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.     

用优化聚束滤波方法消除低信噪比地震资料中的多次波

针对常规方法如f k,Radon变换不能很好解决的消除低信噪比地震勘探资料的多次波问题,本文提出了优化聚束滤波方法,采用具有静态权的自适应聚束滤波器,并调整聚束滤波器设计的约束准则,去除低信噪比复杂实际资料中的多次波．实际资料处理结果表明,优化聚束滤波方法改善了最小方差无偏聚束滤波方法不能较好地处理低覆盖低信噪资料处理的局限性,在实际处理中计算量增加不大．     

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.     

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.     

IMPROVEMENT OF SIGNAL-TO-NOISE RATIO IN RESISTIVITY PROFILES1

The cross-correlation technique for increasing the anomaly-to-noise ratio is applied to the interpretation of resistivity profiles. To verify the method theoretically, resistivity profiles above a body having the shape of a parallelepiped were simulated with correlated and uncorrelated noise. Seven different electrode geometries are discussed. As a practical test, we considered profiles of a geoelectrical survey to locate tombs at a site of archaeological interest. When the shape and dimensions of the anomaly can be foreseen, the cross-correlation method can be applied and it gives a substantial improvement in the signal-to-noise ratio.     

TRACE INTERPOLATION IN SEISMIC DATA PROCESSING *

Trace interpolation of spatially aliased seismic data is used to improve the quality of multi-trace processing, especially that of migration. We consider non-rectangular sampling lattices. After stating the real sampling requirements for (two-dimensional or 3-D) digitized signals, the paper explains geometrically the effect of migration and of the 2-D dip filtering upon the aliased events, as well as our ability to interpolate traces from undersampled seismic data.     

A STRATIGRAPHIC CASE HISTORY USING THREE-DIMENSIONAL SEISMIC DATA IN THE GULF OF THAILAND *

A three-dimensional marine seismic survey was conducted in the Gulf of Thailand to aid in the development of a gas field indicated by three wildcat wells. The results and interpretation reported previously demonstrated improved fault resolution and better structural definition. Five successful appraisal wells have now been drilled, and these show that most of the sands have limited extent. Widespread character changes in the seismic data also support stratigraphic variations in many of the sands. Several new methods of 3D stratigraphic interpretation have been developed while investigating the depositional history of this area. Anomalous seismic amplitudes, tied to sands penetrated by wells and mapped from Seiscrop^TM horizontal sections in time and depth, have indicated the distribution of bars and channels. Horizon Seiscrop sections, each sliced through a single bed, have been used to delineate these depositional features directly. G-LOG^TM sections, displaying seismic logs derived by rigorous wave equation inversion, confirm the existence of these features. Sands greater than 10 m thick have proved mappable.     

地震水化学样品全分析数据统计处理中闭合效应的排除

在进行水化学样品全分析数据的统计处理中，应用原始数据和经过标准化处理后的数据，进行统计量计算时出现了不一致性。如本无相关关系的原始数据子成份，在经标准化处理后的数据子成份中却出现了负相关；原始数据和标准化数据的协方差阵相差甚远；因子分析图解中出现了曲面结构等。本文根据ＪｏｈｎＡｉｔｃｈｉｓｏｎ提出的对数比法，结合实例，对这一问题进行了探索，论证了对数比法在水化学资料处理中的可行性。     

用地震反射波全部时間值求有效速度

本文讨论了用地震反射波的全部时间值求有效速度的方法,得出了四种计算有效速度的公式。经过实际运用,认为有一定的效果,同时可用来计算断层面引起的绕射波的有效速度,对识别绕射波提供了一些线索。本文仅作为地震勘探工作交流实际经验而提出。     

用地震反射波全部时間值求有效速度

本文讨论了用地震反射波的全部时间值求有效速度的方法,得出了四种计算有效速度的公式。经过实际运用,认为有一定的效果,同时可用来计算断层面引起的绕射波的有效速度,对识别绕射波提供了一些线索。本文仅作为地震勘探工作交流实际经验而提出。     

SIGNAL ENHANCEMENT OF VIBRATORY SOURCE DATA IN THE PRESENCE OF ATTENUATION*

Amplitude spectra of input FM signals used in the vibratory source method of seismic exploration often show undesirable oscillations near the initial and terminal frequencies. These oscillations have an effect on the correlation background and distort the output signal. Considerable improvement in reducing the amplitude of these oscillations is obtained using a proper taper fuction. Attention is given to the relation between the tapering time and bandwidth of the spectrum. Analyses of the spectra of the received data from vibratory sources show considerable attenuation in comparison with the original field sweep. Since the matched filtering process will result in a series of waveforms which have the shape of the autocorrelation of the input signal, consideration is given to the autocorrelation function and its zero-lag coefficient of the FM signal in the presence of attenuation. A method has been developed which compensates for the attenuation and recovers the distortion of waveforms when the received data is correlated. The design of a waveform shaping filter for vibratory source data is given to reduce the influence of phase distortion on the received waveforms as well as to increase S/N ratio resolution. Parameters used for this filter are based on the properties of the FM signal and its autocorrelation function. Several examples from field data are presented to illustrate the methods. The results indicate that the use of the above techniques yields sections with good frequency resolution and improved S/N ratio.     

POROSITY PREDICTION FROM SEISMIC DATA*

The inversion of seismic traces allows the estimation of reservoir porosity from an analysis of transit times derived from the pseudo-velocity logs. A four-step computational procedure is illustrated consisting of (i) inversion of seismic traces and calculation of interval velocities; (ii) accurate stratigraphic interpretation; (iii) determination of the petrophysical parameters for the porosity evaluation; (iv) analysis of the reliability of the results and final corrections. Both the possibilities and the limits of the method are discussed. One of the causes of error is the fact that impedances—and not velocities—are readily obtainable from seismic data. Moreover, the porosity due to fracturation contributes only slightly to velocity, while it often contributes most importantly to the permeability. Results are shown for two of the most significant reservoir types, i.e. carbonatic and clastic. Two cases belonging to the latter type will be examined. In the first case the primary porosity is dominant. The second case is very complex and both primary and secondary porosity are present.     

OPTIMUM DIGITAL FILTERS FOR SIGNAL TO NOISE RATIO ENHANCEMENT*

One of the main objectives of seismic digital processing is the improvement of the signal-to-noise ratio in the recorded data. Wiener filters have been successfully applied in this capacity, but alternate filtering devices also merit our attention. Two such systems are the matched filter and the output energy filter. The former is better known to geophysicists as the crosscorrelation filter, and has seen widespread use for the processing of vibratory source data, while the latter is. much less familiar in seismic work. The matched filter is designed such that ideally the presence of a given signal is indicated by a single large deflection in the output. The output energy filter ideally reveals the presence of such a signal by producing a longer burst of energy in the time interval where the signal occurs. The received seismic trace is assumed to be an additive mixture of signal and noise. The shape of the signal must be known in order to design the matched filter, but only the autocorrelation function of this signal need be known to obtain the output energy filter. The derivation of these filters differs according to whether the noise is white or colored. In the former case the noise autocorrelation function consists of only a single spike at lag zero, while in the latter the shape of this noise autocorrelation function is arbitrary. We propose a novel version of the matched filter. Its memory function is given by the minimum-delay wavelet whose autocorrelation function is computed from selected gates of an actual seismic trace. For this reason explicit knowledge of the signal shape is not required for its design; nevertheless, its performance level is not much below that achievable with ordinary matched filters. We call this new filter the “mini-matched” filter. With digital computation in mind, the design criteria are formulated and optimized with time as a discrete variable. We illustrate the techniques with simple numerical examples, and discuss many of the interesting properties that these filters exhibit.     

COMPLETE INVERSION OF ZERO-OFFSET SEISMIC DATA*

The one-dimensional seismic inverse problem consists of recovering the acoustic impedance (or reflectivity function) as a function of traveltime from the reflection response of a horizontally layered medium excited by a plane-wave impulsive source. Most seismic sources behave like point sources, and the data must be corrected for geometrical spreading before the inversion procedure is applied. This correction is usually not exact because the geometrical spreading is different for primary and multiple reflections. An improved algorithm is proposed which takes the geometrical spreading from a point source into account. The zero-offset reflection response from a stack of homogeneous layers of variable thickness is used to compute the thickness, velocity and density of each layer. This is possible because the geometrical spreading contains additional information about the velocities.     

LINEARIZED INVERSION OF SEISMIC REFLECTION DATA*

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).     

频率-波数域递推计算海底多分量地震记录中的反射系数

在频率-波数域中采用解析法,解出多层条件下海底实测的多分量地震数据分解成上行和下行P波和S波的算法,导出海底各层地震反射系数随入射角变化(简称RVA)的递推计算公式,为海底多波多分量AVO弹性参数的反演及流体因子预测提供基础数据.合成数据的计算结果表明,本文给出的算法能较可靠地从海底多波多分量记录中提取RVA信息.     

ADAPTIVE PREDICTIVE DECONVOLUTION OF SEISMIC DATA*

The Wiener prediction filter has been an effective tool for accomplishing dereverberation when the input data are stationary. For non-stationary data, however, the performance of the Wiener filter is often unsatisfactory. This is not surprising since it is derived under the stationarity assumption. Dereverberation of nonstationary seismic data is here accomplished with a difference equation model having time-varying coefficients. These time-varying coefficients are in turn expanded in terms of orthogonal functions. The kernels of these orthogonal functions are then determined according to the adaptive algorithm of Nagumo and Noda. It is demonstrated that the present adaptive predictive deconvolution method, which combines the time-varying difference equation model with the adaptive method of Nagumo and Noda, is a powerful tool for removing both the long- and short-period reverberations. Several examples using both synthetic and field data illustrate the application of adaptive predictive deconvolution. The results of applying the Wiener prediction filter and the adaptive predictive deconvolution on nonstationary data indicate that the adaptive method is much more effective in removing multiples. Furthermore, the criteria for selecting various input parameters are discussed. It has been found that the output trace from the adaptive predictive deconvolution is rather sensitive to some input parameters, and that the prediction distance is by far the most influential parameter.     

TUTORIAL THE PROGRESSIVE ATTENUATION OF HIGH-FREQUENCY ENERGY IN SEISMIC REFLECTION DATA*

Seismic reflection data always exhibit a progressive loss of high-frequency energy with time. This effect is partly attributable to irreversible processes such as the conversion of elastic energy into heat (commonly known as absorption), and partly to reversible processes associated with interference between reflected waves arriving at different times. This paper looks only at reversible linear elastic effects at normal incidence and asks the following question: if there were no such absorption, would there still be a progressive loss of high-frequency energy? Using normal incidence and a layered elastic earth model we prove the following results. 1. The normal incidence response of a sequence of plane parallel elastic layers is non-white. 2. The pressure wave reflected by a layer that is thin compared with a wavelength is differentiated with respect to the incident wave. 3. The transmission response of a thin layer is consequently low-pass and the transmission response of a sequence containing many thin layers is very low-pass. 4. The well-known effect of the transport of acoustic energy by peg-leg multiples within thin layers is identical with this low-pass transmission response. 5. It follows that the high frequency energy is reflected back early in the seismogram. 6. By comparison, very low-frequencies are transmitted through the layered sequence easily and are reflected with difficulty. There is probably a lack of low-frequency energy in the reflection seismogram, by comparison with the spectrum of the incident plane wave. It follows that any meaningful evaluation of frequency-dependent absorption in seismic data cannot take place unless the frequency-dependent linear elastic effects are taken into account first.     

频率-波数域递推计算海底多分量地震记录中的反射系数

在频率-波数域中采用解析法,解出多层条件下海底实测的多分量地震数据分解成上行和下行P波和S波的算法,导出海底各层地震反射系数随入射角变化(简称RVA)的递推计算公式,为海底多波多分量AVO弹性参数的反演及流体因子预测提供基础数据.合成数据的计算结果表明,本文给出的算法能较可靠地从海底多波多分量记录中提取RVA信息.