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.     

COHERENCY WEIGHTING—AN EFFECTIVE APPROACH TO THE SUPPRESSION OF LONG LEG MULTIPLES*

Long leg multiples can be suppressed by a method which provides an alternative to weighted common-depth-point stacking and multichannel stacking filtering. The suppression is achieved by coherency weighting whereby the time-dependent weighting factor decreases as the semblance of the multiple reflections increases. The algorithm of the method is described. Its efficiency is discussed in relation to the input data and results of its application to marine seismic data are presented. For practical application, the stacking velocity of the multiples has to be known. As the process is based on stacking velocities, different types of multiples can be handled, for instance water-bottom multiples or internal multiples. The parameter analysis shows that the degree of multiple suppression can easily be controlled by adapting the parameters of the procedure to the field conditions. During the suppression of multiples, the primaries are saved according to the moveout differences between the two. The non-linear behaviour of the process causes signal suppression and distortion effects, which have to be corrected by AGC normalization and low-pass filtering. Among the various applications available, only the suppression of long leg water-bottom multiples is treated here. The results show that their suppression on the basis of moveout differences is efficient even when standard length streamers are used in regions with water depth of up to 1500 m and more, if the stacking velocity of the primaries is about 10 to 20% higher than that of the multiples. Even if those parts of the primaries which are masked by the multiples are suppressed in the individual common-depth-point gathers by the procedure, the remaining primaries in the AGV stacked section are largely uncovered by the multiple suppression.     

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.     

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。     

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.     

基于保幅拉东变换的多次波衰减

为在去除多次波时有效保护地震一次反射波数据的AVO现象,给后续反演、解释提供准确的地震数据,本文提出了一种基于保幅拉东变换的多次波衰减方法,该方法是对常规抛物拉东变换的修改,把常规的稀疏拉东变换在拉东域分成两部分：一部分用于模拟零偏移距处的反射波能量,增加的另一部分用于模拟反射波振幅的AVO特性.该方法不仅考虑了反射波同相轴的形状,还考虑了反射波同相轴振幅幅度的变化,从而可把反射波信息进行有效转换,进而有利于多次波的消除,更好地恢复有效波的能量.在把地震数据由时间域转换到拉东域时,本文采用了IRLS算法实现保幅拉东算子的反演.模型数据和实际地震道集的试算分析表明,与常规拉东变换相比,保幅拉东变换在去除多次波的同时可有效保护一次反射波的AVO现象.     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.     

柴达木盆地低頻地震探測的“迴折”波和多次波

在柴达木盆地,利用低頻折射地震的方法,曾經得到許多不同类型的波,其中包括有: （i）沉积岩首波; （ii）基岩首波; （iii）大角度反射波; （iv）“迴折”波; （v）不同类型的多次波; （vi）地壳深界面的反射波. 本文专門討論“迴折”波和不同类型的多次波的性貭,以及辨认他們的主要标志;其他波的性貭,将在另文中討論.     

ESSAI D'UNE APPLICATION DE LA TRANSFORMATION DE KARHUNEN-LOÈVE AU TRAITEMENT SISMIQUE *

Multispectral recordings used for remote sensing are not without analogy with seismic records from CDP field set-ups. These seismic data may be regarded as “photographs’ of deep regions of the earth taken from various angles. The Karhunen-Loève (K.L.) transformation is commonly used for multispectral data processing, where it helps emphasize some features of remote sensing information. The same method may be applied to seismic data processing. Signal-to-noise ratio is improved on synthetic or field examples when K.L. transformation is applied instead of conventional CDP stacking. Residual statics seem to be diminished by a significant factor.     

THE SECTIONAL AUTO-CORRELOGRAM AND THE SECTIONAL RETRO-CORRELOGRAM *

The auto-correlation function of a seismic trace contains information on all the multiple reflection activity present in the trace. The interpretation of this information is facilitated by the arrangement of autocorrelation functions in cross-sectional form, in the manner of a normal record section. This is the concept of the Sectional Auto-Correlogram. Specifically, the Sectional Auto-Correlogram will. Show if the record section does not include significant multiples, thus allowing confident picking of the primary reflections. Show if the record section does include significant multiples, giving their travel times and inclinations (and, under certain circumstances, their reflection coefficients). Indicate by what process the multiples should be treated. Yield an authoritative measure of the success of a multiple-attenuating treatment. Delineate shallow horizons, even those whose primary reflections are too early to be recorded satisfactorily. Give the true travel time of a primary reflector, and the sign of its reflection coefficient. The Sectional Auto-Correlogram allows the study of primary reflectors by consideration of the multiples generated by them, and in this sense may be said to turn multiple reflections to advantage. Thus a primary reflection at a certain time is defined if we find that every reflection on the record is followed by a multiple after this certain time. Alternatively, a primary reflection at a certain time is defined if, after that certain time, we can find a repetition of the entire record. The Sectional Auto-Correlogram also has secondary uses in fault identification, crustal studies and weathering problems.     

PART I: THE SECTIONAL AUTO-CORRELOGRAM

The auto-correlation function of a seismic trace contains information on all the multiple reflection activity present in the trace. The interpretation of this information is facilitated by the arrangement of autocorrelation functions in cross-sectional form, in the manner of a normal record section. This is the concept of the Sectional Auto-Correlogram. Specifically, the Sectional Auto-Correlogram will… Show if the record section does not include significant multiples, thus allowing confident picking of the primary reflections. Show if the record section does include significant multiples, giving their travel times and inclinations (and, under certain circumstances, their reflection coefficients). Indicate by what process the multiples should be treated. Yield an authoritative measure of the success of a multiple-attenuating treatment. Delineate shallow horizons, even those whose primary reflections are too early to be recorded satisfactorily. Give the true travel time of a primary reflector, and the sign of its reflection coefficient. The Sectional Auto-Correlogram allows the study of primary reflectors by consideration of the multiples generated by them, and in this sense may be said to turn multiple reflections to advantage. Thus a primary reflection at a certain time is defined if we find that every reflection on the record is followed by a multiple after this certain time. Alternatively, a primary reflection at a certain time is defined if, after that certain time, we can find a repetition of the entire record. The Sectional Auto-Correlogram also has secondary uses in fault identification, crustal studies and weathering problems.     

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.     

NEW FILTERING METHODS WITH “VIBROSEIS”*

In order to obtain high resolution correlograms, it is of importance amongst other things to get reflection signals with large bandwidth. An advantage of the VIBROSEIS *** *** Trade Mark and Service book of the Continental Oil Company.
method is that the frequencies radiated by the vibrators can be matched to the transmission response of the subsurface involved. By choosing the right frequency range, the highest possible amplitude and most favourable form may be given to the reflection signals. In a reflection correlogram, individual signals cannot be considered in isolation. Signals of different origin are interfering with one another. They very often have different amplitudes, so that it may be desirable in many cases to filter out events of certain apparent velocity. With the VIBROSEIS method this may be achieved quite simply. All frequencies of the noise signal are uniformly suppressed. The advantage is that noise signals, e.g. refraction signals, which cannot be sufficiently attenuated by wavelength filtering, may be completely eliminated by this velocity filtering without affecting the bandwith of the desired signal. The total dynamic range of the tape recording can be used for the registration of wanted events. To perform this kind of filtering several vibrators are necessary in the field; each of them is controlled by an individual signal. There is an unavoidable error of static and dynamic corrections which causes the results of reflection measurements to deteriorate when using multiple coverage. High frequency components especially are seriously affected by destructive interference. This difficulty can be avoided by using a VIBROSEIS signal with high frequency component amplitudes supported. For the probability of error of corrections a normal distribution is assumed. A smoothed amplitude characteristic may be achieved after stacking. The amplitude characteristic of seismic devices is commonly reduced to about 100 cps bandwidth. For further improvement of resolution of VIBROSEIS correlograms it is necessary to apply special filtering methods. This is of particular interest when any kind of gain control is used to display weak events more clearly. With increasing amplification the sidelobes of the strong signals may reach the size of the weak events. In order to eliminate this effect, the amplitude characteristic of the VIBROSEIS signal is adjusted for optimum suppression of side-lobes.     

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.     

NEW FILTERING METHODS WITH “VIBROSEIS”*

In order to obtain high resolution correlograms, it is of importance amongst other things to get reflection signals with large bandwidth. An advantage of the VIBROSEIS *** *** Trade Mark and Service book of the Continental Oil Company.
method is that the frequencies radiated by the vibrators can be matched to the transmission response of the subsurface involved. By choosing the right frequency range, the highest possible amplitude and most favourable form may be given to the reflection signals. In a reflection correlogram, individual signals cannot be considered in isolation. Signals of different origin are interfering with one another. They very often have different amplitudes, so that it may be desirable in many cases to filter out events of certain apparent velocity. With the VIBROSEIS method this may be achieved quite simply. All frequencies of the noise signal are uniformly suppressed. The advantage is that noise signals, e.g. refraction signals, which cannot be sufficiently attenuated by wavelength filtering, may be completely eliminated by this velocity filtering without affecting the bandwith of the desired signal. The total dynamic range of the tape recording can be used for the registration of wanted events. To perform this kind of filtering several vibrators are necessary in the field; each of them is controlled by an individual signal. There is an unavoidable error of static and dynamic corrections which causes the results of reflection measurements to deteriorate when using multiple coverage. High frequency components especially are seriously affected by destructive interference. This difficulty can be avoided by using a VIBROSEIS signal with high frequency component amplitudes supported. For the probability of error of corrections a normal distribution is assumed. A smoothed amplitude characteristic may be achieved after stacking. The amplitude characteristic of seismic devices is commonly reduced to about 100 cps bandwidth. For further improvement of resolution of VIBROSEIS correlograms it is necessary to apply special filtering methods. This is of particular interest when any kind of gain control is used to display weak events more clearly. With increasing amplification the sidelobes of the strong signals may reach the size of the weak events. In order to eliminate this effect, the amplitude characteristic of the VIBROSEIS signal is adjusted for optimum suppression of side-lobes.     

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.     

数据自相关多次波偏移成像

在常规偏移方法中一般都需要压制地震数据中的多次波,仅利用一次波信息成像,把自由表面反射的多次波视为噪声,但是在多次波中也包含着地下结构信息,应该将其充分利用到成像中来.事实上,已经有不少成像方法试图利用多次波信息,但是大部分方法都需要对多次波进行预测.本文提出了基于傅里叶有限差分偏移算子的数据自相关偏移方法.在这种偏移方法中,对含有一次波和多次波的地震数据,分别进行下行和上行延拓,然后直接利用常规的互相关成像条件成像.由于波场延拓采用了傅里叶有限差分算子,其计算效率高,能够很好地对复杂介质中的地震数据进行延拓.在数值试验中,使用了一个含散射点的三层模型和Marmousi模型.合成数据测试结果表明,这种方法可以对更大范围的地下构造成像,比常规的只利用一次波的傅里叶有限差分法照明度更好,并且在浅层可以提供更高的分辨率.我们提出的数据自相关策略易于实现且避免了繁杂的多次波预测,这对于复杂地下构造成像可能有着重大意义.     

基于自适应变步长波场延拓的可控层分阶层间多次波模拟

地下低速夹层的存在导致地震数据中包含较强能量的层间多次波,有效识别和预测深部储层上覆地层产生的层间多次波是提高深部储层解释精度的重要环节,而准确模拟层间多次波是辅助识别地震数据中层间多次波的一种非常有效的方法.本文提出了一种基于自适应变步长波场延拓的可控地层分阶层间多次波模拟方法,该方法基于自适应变步长波场延拓,以递归循环的方式实现分阶层间多次波的模拟.通过对模型添加双重层位约束,可以模拟指定地层产生的各阶层间多次波.利用二维反周期延拓方法压制波场延拓的边界反射优于传统方法,例如吸收边界法.提出自适应变步长波场延拓技术,大大提升了波场模拟的效率.理论和数值例子表明,本文方法模拟的一次波和各阶层间多次波与常用的有限差分方法模拟结果具有很好的一致性,且克服了有限差分方法无法分阶模拟波场的不足,显著提升了层间多次波识别的效率.     

THE SUPPRESSION OF SURFACE MULTIPLES ON SEISMIC RECORDS*

A new approach is presented for the suppression of multiples reflected at the surface of a horizontally layered fluid or elastic medium, recorded at non-zero offsets from the source. The scheme used is to extract the effect of the free surface in the frequency-wavenumber domain and then to replace this surface by a non-reflecting boundary. The multiple suppression operator requires a detailed knowledge of the source time function and the elastic properties of the medium between the source and the surface. For a stratified fluid or a liquid layer overlying a stratified elastic medium, complete multiple suppression can be achieved with noise free data. If only the vertical component is available for an elastic medium an approximate approach may be used which removes most of the multiple energy. Good results may be achieved with this multiple suppression scheme in the presence of noise. The method is designed to be used before records are stacked in a CDP gather.