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.     

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.     

ESTIMATION OF THE SIGNAL-TO-NOISE RATIO OF SEISMIC DATA WITH AN APPLICATION TO STACKING*

The amplitude of the signal and the energy of the noise on each of at least three traces can be estimated provided that the signal has the same form (but not necessarily the same amplitude) on these traces and that the noise on any trace is correlated with neither the signal nor the noise on any other trace. This estimation of signal amplitude and noise energy can be achieved by a rather simple algorithm. The accuracy of the estimate depends, of course, on the degree to which the assumption that signal and noise on the different traces are mutually uncorrelated is actually met. The accuracy tends to improve with increasing number of traces.     

地震数据叠前偏移成像及其在浅层地震勘探中的应用研究

文中讨论了在浅层地震勘探中地质结构和构造的复杂性以及对浅层地震勘探成果要求精度较高的特殊性,指出了在浅层地震勘探中发展叠前深度偏移的重要性,并对相移法叠前深度偏移的基本原理和实现方法进行了详细论述,编制了相应的软件。通过使用该方法对 2种理论试验模型进行试算,获得的深度偏移剖面层位清晰,构造明显,较准确地体现了理论模型地质结构和构造的特征,效果良好。然后又使用实际浅层地震反射资料进行了叠前偏移计算,所得结果与已知地质结构和构造相吻合,也取得了较好的结果,证实了该方法及软件的可靠性和实用性,可用于实际浅层地震反射勘探资料的叠前深度偏移处理     

共反射面元叠加的应用理论--从共反射点到共反射面元

共反射面元（CRS）叠加是目前认为最好的生成零炮检距剖面的方式. 共反射面元 意指地下某一反射点邻近的一个反射弧段,该弧段在时空域内的走时响应称为CRS叠加面,该 叠加面可视为反射弧段上各共反射点（CRP）的时空域内走时响应的组合. 在一般的共反射 点走时关系基础上,引入两种特征波——Normal波和Normal Incidence Point波,就可以在 傍轴近似假设下,将CRP走时关系推广到反射点邻近的各反射点,将这些反射点的CRP走时关系 加以组合就得到了关于该反射点的共反射面元的走时关系. 考察从共反射点（CRP）到共反 射面元(CRS)的过渡,这一过程提供了CRS叠加的应用理论基础.     

AN OPTIMIZED TECHNIQUE FOR DETERMINING STACKING VELOCITY FROM SEISMIC REFLECTION DATA*

A new method of estimating seismic stacking velocity from reflection seismograms is based on Fibonacci search technique and provides the highest rate of reduction of the interval of uncertainty of the stacking velocity. A review of the Fibonacci search strategy is presented, the application of the method is illustrated with synthetic and field examples.     

快速有效的转换波共转换点叠加技术

转换波共转换点(Common Conversion Point简称CCP)叠加的关键在于CCP抽道集和非双曲线正常时差校正NMO(Normal MoveOut). 目前方法的精度限制了其在中-浅层或大炮检距情况下的应用. 我们对CCP叠加技术进行了系统研究,导出了新的CCP位置计算公式和非双曲线时距关系式,并给出了具体的CCP抽道集方法. 理论模型试验和实验资料处理表明本文方法精度高、简便易行,特别是对于中-浅层和大炮检距情况也能得到良好的叠加效果.     

快速有效的转换波共转换点叠加技术

转换波共转换点(Common Conversion Point简称CCP)叠加的关键在于CCP抽道集和非双曲线正常时差校正NMO(Normal MoveOut). 目前方法的精度限制了其在中-浅层或大炮检距情况下的应用. 我们对CCP叠加技术进行了系统研究,导出了新的CCP位置计算公式和非双曲线时距关系式,并给出了具体的CCP抽道集方法. 理论模型试验和实验资料处理表明本文方法精度高、简便易行,特别是对于中-浅层和大炮检距情况也能得到良好的叠加效果.     

共深度点勘探与地震映像勘探在第四系覆盖层较薄地区的应用研究

对两处第四系覆盖层较薄场地（一般小于50m）进行共深度点勘探和地震映像勘探。结果表明在第四系覆盖层较薄地区地震映像勘探效果优于共深度点勘探。     

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.     

WEIGHTED STACKING OF SEISMIC DATA USING AMPLITUDE-DECAY RATES AND NOISE AMPLITUDES1

The signal-to-noise (S/N) ratio of seismic reflection data can be significantly enhanced by stacking. However, stacking using the arithmetic mean (straight stacking) does not maximize the S/N ratio of the stack if there are trace-to-trace variations in the S/N ratio. In this case, the S/N ratio of the stack is maximized by weighting each trace by its signal amplitude divided by its noise power, provided the noise is stationary. We estimate these optimum weights using two criteria: the amplitude-decay rate and the measured noise amplitude for each trace. The amplitude-decay rates are measured relative to the median amplitude-decay rate as a function of midpoint and offset. The noise amplitudes are measured using the data before the first seismic arrivals or at late record times. The optimum stacking weights are estimated from these two quantities using an empirical equation. Tests with synthetic data show that, even after noisy-trace editing, the S/N ratio of the weighted stack can be more than 10 dB greater than the S/N ratio of the straight stack, but only a few decibels more than the S/N ratio of the trace equalized stack. When the S/N ratio is close to 0 dB, a difference of 4 dB is clearly visible to the eye, but a difference of 1 dB or less is not visible. In many cases the S/N ratio of the trace-equalized stack is only a few decibels less than that of the optimum stack, so there is little to be gained from weighted stacking. However, when noisy-trace editing is omitted, the S/N ratio of the weighted stack can be more than 10 dB greater than that of the trace-equalized stack. Tests using field data show that the results from straight stacking, trace-equalized stacking, and weighted stacking are often indistinguishable, but weighted stacking can yield slight improvements on isolated portions of the data.     

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.     

SEISMIC REFLECTION APPLIED TO SEDIMENTOLOGY AND GAS DISCOVERY IN THE GULF OF CADIZ*

In the Gulf of Cadiz, a Tertiary basin became filled by clastic series during Miocene and Pliocene times. This terrigenous influx, derived from the Iberic Meseta in the north, is characterized by a sandy episode during the Tortonian and Messinian. The sand deposits were probably connected with uplift and major erosion of the Meseta during the sliding of the olistostrome, which occupied the south of the basin from late Helvetian to middle Tortonian. High resolution seismic techniques produced a good picture of the stratigraphy and of the depositional environment of the sands. A further study, using the amplitude of the reflections, inversion of seismic traces into acoustic impedance traces, and modeling, provides a remarkable example of the possibilities of seismic stratigraphy for depicting the lateral evolution of facies and localizing hydrocarbon occurrences. Out of seven exploratory wells based upon seismic information, six encountered gas-bearing sands with economic potential.     

OPTIMUM HYPERBOLIC MOVEOUT FILTERS WITH APPLICATIONS TO SEISMIC DATA*

Optimum multichannel filters can be designed to process seismic events falling on hyperbolic moveout curves using the conventional least-squares method. Contrary to the linear moveout filters, autocorrelation and crosscorrelation functions inherent in the normal equations have to be computed numerically. However, computation times of filter coefficients are comparable to linear moveout operators. For a given source-receiver geometry and assuming straight ray-path, relative moveout of a seismic reflection event is dependent on the two way arrival time and rms velocity. Consequently, to avoid overlapping of pass and reject moveout windows, hyperbolic moveout filters have to be designed over time gates rather than for the whole record lengths. Hyperbolic and hyperbolic-linear moveout filters applied to synthetic and field seismic reflection traces show good signal-to-noise (S/N) ratio improvements. Results of some combined synthetic and field data examples are presented.     

PROCESSING OF PS-REFLECTION DATA APPLYING A COMMON CONVERSION-POINT STACKING TECHNIQUE1

Converted waves require special data processing as the wave paths are asymmetrical. The CMP concept is not applicable for converted PS waves, instead a sorting algorithm for a common conversion point (CCP) has to be applied. The coordinates of the conversion points in a single homogeneous layer can be calculated as a function of the offset, the reflector depth and the velocity ratio v_P/ v_s. For multilayered media, an approximation for the coordinates of the conversion points can be made. Numerical tests show that the traveltime of PS reflections can be approximated with sufficient accuracy for a certain offset range by a two-term series truncation. Therefore NMO corrections can be calculated by standard routines which use the hyperbolic approximation of the reflection traveltime curves. The CCP-stacking technique has been applied to field data which have been generated by three vertical vibrators. The in-line horizontal components have been recorded. The static corrections have been estimated from additional P- and SH-wave measurements for the source and geophone locations, respectively. The data quality has been improved by processes such as spectral balancing. A comparison with the stacked results of the corresponding P- and SH-wavefield surveys shows a good coherency of structural features in P-, SH- and PS-time sections.     

METHOD FOR DETERMINATION OF VELOCITY AND DEPTH FROM SEISMIC REFLECTION DATA1

The estimation of velocity and depth is an important stage in seismic data processing and interpretation. We present a method for velocity-depth model estimation from unstacked data. This method is formulated as an iterative algorithm producing a model which maximizes some measure of coherency computed along traveltimes generated by tracing rays through the model. In the model the interfaces are represented as cubic splines and it is assumed that the velocity in each layer is constant. The inversion includes the determination of the velocities in all the layers and the location of the spline knots. The process input consists of unstacked seismic data and an initial velocity-depth model. This model is often based on nearby well information and an interpretation of the stacked section. Inversion is performed iteratively layer after layer; during each iteration synthetic travel-time curves are calculated for the interface under consideration. A functional characterizing the main correlation properties of the wavefield is then formed along the synthetic arrival times. It is assumed that the functional reaches a maximum value when the synthetic arrival time curves match the arrival times of the events on the field gathers. The maximum value of the functional is obtained by an effective algorithm of non-linear programming. The present inversion algorithm has the advantages that event picking on the unstacked data is not required and is not based on curve fitting of hyperbolic approximations of the arrival times. The method has been successfully applied to both synthetic and field data.     

A NEW APPROACH TO THE INVERSION OF SEISMIC DATA*

A new inversion method for seismic reflection data is based on impedance concepts and uses transformations to reduce the essentially non-linear problem to a linear eigenvalue formulation without approximation. A set of reflection data has been inverted using this method. The characteristic impedances of the layers so determined are compared with log data from a reference borehole.     

STACKING OF P-SV SEISMIC REFLECTION DATA USING DIP MOVEOUT1

The moveout of P-SV mode-converted seismic reflection events in a common-midpoint gather is non-hyperbolic. This is true even if the medium has constant P- and SV-wave velocities. Furthermore, reflection-point smear occurs even along horizontal reflectors. These effects reduce the resolution of the zero-offset stack. In such a medium, the generalization of the dip moveout transformation to P-SV data can be calculated analytically. The resulting P-SV dip moveout operators solve the problem of reflection-point smear, and image any reflector regardless of dip or depth. The viability of this technique is demonstrated on synthetic and field data.     

RESOLUTION ENHANCEMENT OF WELL LOG AND SEISMIC DATA*

A new method with general applications for seismic data is presented for spectral extrapolation. The method gives a restored image that is optimum in the sense of minimum norm and can be adapted to incorporate any constraints on the reconstruction. As an illustration of the technique it is first applied to a synthesized (noise-free) image. Then it is shown that enhancement of a density log (run in a hole drilled entirely in Coal Measures rocks) is possible using constraints taken from the geologist's log. A synthetic trace with significantly improved event arrival times and general character is obtained.     

DEPTH IMAGING OF OFFSET VERTICAL SEISMIC PROFILE DATA1

Depth migration consists of two different steps: wavefield extrapolation and imaging. The wave propagation is firmly founded on a mathematical frame-work, and is simulated by solving different types of wave equations, dependent on the physical model under investigation. In contrast, the imaging part of migration is usually based on ad hoc‘principles’, rather than on a physical model with an associated mathematical expression. The imaging is usually performed using the U/D concept of Claerbout (1971), which states that reflectors exist at points in the subsurface where the first arrival of the downgoing wave is time-coincident with the upgoing wave. Inversion can, as with migration, be divided into the two steps of wavefield extrapolation and imaging. In contrast to the imaging principle in migration, imaging in inversion follows from the mathematical formulation of the problem. The image with respect to the bulk modulus (or velocity) perturbations is proportional to the correlation between the time derivatives of a forward-propagated field and a backward-propagated residual field (Lailly 1984; Tarantola 1984). We assume a physical model in which the wave propagation is governed by the 2D acoustic wave equation. The wave equation is solved numerically using an efficient finite-difference scheme, making simulations in realistically sized models feasible. The two imaging concepts of migration and inversion are tested and compared in depth imaging from a synthetic offset vertical seismic profile section. In order to test the velocity sensitivity of the algorithms, two erroneous input velocity models are tested. We find that the algorithm founded on inverse theory is less sensitive to velocity errors than depth migration using the more ad hoc U/D imaging principle.