阶特性)的基础上,利用正交多项式变换进一步分析同相轴的高阶多项式分布特性,用正交多项式谱表征同相轴AVO特性;根据一次波和多次波速度差异和同相轴能量分布特征实现多次波压制.该方法的优点是仅用一个曲率参数就可描述同相轴剩余时差参数,提高了一次波和多次波的剩余时差分辨率.实验结果表明,该方法可以有效压制多次波并保留一次波AVO特性.     

SIGNAL-TO-NOISE RATIO ENHANCEMENT IN MULTICHANNEL SEISMIC DATA VIA THE KARHUNEN-LOÉVE TRANSFORM*

The Karhunen-Loéve transform, which optimally extracts coherent information from multichannel input data in a least-squares sense, is used for two specific problems in seismic data processing. The first is the enhancement of stacked seismic sections by a reconstruction procedure which increases the signal-to-noise ratio by removing from the data that information which is incoherent trace-to-trace. The technique is demonstrated on synthetic data examples and works well on real data. The Karhunen-Loéve transform is useful for data compression for the transmission and storage of stacked seismic data. The second problem is the suppression of multiples in CMP or CDP gathers. After moveout correction with the velocity associated with the multiples, the gather is reconstructed using the Karhunen-Loéve procedure, and the information associated with the multiples omitted. Examples of this technique for synthetic and real data are presented.     

Multiple suppression by 2D filtering in the parabolic τ–p domain: a wave-equation-based method1

The filter for wave-equation-based water-layer multiple suppression, developed by the authors in the x-t, the linear τ-p, and the f-k domains, is extended to the parabolic τ-2 domain. The multiple reject areas are determined automatically by comparing the energy on traces of the multiple model (which are generated by a wave-extrapolation method from the original data) and the original input data (multiples + primaries) in τ-p space. The advantage of applying the data-adaptive 2D demultiple filter in the parabolic τ-p domain is that the waves are well separated in this domain. The numerical examples demonstrate the effectiveness of such a dereverberation procedure. Filtering of multiples in the parabolic τ-p domain works on both the far-offset and the near-offset traces, while the filtering of multiples in the f-k domain is effective only for the far-offset traces. Tests on a synthetic common-shot-point (CSP) gather show that the demultiple filter is relatively immune to slight errors in the water velocity and water depth which cause arrival time errors of the multiples in the multiple model traces of less than the time dimension (about one quarter of the wavelet length) of the energy summation window of the filter. The multiples in the predicted multiple model traces do not have to be exact replicas of the multiples in the input data, in both a wavelet-shape and traveltime sense. The demultiple filter also works reasonably well for input data contaminated by up to 25% of random noise. A shallow water CSP seismic gather, acquired on the North West Shelf of Australia, demonstrates the effectiveness of the technique on real data.     

STACKING FILTERS AND THEIR CHARACTERIZATION IN THE (f—k) DOMAIN *

The implementation of a stacking filter involves the filtering of each trace with an individual filter and the subsequent summing of all outputs. The actual position of a trace in space as well as certain simultaneous shifts of traces and filter components in time do not influence the process. The resulting output is consequently invariant to various arbitrary coordinate transformations. For a certain useful class of ensembles of non-linear moveout arrival times for signals a particular transformation can be found which transforms a given ensemble into one consisting only of straight lines. It is thus possible to reduce, for instance, the analysis of a stacking filter designed for hyperbola-like moveout curves to the analysis of a velocity filter with linear moveout curves. As the (f—k) transform is a very useful concept to describe a velocity filter, it can consequently be applied to characterize a stacking filter in regard to its performance on input signals with non-linear moveout.     

3D targeted multiple attenuation

Short-period multiple reflections pose a particular problem in the North Sea where predictive deconvolution is often only partially successful. The targeted multiple attenuation (TMA) algorithm comprises computation of the covariance matrix of preflattened prestack or post-stack seismic data, the determination of the dominating eigenvectors of the covariance matrix, and subtraction of the related eigenimages followed by reverse flattening. The main assumption made is that the flattened multiple reflections may be represented by the first eigenimage(s) which implies that the spatial amplitude variations of primaries and associated multiples are similar. This assumption usually limits the method to short-period multiple reflections. TMA is applicable post-stack or prestack to common-offset gathers. It is computationally fast, robust towards random noise, irregular geometry and spatial aliasing, and it preserves the amplitudes of primaries provided they are not parallel to the targeted multiples. Application of TMA to 3D wavefields is preferable because this allows a better discrimination between primaries and multiples. Real data examples show that the danger of partially removing primary energy can be reduced by improving the raw multiple model that is based on eigenimages, for example by prediction filtering.     

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.     

时距平面剩余时差选择加权叠加压制多次波方法及效果

一个CDP道集经动校正后,多次波仍存在剩余时差δt,它随炮检距呈抛物线变化。由δt的变化即可求出多次波剩余波数△K的分布规律。据此,可设计一个理想的叠加剩余波数响应,用于动校正后的CDP道集的加权叠加。在t～x平面选择δt,即可改变叠加剩余波数响应,从而改变各道的加权系数,实现最佳压制多次波的效果。     

Multiple attenuation using λ-f domain high-resolution Radon transform

The parabolic Radon transform has been widely used in multiple attenuation. To further improve the accuracy and efficiency of the Radon transform, we developed the 2- fdomain high-resolution Radon transform based on the fast and modified parabolic Radon transform presented by Abbad. The introduction of a new variable 2 makes the transform operator frequency-independent. Thus, we need to calculate the transform operator and its inverse operator only once, which greatly improves the computational efficiency. Besides, because the primaries and multiples are distributed on straight lines with different slopes in the 2-fdomain, we can easily choose the filtering operator to suppress the multiples. At the same time, the proposed method offers the advantage of high-resolution Radon transform, which can greatly improve the precision of attenuating the multiples. Numerical experiments suggest that the multiples are well suppressed and the amplitude versus offset characteristics of the primaries are well maintained. Real data processing results further verify the effectiveness and feasibility of the method.     

广义Radon变换与叠前地震数据处理

在本文中,首先讨论了与几种地震层析成像对应的Radon变换公式,并导出了叠前地震记录的数学模型.在分析叠前地震记录与广义Radon变换的关系的基础上,讨论了速度分析、滤波、动校正、叠加等地震数据处理的数学物理意义.为展示广义Radon变换在地震数据处理中的应用,给出了用于滤波和消除多次波的方法及算例.     

多次波分阶逆时偏移成像

本文深入分析了多次波逆时偏移的成像原理和串扰假象产生机制,并提出了多次波分阶逆时偏移策略,即首先应用自由界面多次波衰减方法对原始炮集记录中的多次波进行剔除得到一次波记录,然后应用一次波记录预测获得各阶多次波记录,最后将各阶多次波记录分别进行逆时偏移成像.模型实验结果表明,多次波分阶逆时偏移其各阶多次波成像剖面均可对真实界面正确成像且其能够有效压制串扰假象,其中一阶多次波逆时偏移剖面的成像精度最高,其深层成像质量明显优于常规多次波逆时偏移.     

表面多次波最小二乘逆时偏移成像

使用相同的炮记录,多次波偏移能提供比反射波偏移更广的地下照明和更多的地下覆盖但是同时产生很多的串声噪声.相比传统逆时偏移,最小二乘逆时偏移反演的反射波成像结果具有更高的分辨率和更均衡的振幅.我们主要利用最小二乘逆时偏移压制多次波偏移产生的串声噪声.多次波最小二乘逆时偏移通常需要一定的迭代次数以较好地消除串声噪声.若提前将一阶多次波从所有阶数的多次波中过滤出来,使用相同的迭代次数,一阶多次波的最小二乘逆时偏移能够得到具有更高信噪比的成像剖面,而且能够提供与多次波最小二乘逆时偏移相似的有效地下结构成像.     

Migration methods for imaging different-order multiples

Multiples contain valuable information about the subsurface, and if properly migrated can provide a wider illumination of the subsurface compared to imaging with VSP primary reflections. In this paper we review three different methods for migrating multiples. The first method is model-based, and it is more sensitive to velocity errors than primary migration; the second method uses a semi-natural Green's function for migrating multiples, where part of the traveltimes are computed from the velocity model, and part of the traveltimes (i.e., natural traveltimes) are picked from the data to construct the imaging condition for multiples; the third method uses cross-correlation of traces. The last two methods are preferred in the sense that they are significantly less sensitive to velocity errors and statics because they use “natural data” to construct part of the migration imaging conditions. Compared with the interferometric (i.e., crosscorrelation) imaging method the semi-natural Green's function method is more computationally efficient and is sometimes less prone to migration artifacts. Numerical tests with 2-D and 3-D VSP data show that a wider subsurface coverage, higher-fold and more balanced illumination of the subsurface can be achieved with multiple migration compared with migration of primary reflections only. However, there can be strong interference from multiples with different orders or primaries when multiples of high order are migrated. One possible solution is to filter primaries and different orders of multiples before migration, and another possible solution is least squares migration of all events. A limitation of multiple migration is encountered for subsalt imaging. Here, the multiples must pass through the salt body more than twice, which amplifies the distortion of the image.     

Utilization of multiple scattering: the next big step forward in seismic imaging

Surface removal and internal multiple removal are explained by recursively separating the primary and multiple responses at each depth level with the aid of wavefield prediction error filtering. This causal removal process is referred to as “data linearization.” The linearized output (primaries only) is suitable for linear migration algorithms. Next, a summary is given on the migration of full wavefields (primaries + multiples) by using the concept of secondary sources in each subsurface gridpoint. These secondary sources are two‐way and contain the gridpoint reflection and the gridpoint transmission properties. In full wavefield migration, a local inversion process replaces the traditional linear imaging conditions. Finally, Marchenko redatuming is explained by iteratively separating the full wavefield response from above a new datum and the full wavefield response from below a new datum. The redatuming output is available for linear migration (Marchenko imaging) or, even better, for full wavefield migration. Linear migration, full wavefield migration, and Marchenko imaging are compared with each other. The principal conclusion of this essay is that multiples should not be removed, but they should be utilized, yielding two major advantages: (i) illumination is enhanced, particularly in the situation of low signal‐to‐noise primaries; and (ii) both the upper side and the lower side of reflectors are imaged. It is also concluded that multiple scattering algorithms are more transparent if they are formulated in a recursive depth manner. In addition to transparency, a recursive depth algorithm has the flexibility to enrich the imaging process by inserting prior geological knowledge or by removing numerical artefacts at each depth level. Finally, it is concluded that nonlinear migration algorithms must have a closed‐loop architecture to allow successful imaging of incomplete seismic data volumes (reality of field data).     

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 (V_P/V_S) 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.