PARTIAL COHERENCE MATCHING OF SYNTHETIC SEISMOGRAMS WITH SEISMIC TRACES*

A crucial step in the use of synthetic seismograms is the estimation of the filtering needed to convert the synthetic reflection spike sequence into a clearly recognizable approximation of a given seismic trace. In the past the filtering has been effected by a single wavelet, usually found by trial and error, and evaluated by eye. Matching can be made more precise than this by using spectral estimation procedures to determine the contribution of primaries and other reflection components to the seismic trace. The wavelet or wavelets that give the least squares best fit to the trace can be found, the errors of fit estimated, and statistics developed for testing whether a valid match can be made. If the composition of the seismogram is assumed to be known (e.g. that it consists solely of primaries and internal multiples) the frequency response of the best fit wavelet is simply the ratio of the cross spectrum between the synthetic spike sequence and the seismic trace to the power spectrum of the synthetic spike sequence, and the statistics of the match are related to the ordinary coherence function. Usually the composition cannot be assumed to be known (e.g. multiples of unknown relative amplitude may be present), and the synthetic sequence has to be split into components that contribute in different ways to the seismic trace. The matching problem is then to determine what filters should be applied to these components, regarded as inputs to a multichannel filter, in order to best fit the seismic trace, regarded as a noisy output. Partial coherence analysis is intended for just this problem. It provides fundamental statistics for the match, and it cannot be properly applied without interpreting these statistics. A useful and concise statistic is the ratio of the power in the total filtered synthetic trace to the power in the errors of fit. This measures the overall goodness-of-fit of the least squares match. It corresponds to a coherent (signal) to incoherent (noise) power ratio. Two limits can be set on it: an upper one equal to the signal-to-noise ratio estimated from the seismic data themselves, and a lower one defined from the distribution of the goodness-of-fit ratios yielded by matching with random noise of the same bandwidth and duration as the seismic trace segment. A match can be considered completely successful if its goodness-of-fit reaches the upper limit; it is rejected if the goodness-of-fit falls below the lower one.     

A STUDY OF THE SEISMIC SIGNATURES OF SEDIMENTATION MODELS USING SYNTHETIC SEISMOGRAMS*

In modern exploration for hydrocarbons there is a great emphasis on the location of stratigraphic traps and estimation of lithologic information like sand-shale ratios from seismic data. In order to investigate the possibilities of success in this endeavour we have studied the synthetic seismograms for wave form and spectral characteristic for four basic sedimentation models: (I) interbedded sand-shale model representing the sediments of generally fluviatile origin, (2) interbedded coal-shale model representing deltaic deposits, (3) sedimentary models representing transgression and regression of shore lines, and (4) a basal sand model. The results have shown that for the first two models a change in the sand-shale or coal-shale ratio results in a characteristically different seismogram. The nature of the seismogram, however, is also strongly dependent on how the sand-shale or coal shale layers are arranged to ultimately give the same number of total layers, thus implying the same coal-shale or sand-shale ratios. The transgression, regression, and basal sand models also produce characteristically different seismic signatures. The spectra of these seismograms show attendant characteristic changes. However, it seems that in the case of real data which are disturbed by noise and the effects of overlying layers these characteristic features may not always be distinguishable.     

CALCULATION OF SYNTHETIC REFLECTION SEISMOGRAMS IN THE FREQUENCY DOMAIN *

Calculation of reflection seismograms in the frequency domain makes it possible to treat absorption correctly, i.e. makes it possible to include dispersion (= causality) and frequency dependent reflection coefficients. In the paper it is shown how such a calculation can be done in a reasonably efficient manner.     

INVESTIGATION OF THE SEISMIC RESPONSE OF CYCLICALLY LAYERED CARBONIFEROUS ROCK BY MEANS OF SYNTHETIC SEISMOGRAMS *

Seismic exploration for coal as well as basic scientific research indicate the existence of unsolved problems. These problems arise partly because the requirements are different from those in exploration for gas and oil and are partly due to the geological situation. The medium to be investigated is composed of cyclically changing layers with extremely high velocity and density contrast. Furthermore, the structure of the carboniferous rock is highly fractured and folded. This leads to difficulties in interpreting the seismic response of carboniferous rock. To overcome these difficulties synthetic seismograms are a useful tool. Calculating synthetic seismograms the carboniferous rock has been modelled as a sequence of seams and rock. The following results have been obtained

• (i) A single seam gives rise to a distinct reflection signal even for a thickness of 1/50 of the wavelenght.
• (ii) Individual reflections are not visible from a sequence of layers containing a great number of seams and interfaces. Due to constructive interference only a few high amplitudes appear. These high amplitudes are labelled “interference reflections”.
• (iii) With increasing travel time the interference reflections are mainly composed of short lag multiples such that the primary reflections have no significant influence.
• (iv) The sequence of seams acts on the reflected seismic signal as a high pass filter and on the transmitted signal as a low pass filter. The cut-off frequencies are determined by the average seam thickness, and the steepness of the slopes increases with increasing number of seams.
• (v) The interference reflections can be used for determining the geological structure at least for the upper part of the sequence.

     

WAVEFRONT DIVERGENCE,MULTIPLES, AND CONVERTED WAVES IN SYNTHETIC SEISMOGRAMS*

Synthetic seismograms can be very useful in aiding understanding of wave propagation through models of real media, verification of geologic models derived from interpretation of field seismic data, and understanding the nature and complexity of wave phenomena. If meaningful results are to be obtained from synthetic seismograms, the method of their computation must, in general, include three-dimensional geometrical spreading of wavefronts associated with highly concentrated (i.e., point) sources. The method should also adequately represent the seismic response of solid-layered media by including enough primaries, multiples, and converted phases to accurately approximate the total wavefield. In addition to these features, it is also very helpful, although not always essential, if the method of seismogram computation provides for explicit identification of wave type and ray path for each arrival. Various seismograms, computed via asymptotic ray theory and an automatic ray generation scheme, are presented for a highly simplified North Sea velocity structure. This is done to illustrate the importance of the above features and to demonstrate the inadequacy of the plane-wave synthesis method of seismogram computation for point sources and the limitations of acoustic models of solid-layered media.     

EFFECTS OF DATA ERRORS AND ACCURACY IN SECOND DERIVATIVE COMPUTATION BY RATIONAL APPROXIMATION*

The effects of systematic (constant) and random errors in the observed data have been investigated analytically for rational approximation method of computing second derivative involving a summation of the products of the averages of the gravity field with the corresponding weight coefficients, both in numerator as well as in denominator. A theoretical gravity anomaly over three spheres has been analyzed to demonstrate the high accuracy in the approximation. Since the sums of the weight coefficients in numerator and denominator are zero and one respectively, the regional gravity anomaly, even though approximated by a constant value over the entire area under computation, can produce substantially large error in the calculated derivative value. This is happening because of the contribution of the regional field in the denominator. Thus, inspite of the high accuracy in rational approximation, the method has limited application to field cases where a combined gravity field consisting of regional and residual anomalies is usually used. Master curves are presented for the constant and random errors by which a rough estimate of the percentage of error in second derivative computation can be made provided one has some idea of the magnitudes of the regional field and random error.     

SYNTHETIC SEISMOGRAMS AT NON-VERTICAL INCIDENCE*

Synthetic seismograms are usually computed for reflections from vertical incidence of P waves for a horizontally layered medium. In actual practice the angle of incidence departs from the vertical, as receivers are usually located at some distance from the source. At angles other than the vertical, the conversion of P- to S-wave energy and changes in the reflection coefficient affect the shape of the synthetic seismograms. The effect of non-vertical incidence on synthetic seismograms is examined in this paper. Seismograms at non-vertical incidence have been computed using the plane-wave approach of Haskell (1953) for a layered medium. The use of plane waves is an approximation to the actual case of spherical wavefronts from a surface source. Using plane-wave theory, the expected wave forms as a function of angle of incidence were computed numerically for several simple models. The results indicate that the synthetic seismograms do not change significantly for angles of incidence between o and 25 degrees. For larger angles the changes in the wave forms may be severe. The effect is more pronounced for high-velocity layers than for low-velocity layers.     

UPSWEEP SIGNALS WITH HIGH-FREQUENCY ATTENUATION AND THEIR USE IN THE CONSTRUCTION OF VIBROSEIS® SYNTHETIC SEISMOGRAMS*

An analytical relationship for the autocorrelation function of an upsweep with high-frequency attenuation is used in the construction of synthetic seismograms. Field experiments were conducted in two areas to investigate the attenuation of upsweep where the near-surface materials were different. The results showed that the attenuation of high frequencies occurs at the source point depending on the near-surface lithology. The attenuation effect is usually neglected in the construction of the input wavelet of synthetic seismograms for Vibroseis data. In this study, the high-frequency attenuation of upsweep was considered in the construction of the input wavelet for the synthetic seismogram in an area where the Vibroseis technique was used. The synthetic seismogram generated in this manner had a better correlation with the Vibroseis section than that of corresponding synthetics using minimum-phase and the unattenuated autocorrelation wavelet of the upsweep.     

频率域中的合成地震记录

波动理论的合成地震记录是地震资料处理和解释中的重要研究课题。 目前,制作波动理论的合成记录主要是用Trorey的克希霍夫方法,正在研究的有有限差分法和有限元素法。本文提出一种新的方法,在频率域中制作波动理论的合成记录,给出了与克希霍夫绕射波方程等价的频率域中的绕射波方程。在国产DJS-11型计算机上,应用两种绕射波方程实现了合成地震记录,并且进行了比较,认为频率域方法是有效的,可以用于波动方程偏移和地震资料解释,进一步工作有可能获得多层变速模型的波动理论记录。     

频率域中的合成地震记录

波动理论的合成地震记录是地震资料处理和解释中的重要研究课题。 目前,制作波动理论的合成记录主要是用Trorey的克希霍夫方法,正在研究的有有限差分法和有限元素法。本文提出一种新的方法,在频率域中制作波动理论的合成记录,给出了与克希霍夫绕射波方程等价的频率域中的绕射波方程。在国产DJS-11型计算机上,应用两种绕射波方程实现了合成地震记录,并且进行了比较,认为频率域方法是有效的,可以用于波动方程偏移和地震资料解释,进一步工作有可能获得多层变速模型的波动理论记录。     

MODELLING CHANNEL WAVES WITH SYNTHETIC SEISMOGRAMS IN AN ANISOTROPIC IN-SEAM SEISMIC SURVEY1

In-seam seismic surveys with channel waves have been widely used in the United Kingdom and elsewhere to map coal-seams and to detect anomalous features such as dirt bands, seam thinning and thickening, and particularly in-seam faulting. Although the presence of cleat-induced anisotropy has been recognized in the past, almost all previous analyses have assumed homogeneous isotropic or transversely isotropic coal-seams. Channel waves, however, exhibit properties which cannot be fully explained without introducing anisotropy into the coal-seam. In particular, Love-type channel waves are observed for recording geometries where, in a homogeneous isotropic or transversely isotropic structure, the source would not be expected to excite transverse motion. Similarly, modes of channel-wave propagation display the coupled three-component motion of generalized modes in anisotropic substrates, which would not be expected for Rayleigh and Love wave motion in isotropy or in transversely isotropic media with azimuthal isotropy. We model the observed in-seam seismic channel waves with synthetic seismograms to gain an understanding of the effects of cleat-induced anisotropy on the behaviour of channel waves. The results show a reasonable good match with the observations in traveltime, relative amplitudes, dispersion characteristics and particle motions. We demonstrate that anisotropy in the surrounding country rocks contributes significantly to the coupling of channel wave particle motion, although its effect is not as strong as the anisotropy in the coal-seam. We conclude that the effects of cleat- and stress-induced anisotropy are observed and can be modelled with synthetic seismograms, and that anisotropy must be taken into account for the detailed interpretation of channel waves.     

在格陵兰地区地震图上记录到的一个附加震相——i震相的特征

在1976 ～1983 年期间,格陵兰地区共记录到53 个地震.所有的地震资料都用检查地震记录图纸的方式进行了复核审查,得到了该地区Pn ,Pg ,P11(PMP) ,Sn 和Lg 波的走时曲线及其视速度,这些结果与加拿大的走时曲线相一致.发现有9 个地震的11 张地震图上记录到一个附加的i震相.初步研究认为,i 震相的存在与震中距、震源深度和地震方向有关,不过此现象尚须进一步研究.     

INFLUENCE OF AMPLITUDE AND PHASE ERRORS ON MIGRATION RESULTS*

Random amplitude and phase errors in seismic input data introduce a coherent distribution of migration half-circles or “smiles”, the occurrence of which may cause a significant decrease of signal-to-noise ratio. In addition, the effect of quantization errors is discussed for different wordlengths, used both during acquisition and during data processing. Results of sign-bit recordings are shown.     

研究地震空区及条带附近地震破裂特征方法的误差讨论

较详细地讨论了确定中小地震破裂面方向和环境应力值方法的误差.分析表明,引起破裂方向误差的主要因素是台站包围震中的张角和制作广义方向性函数理论量板的精细程度.若对于θ角(台站和震中的连线与主破裂方向之间的夹角)每隔15°给出一条理论曲线,当台站包围震中张角大于60°时,其误差可小于15°.引起环境应力值τ0相对误差的主要因素是震级误差.若震级误差为0.3,可引起τ0的相对误差为70%.     

INVERSION OF SEISMOGRAMS AND PSEUDO VELOCITY LOGS*

Pseudo velocity logs can be obtained by seismogram inversion, using true amplitude processing and detailed investigation of move-out velocities. The precision of the results depends on the quality of the seismic data and on the possibility of deconvolving without increasing the noise. An investigation is made of the deformation of pseudo logs due to seismic signal variations and to imperfections of deconvolution. Both marine and land examples are shown, in some cases with adjustment on well logs. When the dips are large, time sections must be migrated and pseudo velocity logs must be computed from migrated sections. Comparison of sonic logs with pseudo velocity logs obtained in the same area is usually good enough to obtain information on lithological parameter variations by adjustment of pseudo velocity logs on sonic logs. Even when no well is available, pseudo velocity logs can give some indications on the nature of sediments between seismic horizons.     

理论地震图计算方法

近二十多年来,随着理论地震学和计算技术的发展,理论地震图的计算技术有了飞速发展.目前已能对不同的介质模型和震源计算各种体波、面波、地球自由震荡和静态位移场.它们在研究天然地震震源过程、地球内部结构、近场强地面运动、核爆作监测以及地震勘探等领域中发挥了越来越大的作用. 目前常用的理论地震图计算方法主要包括积分变换法、离散数值方法和射线方法几大类.本文对这些方法分类进行了简单介绍,并评论了各种方法的特点和各自的适用范围.     

新疆竖直摆倾斜仪的观测精度与震兆异常

对竖直摆倾斜仪在新疆近10年的运行情况做系统分析后认为，该类仪器观测精度较高且功耗小，管理方便，其中井下仪器稳定性好。受干扰小，性能明显优于峒体仪器，地震前显示了一定的中短期前兆异常。     

震源区和接收区结构不同情况下体波合成地震图的矩阵-射线方法

本文进一步扩展了合成地震图的广义射线方法.由于算法中将地球模型划分成震源区、接收区和地幔区,因此可用于计算震源区与接收区速度结构不同时的体波合成地震图.新算法把广义射线理论与传播矩阵理论结合起来,并采用了分层Q值模型,从而可以自动包括指定介质层内所有多次波的混响.为简便数据准备,设计了射线编码自动生成算法. 本文算法与Kind扩展的反射率法用相同的地球模型进行了数值结果对比,结果表明,矩阵-射线方法用于计算体波地震图时,不但有足够好的精度,而且还具有速度快并适于单个震相研究的优点.在计算由10个接收点组成的地震剖面时,其计算时间仅为反射率法的7％左右.     

ON THE ROLE OF PARTIAL RAY EXPANSION IN THE COMPUTATION OF RAY SYNTHETIC SEISMOGRAMS FOR LAYERED STRUCTURES1

This paper presents results of testing an efficient ray generation scheme needed whenever ray synthetic seismograms are to be computed for layered models with more than 10‘ thick’layers. Our ray generation algorithm is based on the concept of kinematically equivalent waves (the kinematic analogs) having identical traveltimes along different ray-paths between the source and the receiver, both located on the surface of the model. These waves, existing in any medium composed of laterally homogeneous parallel layers, interfere at any location along the recording surface, thereby producing a composite wavelet whose amplitude and shape depend directly on the number of kinematic analogs (the multiplicity factor). Hence, explicit knowledge of the multiplicity factor is crucial for any analysis based on the amplitude and shape of individual wavelets, such as wavelet shaping, Q estimation, or linearized wavelet inversion. For unconverted waves, such as those discussed in this paper, the multiplicity factor can be computed analytically using formulae given in the Appendix; for converted waves, the multiplicity factor should be computed numerically, using the algorithm employed for the computation of the seismograms presented in a previous paper by one of the authors.     

层状地壳模型地面地下记录地震波的理论地震图和频谱计算

本文首先发展了计算层状介质地面及地下记录地震波理论地震图的部分分离变量—有限差分计算方法,其最主要的环节是引进了吸收边界条件,使计算工作量大大减少,得以在实际工作中推广应用。其次,应用矩阵方法计算地面及地下记录的地震波的理论频谱。最后给出了用上述方法得到的华北地区两种不同的理论地壳模型情况下的理论地震图和频谱计算结果。应用这些理论结果,可根据实际地震观测资料对地壳介质模型进行分析、评判和优选。