改进的多道预测算子压制浅水多次波方法

在浅水情况下,由于观测数据中缺少近偏移距信息,水层多次波的压制面临挑战.利用多道预测算子压制水层多次波是浅水环境下压制多次波的重要方法之一,这种方法先从输入数据中估计出多道预测算子,再将预测算子和输入数据做褶积预测出水层相关多次波.然而,估计的多道预测算子很容易受噪声污染,从而影响多次波模型的精度.所以,我们提出了改进的多道预测算子压制浅水多次波方法.该方法先从数据中估计出多道预测算子,并利用估计的算子构建出精确的水层模型;然后,通过计算算子的走时信息、估计振幅信息、合成新算子三个步骤来修正原始的多道预测算子.修正的算子不仅不受噪声影响,还含有精确的走时信息、可靠的振幅信息;最后,该方法用修正的算子来预测多次波,并结合自适应相减,将预测的多次波从输入数据中去除.通过合成数据和实际资料的验证表明,相比于原始的多道预测算子压制多次波方法,改进的方法能够取得更好的压制效果.     

EFFICIENT MULTICHANNEL FILTERING OF SEISMIC DATA1

Multichannel filters are used to eliminate coherent noise from surface seismic data, for wavefield separation from VSP stacks, and for signal enhancement. Their success generally depends on the choice of the filter parameters and the domain of application. Multichannel filters can be applied to shots (monitors), common-receiver traces, CDP traces and stacked sections. Cascaded applications in these domains are currently performed in the seismic industry for better noise suppression and for signal enhancement. One-step shot-domain filtering is adequate for some applications. However, in practice, cascaded applications in shot-and common-receiver domains usually give better results when the S/N ratio is low. Multichannel filtering after stacking (especially after repeated applications in shot and/or receiver domains) may create undesirable results such as artificial continuations, or smearing and smoothing of small features such as small throw faults and fine stratigraphic details. Consequently, multichannel filtering after stacking must be undertaken with the utmost care and occasionally only as a last resort. Multichannel filters with fan-shaped responses (linear moveout filters) should be applied after NMO correction. These are the filters commonly used in the seismic industry where they have such names as velocity filters, moveout filters, f-k filters and coherency filters. Filtering before NMO correction may result in break-up and flattening especially of those shallow reflection events with relatively higher curvatures and diffractions. NMO correction is needed prior to wavefield separation from VSP stacks for the same practical reasons outlined above whenever source-receiver offsets are involved. Creation of artificial lineup and smearing at the outputs of multichannel filters is presently the common practical concern. Optimum multichannel filters with well-defined pass, reject and transition bands overcome the latter problems when applied before stacking and after NMO correction. The trace dimension of these filters must be kept small to avoid such lineups and the smoothing of small structures. Good results can be obtained with only five traces, but seven traces seems to be a better compromise both in surface and well seismic applications. The so-called f-k filtering and τ-p domain filtering are no exceptions to the above practical considerations. Residual static computations after multichannel filtering also need special consideration. Since multichannel filtering improves spatial continuity, residual static algorithms using local correlation, i.e. nonsurface-consistent algorithms, may be impractical especially after multichannel filtering.     

GUIDED LOW-FREQUENCY NOISE FROM AIRGUN SOURCES*

The presence of the water layer in marine seismic prospecting provides an effective waveguide for acoustic energy trapped between the sea-bed and the sea-surface. This energy persists to large ranges and can be the dominant early feature on far-offset traces. On airgun records, there is commonly a lower frequency set of arrivals following the water-trapped waves. These arrivals are not as obvious with higher frequency watergun sources. By using a combination of intercept-time/slowness (τ—p) mapping on observational data and theoretical modelling, we are able to identify the origin of the events. If a very rapid increase in a seismic wavespeed occurs beneath the sea-bed sediments, a new waveguide is formed bounded by the sea surface and this transition zone. The low frequency waves are principally guided within this thicker waveguide. Numerical filtering in the τ—p domain followed by trace reconstruction is very effective in removing the low frequency noise.     

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.     

FREQUENCY WAVENUMBER APPROACH OF THE τ-p TRANSFORM: SOME APPLICATIONS IN SEISMIC DATA PROCESSING*

The τ-p transform is an invertible transformation of seismic shot records expressed as a function of time and offset into the τ (intercept time) and p (ray parameter) domain. The τ-p transform is derived from the solution of the wave equation for a point source in a three-dimensional, vertically non-homogeneous medium and therefore is a true amplitude process for the assumed model. The main advantage of this transformation is to present a point source shot record as a series of plane wave experiments. The asymptotic expansion of this transformation is found to be useful in reflection seismic data processing. The τ-p and frequency-wavenumber (or f-k) processes are closely related. Indeed, the τ-p process embodies the frequency-wavenumber transformation, so the use of this technique suffers the same limitations as the f-k technique. In particular, the wavefield must be sampled with sufficient spatial density to avoid wavenumber aliasing. The computation of this transform and its inverse transform consists of a two-dimensional Fast Fourier Transform followed by an interpolation, then by an inverse-time Fast Fourier Transform. This technique is extended from a vertically inhomogeneous three-dimensional medium to a vertically and laterally inhomogeneous three-dimensional medium. The τ-p transform may create artifacts (truncation and aliasing effects) which can be reduced by a finer spatial density of geophone groups by a balancing of the seismic data and by a tapering of the extremities of the seismic data. The τ-p domain is used as a temporary domain where the attack of coherent noise is well addressed; this technique can be viewed as ‘time-variant f-k filtering’. In addition, the process of deconvolution and multiple suppression in the τ-p domain is at least as well addressed as in the time-offset domain.     

A LAYER-STRIPPING TECHNIQUE FOR THE SUPPRESSION OF WATER-BOTTOM MULTIPLE REFLECTIONS*

A new method to suppress water-bottom multiples (water-bottom reverberations) uses the fact that in the domain of intercept time and ray parameter (τ–p domain) the water-bottom reverberations are strictly periodical for a horizontal flat sea bottom. Using this property a comb filter can be designed. The window of the filter should be approximately equal to the duration of a source pulse. The algorithm finds the maximum of the periodical energy throughout the τ–p domain and then designs the comb filter which eliminates the water bottom reverberations from each trace in the τ– p domain. This process can be repeated for higher order reverberations. Finally the τ–p domain with attenuated multiples is transformed back to the conventional x -- t space. The method is illustrated on a variety of synthetic data and on a set of real marine CMP data acquired in the North Sea near the Norwegian shore.     

Multiple attenuation: coping with the spatial truncation effect in the Radon transform domain

The limited size of the spatial aperture of a seismic gather causes multiple- and primary-reflection energy to spread out and cross-hatch the image of the parabolic Radon transform. This spatial truncation effect devastatingly impairs the separation of primary and multiple reflections in a Radon demultiple process. It is difficult to suppress the spatial truncation effect completely, but it is at least possible to model or to identify implicitly such an effect and then to design automatically a mute function, i.e. a 2D mask filter in the Radon transform domain. This is referred to as the adaptive surgical mute scheme. By using this scheme, it is possible to extract the multiple-reflection energy cleanly from the Radon transform image, so that the multiple reflections can be more effectively attenuated. It is also possible to preserve the diffused primary-reflection energy after the surgical mute, so that the final multiple-attenuated seismic profile is amplitude-preserved.     

混合域高分辨率抛物Radon变换及在衰减多次波中的应用

高分辨率Radon变换存在计算效率和分辨率不能兼得的困境.时间域算法可以获得很高的分辨率,但计算效率非常低;频率域算法具有良好计算效率,但分辨率不理想.为此发展了混合域高分辨率抛物Radon变换,即对频率域抛物Radon变换引入时变的稀疏权.本文给出了一种新的混合域高分辨率抛物Radon变换实现方法,并将该算法应用于叠前数据衰减多次波.文中给出了Radon变换和衰减多次波的流程.理论和实际数据算例表明本文方法既有较高的分辨率又有很高的计算效率.     

A FILTER,DELAY AND SPREAD TECHNIQUE FOR 3D DMO1

The calculation of dip moveout involves spreading the amplitudes of each input trace along the source-receiver axis followed by stacking the results into a 3D zero-offset data cube. The offset-traveltime (x–t) domain integral implementation of the DMO operator is very efficient in terms of computation time but suffers from operator aliasing. The log-stretch approach, using a logarithmic transformation of the time axis to force the DMO operator to be time invariant, can avoid operator aliasing by direct implementation in the frequency-wavenumber (f–k) domain. An alternative technique for log-stretch DMO corrections using the anti-aliasing filters of the f–k approach in the x-log t domain will be presented. Conventionally, the 2D filter representing the DMO operator is designed and applied in the f–k domain. The new technique uses a 2D convolution filter acting in single input/multiple output trace mode. Each single input trace is passed through several 1D filters to create the overall DMO response of that trace. The resulting traces can be stacked directly in the 3D data cube. The single trace filters are the result of a filter design technique reducing the 2D problem to several ID problems. These filters can be decomposed into a pure time-delay and a low-pass filter, representing the kinematic and dynamic behaviour of the DMO operator. The low-pass filters avoid any incidental operator aliasing. Different types of low-pass filters can be used to achieve different amplitude-versus-offset characteristics of the DMO operator.     

基于稀疏反演三维表面多次波压制方法

三维表面多次波压制是海洋地震资料预处理中的重要研究课题,基于波动理论的三维表面多次波压制方法(3DSRME)是数据驱动的方法,理论上来说,可有效压制复杂构造地震数据表面多次波.但该方法因对原始地震数据采集要求高而很难在实际资料处理中广泛应用.本文基于贡献道集的概念,将稀疏反演方法引入到表面多次波压制中,应用稀疏反演代替横测线积分求和,无需对横测线进行大规模重建,进而完成三维表面多次波预测,这样可有效解决实际三维地震数据横测线方向稀疏的问题.基于纵测线多次波积分道集为抛物线的假设,为保证预测后三维表面多次波和全三维数据预测的多次波在运动学和动力学特征上基本一致,文中对预测数据实施基于稳相原理的相位校正.理论模型和实际数据的测试结果表明,本文基于稀疏反演三维表面多次波压制方法可在横测线稀疏的情况下,有效压制三维复杂介质地震资料中的表面多次波,从而更好地提高海洋地震资料的信噪比,为高分辨率地震成像提供可靠的预处理数据保障.     

Antialiasing conditions in the delay‐time Radon transform

The delay‐time Radon transform parametrizes coherent events in a seismic gather by the far‐offset trace delay time, instead of the conventional parabolic curvature or ray parameter. The reformulation may give a different physical insight into the aliasing effect in the Radon transformation and may also lead to a different algorithm. The delay‐time parametrization enables modelling of a seismic gather as the sum of coherent events with any form of moveout curve. For example, a parabolic curve can be used for traces within a moderate offset range and a linear moveout for far‐offset traces. When using this delay‐time Radon transform, it is the number of traces, rather than the spatial sampling, of the input gather that directly controls aliasing in the Radon transform image. A preconditioning operator that implicitly increases the number of input traces by spatial reconstruction (without physically performing the spatial resampling) may minimize aliasing noise in the Radon transform image.     

Numerical analysis of one-dimensional nonlinear acoustic wave

Numerical investigations on one-dimensional nonlinear acoustic wave with third and fourth order nonlinearities are presented using high-order finite-difference (HFD) operators with a simple flux-limiter (SFL) algorithm. As shown by our numerical tests, the HFDSFL method is able to produce more stable, accurate and conservative solutions to the nonlinear acoustic waves than those computed by finite-difference combined with the flux-corrected-transport algorithm. Unlike the linear acoustic waves, the nonlinear acoustic waves have variable phase velocity and waveform both in time-space (t-x) domain and frequency-wavenumber (f-k) domain; of our special interest is the behaviour during the propagation of nonlinear acoustic waves: the waveforms are strongly linked to the type of medium nonlinearities, generation of harmonics, frequency and wavenumber peak shifts. In seismic sense, these characteristics of nonlinear wave will introduce new issues during such seismic processing as Normal Moveout and f-k filter. Moreover, as shown by our numerical experiment for a four-layer model, the nonlinearities of media will introduce extra velocity errors in seismic velocity inversion.     

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.     

Linear demultiple solution based on the concept of bottom-multiple-generator (BMG) approxiamtion: some new results

Recent advances in the demultiple technique have shown that a multidimensional convolution of a portion of data containing only primaries with the whole data (containing both primaries and multiples) can allow us to predict and attenuate all orders of free‐surface multiples that are relevant for practical purposes. One way of constructing the portion of the data containing only primaries is by muting the actual data just above the first free‐surface multiple to arrive. The location of the mute is generally known as the bottom‐multiple‐generator (BMG) reflector; the portion of the data containing only primaries required for constructing the free‐surface multiples is located above the BMG. The outstanding question about this method is how effective can the technique be when the BMG cuts through several seismic events, as is the case in long‐offset data or in very complex shallow geology. We present new results which demonstrate the fact that the BMG location may cut through several seismic events without affecting the accuracy or the cost of demultiple.     

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.     

IMPROVEMENT OF MULTICHANNEL SEISMIC DATA THROUGH APPLICATION OF THE MEDIAN CONCEPT1

Different types of median-based methods can be used to improve multichannel seismic data, particularly at the stacking stage in processing. Different applications of the median concept are described and discussed. The most direct application is the Simple Median Stack (SMS), i.e. to use as output the median value of the input amplitudes at each reflection time. By the Alpha-Trimmed Mean (ATM) method it is possible to exclude an optional amount of the input amplitudes that differ most from the median value. A more novel use of the median concept is the Weighted Median Stack (WMS). This method is based on a long-gapped median filter. The implicit weighting, which is purely statistical in nature, is due to the edge effects that occur when the gapped filter is applied. By shifting the traces around before filtering, the maximum weight may be given to, for example, the far-offset traces. The fourth method is the Iterative Median Stack (IMS). This method, which also includes a strong element of weighting, consists of a repeated use of a gapped median filter combined with a gradual shortening of the filter after each pass. Examples show how the seismic data can benefit from the application of these methods.     

抛物线Radon变换方法在压制地震多次波中的应用

多次波的存在会降低地震资料的信噪比,影响地震资料处理效果和后续的地质解释精度,压制多次波干扰是地震资料处理中的一个重要环节。利用有限差分方法正演模拟几个典型地质模型的地震波场,之后进行动校正,再通过抛物线Radon变换方法把t-x域一次反射波和多次波变换到τ-q域,由于存在速度的差异,Radon域记录中的一次反射波和多次波的能量互相分开,在Radon域对多次波的能量切除,保留反射波的有效信息,达到压制多次波的效果,提高资料的信噪比。通过对实际地震数据进行抛物线Radon变换结果也进一步验证了该方法在压制多次波中的应用效果。      

一阶多次波聚焦变换成像

将多次波转换成反射波并按传统反射波偏移算法成像,是多次波成像的一种方法.聚焦变换能准确的将多次波转换为纵向分辨率更高的新波场记录,其中一阶多次波转换为反射波.本文对聚焦变换提出了两点改进:1)提出局部聚焦变换,以减小存储量和计算量,增强该方法对检波点随炮点移动的采集数据的适应性;2)引入加权矩阵,理论上证明原始记录的炮点比检波点稀疏时,共检波点道集域的局部聚焦变换可以将多次波准确转换成炮点与检波点有相同采样频率的新波场记录.本文在第一个数值实验中对比了对包含反射波与多次波的原始记录做局部聚焦变换和直接对预测的多次波做局部聚焦变换两种方案,验证了第二种方案转换得到的波场记录信噪比更高且避免了第一个方案中切聚焦点这项比较繁杂的工作.第二个数值实验表明:在炮点采样较为稀疏时,该方法能有效的将一阶多次波转换成反射波;转换的反射波能提供更丰富的波场信息,成像结果更均衡、在局部有更高的信噪比,以及较高的纵向分辨率.     

Combined structure and velocity stacks via the tau–p transform

Reflection and refraction data are normally processed with tools designed to deal specifically with either near- or far-offset data. Furthermore, the refraction data normally require the picking of traveltimes prior to analysis. Here, an automatic processing algorithm has been developed to analyse wide-angle multichannel streamer data without resorting to manual picking or traveltime tomography. Time–offset gathers are transformed to the tau–p domain and the resulting wavefield is downward continued to the depth–p domain from which a velocity model and stacked section are obtained. The algorithm inputs common-depth-point (CDP) gathers and produces a depth-converted stacked section that includes velocity information. The inclusion of long-offset multichannel streamer data within the tau–p transformation enhances the signal from high-velocity refracted basalt arrivals. Downward continuation of the tau–p transformed wavefield to the depth–p domain allows the reflection and refraction components of the wavefield to be treated simultaneously. The high-slowness depth–p wavefield provides the velocity model and the low-slowness depth–p wavefield may be stacked to give structural information. The method is applied to data from the Faeroe Basin from which sub-basalt velocity images are obtained that correlate with an independently derived P-wave model from the line.     

HOMOMORPHIC FILTERING — THEORY AND PRACTICE*

The application of homomorphic filtering in marine seismic reflection work is investigated with the aims to achieve the estimation of the basic wavelet, the wavelet deconvolution and the elimination of multiples. Each of these deconvolution problems can be subdivided into two parts: The first problem is the detection of those parts in the cepstrum which ought to be suppressed in processing. The second part includes the actual filtering process and the problem of minimizing the random noise which generally is enhanced during the homomorphic procedure. The application of homomorphic filters to synthetic seismograms and air-gun measurements shows the possibilities for the practical application of the method as well as the critical parameters which determine the quality of the results. These parameters are:

• a) the signal-to-noise ratio (SNR) of the input data
• b) the window width and the cepstrum components for the separation of the individual parts
• c) the time invariance of the signal in the trace.

In the presence of random noise the power cepstrum is most efficient for the detection of wavelet arrival times. For wavelet estimation, overlapping signals can be detected with the power cepstrum up to a SNR of three. In comparison with this, the detection of long period multiples is much more complicated. While the exact determination of the water reverberation arrival times can be realized with the power cepstrum up to a multiples-to-primaries ratio of three to five, the detection of the internal multiples is generally not possible, since for these multiples this threshold value of detectibility and arrival time determination is generally not realized. For wavelet estimation, comb filtering of the complex cepstrum is most valuable. The wavelet estimation gives no problems up to a SNR of ten. Even in the presence of larger noise a reasonable estimation can be obtained up to a SNR of five by filtering the phase spectrum during the computation of the complex cepstrum. In contrast to this, the successful application of the method for the multiple reduction is confined to a SNR of ten, since the filtering of the phase spectrum for noise reduction cannot be applied. Even if the threshold results are empirical, they show the limits fór the successful application of the method.