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.     

OFFSET CONTINUATION IN THEORY AND PRACTICE*

Offset continuation is a technique that was recently proposed for the dip moveout correction. This correction can be carried out in the time-wavenumber domain using a proper partial differential equation that links sections with different offset. It has been shown that a single spike in a common-offset section—corresponds to a semi-elliptically shaped reflector with foci located at the source and receiver in the section migrated after dip moveout correction. The sections that result after offset continuation, stack, and migration are thus a superposition not only of semicircles, but also of semi-ellipses with different lengths of axes. This effect smears the migration alias-noise which, without offset continuation, would appear as migration circles not close enough together to interfere destructively. Offset continuation can improve the quality of seismic sections in several ways: —the velocity analyses are more readable, less dispersed and dip independent; diffraction tails arrive with the same normal moveout velocity as the apex and thus diffraction-noise can be “stacked out”; —noise produced by aliasing in the migrated section is reduced. In this paper we give a practical and conceptual interpretation of the offset continuation method, with a generalization to three-dimensional volumes of data. A critical examination of several synthetic and field data examples shows the actual possibilities and advantages of offset continuation.     

FULL WAVE EQUATION DOWNWARD CONTINUATION OF SEISMIC REFLECTION DATA*

A new method for suppressing multiple reflections in seismograms is developed. It is based on a downward continuation procedure which uses the full acoustic wave equation (hyperbolic form) as a downward continuation operator. We demonstrate that the downward continuation of the recorded wave field maps a reflectivity function without multiply reflected events. The method is applied successfully to individual traces of plane-wave decomposed (slant-stacked) synthetic and field data.     

GEOMETRICAL OPTICS AND WAVE THEORY OF CONSTANT OFFSET SECTIONS IN LAYERED MEDIA*

Constant offset sections can be mapped to a fixed offset and compared in order to provide a method of velocity analysis. The direct mapping to zero offset prior to stack might provide an alternative processing procedure to NMO and stack. The main advantage of such a procedure would lie in the correct treatment of cross-dips, but interpretational advantages might also follow from the performance of partial stacks biased to either high or low offset information.     

地震波场的共偏移距延拓研究

实现地震波场共偏移距剖面上不同偏移距之间的转换,对于精确的共反射点叠加、速度分析以及研究ＡＶＯ信息等皆具有重要意义。本文从非均匀介质地震记录的微分性质出发,通过对其共反射点变化轨迹的研究,导出基于Ｈａｍｉｌｔｏｎ方程的地震波场共偏移距延拓方程,建立了新的共偏移距延拓算子,通过理论模型的计算验证了此方程的正确性。     

横向线性变速介质中的共炮检距波场延拓

对横向变速介质中振幅保真的共炮检距波场延拓方法进行了研究．在横向线性变速条件下,通过引入新的偏微分方程,给出了该介质中振幅保真的波场延拓方程．这一波场延拓方程是均匀介质中振幅保真延拓方程在横向线性变速介质中的推广．首先由线性变速介质中地震波射线的走时函数,证明了该延拓方程的运动学等价方程对横向线性变速介质中的所有炮检距和各种反射层倾角都适用．然后,通过对模型数据的计算并与传统的ＤＭＯ方法比较,证明了这一波场延拓方程能很好地保持波前的振幅特性,特别是能保持焦散点的波前的特性．     

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.     

横向线性变速介质中的共炮检距波场延拓

对横向变速介质中振幅保真的共炮检距波场延拓方法进行了研究．在横向线性变速条件下,通过引入新的偏微分方程,给出了该介质中振幅保真的波场延拓方程．这一波场延拓方程是均匀介质中振幅保真延拓方程在横向线性变速介质中的推广．首先由线性变速介质中地震波射线的走时函数,证明了该延拓方程的运动学等价方程对横向线性变速介质中的所有炮检距和各种反射层倾角都适用．然后,通过对模型数据的计算并与传统的ＤＭＯ方法比较,证明了这一波场延拓方程能很好地保持波前的振幅特性,特别是能保持焦散点的波前的特性．     

共炮检距二维弹性波地震剖面的偏移方法

在均匀各向同性介质的分界面上入射纵波时，除产生纵波反射Ｐ－Ｐ波外，还会产生转换横波的反射Ｐ－ＳＶ波。同样，当入射波为ＳＶ横波时，在分界面上会同时产生ＳＶ－ＳＶ反射波和ＳＶ－Ｐ反射转换波，对这种二维弹性波地震记录如何进行偏移是正在探讨的问题。为了能够处理实际地震数据，本文提出在共炮检距剖面上进行二维弹性波记录的偏移方法。具体做法是，首先用弹性波方程将两分量的地震记录分解为Ｐ－Ｐ（或ＳＶ－ＳＶ）波和Ｐ－ＳＶ（或ＳＶ－Ｐ）波，然后用我们已导出的适合于处理共炮检距剖面的叠前偏移方法对它们进行处理。用模拟数据进行的试验说明方法正确，效果良好。     

共炮检距二维弹性波地震剖面的偏移方法

在均匀各向同性介质的分界面上入射纵波时,除产生纵波反射Ｐ－Ｐ波外,还会产生转换横波的反射Ｐ－ＳＶ波。同样,当入射波为ＳＶ横波时,在分界面上会同时产生ＳＶ－ＳＶ反射波和ＳＶ－Ｐ反射转换波,对这种二维弹性波地震记录如何进行偏移是正在探讨的问题。为了能够处理实际地震数据,本文提出在共炮检距剖面上进行二维弹性波记录的偏移方法。具体做法是,首先用弹性波方程将两分量的地震记录分解为Ｐ－Ｐ（或ＳＶ－ＳＶ）波和Ｐ－ＳＶ（或ＳＶ－Ｐ）波,然后用我们已导出的适合于处理共炮检距剖面的叠前偏移方法对它们进行处理。用模拟数据进行的试验说明方法正确,效果良好。     

PHASE AND GROUP TIME SECTIONS AND POSSIBILITIES FOR THEIR USE IN SEISMIC INTERPRETATION OF COMPLEX MEDIA*

Interpretation problems are discussed for a new class of models for complex seismic media, called heterogeneous models formed by inclusions (HMI). Examples of such models in geology are destructive deformation zones, tectonic raptures, complex folds, magmatogene formations, fronts of metamorphism and of phase transition, etc., which are of importance in interpretation of seismic data. The wavefields in such media have a complicated interferential character and should be considered as complex wave groups characterized by their phase and group properties. To study the phase and group characteristics of such wavefields, a method of construction and comparative analysis of so-called phase and group sections is introduced. This method is based on a transformation of the wavefield (seismogram) into a normalized seismogram (cos of the phase) and a perigram (a low cut version of the trace envelope). The group sections obtained on the perigrams represent zones of energy concentration and give stable estimates of the average characteristics of model structure. The phase sections are obtained on the normalized seismograms and represent primarily, the inner structure of the model. The method was applied to both synthetic and field data. The results of the combined analysis of the phase and group sections show that in many cases there are significant differences between them. On the basis of this analysis, several types of seismic objects may be distinguished which can serve as a basis for seismic interpretation.     

用平面波延拓方程进行地震数据的叠前速度反演

本文讨论地震勘探数据的叠前速度反演方法及其在海洋地震勘探数据上的反演试验.反演主要的计算步骤是:1.采用Fourier-Hankel变换把球面波分解为平面谐波;2.用平面谐波的延拓方程将上行波与下行波同时向下延拓,并计算每一层底部的反射系数和下一层的波阻抗;3.用最小二乘法从波阻抗中确定该层的声波速度.重复第2步与第3步,直到某一预定深度时结束.通过反演试验,对地震振幅比例的改变,子波变形,以及第1层速度和密度的误差对反演方法的稳定性及其精度的影响进行了分析.还通过实际海洋地震勘探数据的反演试验,对这一方法在地震勘探中的应用前景作了论述.     

用平面波延拓方程进行地震数据的叠前速度反演

本文讨论地震勘探数据的叠前速度反演方法及其在海洋地震勘探数据上的反演试验.反演主要的计算步骤是:1.采用Fourier-Hankel变换把球面波分解为平面谐波;2.用平面谐波的延拓方程将上行波与下行波同时向下延拓,并计算每一层底部的反射系数和下一层的波阻抗;3.用最小二乘法从波阻抗中确定该层的声波速度.重复第2步与第3步,直到某一预定深度时结束.通过反演试验,对地震振幅比例的改变,子波变形,以及第1层速度和密度的误差对反演方法的稳定性及其精度的影响进行了分析.还通过实际海洋地震勘探数据的反演试验,对这一方法在地震勘探中的应用前景作了论述.     

地震折射法中波场延拓技术的应用

从波动方程出发,推导出平面波场传播基本公式,阐述了利用地表观测波场反演地球内部波速结构的理论关系.观测波场可通过-p 变换分解为地表平面波场,其最大振幅的轨迹能稳定地反映出地球内部波速随深度变化的趋势,这一特征可用来对反演解空间进行约束.波场延拓技术可以充分地利用观测波场中包含的丰富信息,在迭代反演中不仅能简单快速地得到反演解,而且所得解具有良好的稳定性,较少受主观因素影响,这是一种很好的反演技术.对波场延拓进行了理论分析与数值模拟,采用了同态反褶积等改善资料信噪比的措施,使解的分辨能力得到了提高.文中对南海北部一个声纳折射剖面进行了分析和计算.结果表明:该区1.4km 深处,存在一个从1.76km/s 到2.21km/s 的速度间断面.间断面上下两层的速度梯度分别为0.54kms-1/km,0.63kms-1/km.最后,从构造演化的角度对浅海构造特征进行了探讨.      

MIGRATION OF SEISMIC INTERFACES*

Most interpretation work is still based on stacked and not on migrated sections. In the case of heavy faulting and considerable velocity contrasts between formations, migration of interpreted interfaces poses a problem. In more detail, the problem may be specified as follows: — a given interpretation of a number of interfaces along with a given heterogeneous velocity field may not always have a plausible solution in the form of migrated interfaces in depth; — fault planes, salt boundaries, etc., are, in most cases, not directly interpretable in a section and are plotted by intuition using interface terminations as a guide; — the velocity field in fault zones is, in most cases, hard to determine. The interpreter may arrive at a plausible solution by repeating the migration process with various possible interpretations and various velocity assumptions. The subject of this paper is an algorithm based on ray-theory which allows one: — to handle faults and velocity variations at faults properly; — to perform migration in steps, working a particular geological unit at a time and proceeding to the next unit once the foregoing one has been properly migrated; — to display ray-paths, where necessary, for investigation of interface distortions, e.g., below fault areas. The algorithm is designed and implemented for application in an interactive environment. Inspection of intermediate and final results, investigation of interface distortions and modifications are performed on a graphics screen. Thus, various possible interpretations and velocity assumptions may be investigated within a short time. Interfaces interpreted on migrated sections may be over-migrated because of neglection of the influence of refraction in most section migration programs. This over-migration may also be corrected using the above algorithm in the “image ray” mode.     

共偏移距地震反射波方法用于城市活断层探测

在简要介绍共偏移距地震反射波勘探方法原理、现场数据采集和室内资料处理方法的基础上,结合福州和沈阳2个城市的活断层探测实例,探讨了采用共偏移距地震反射波方法进行活断层探测的有效性和局限性。结果表明,该方法具有分辨率高、对地下构造的重现性好、探测结果可实时分析解释等特点,在第四纪覆盖层较薄、基岩面起伏变化较大的地区采用该方法可快速对被测目标进行准确定位     

A SPATIAL ANALYSIS OF UPWARD CONTINUATION OF POTENTIAL FIELD DATA *

A spatial analysis of both continuous and discrete operators for upward continuation help us realize the problems and limitations which have been encountered before (Henderson 1960, Kontis 1971) but remained unsolved in practical application of upward continuation computation due to the finite length of data and operator in spatial domain. Various numerical examples show that an improvement of accuracy of continuation computations can be achieved through proper sampling and sufficient length of data.     

VELOCITY DISPERSION OF SEISMIC WAVES*

In well velocity surveys made to calibrate Sonic (CV) Logs the calibration survey uses frequencies around 50 Hz whereas the Sonic Logging tool uses frequencies around 20 kHz. There thus exists the possibility of making a direct measure of velocity dispersion. In any one survey the disturbing factors, both instrumental and operational, will often mask any dispersive effect that might exist. Consequently this paper reports on a statistical analysis of the velocity differences resulting from calibration surveys and Sonic logs. Only Borehole Compensated Sonic Logs were used. Four areas were investigated: the North Sea, Abu Dhabi, Libya and Alaska. After rejecting logs and calibration records which were obviously in error there remained 424000 feet (about 130 km) of usable log distributed throughout 66 wells. The four areas were analysed separately and in no case was the estimated dispersion significantly different from zero. However, the mean values did correlate with lithology from (? 0.17 ± 0.18)% for the essentially carbonate section in Abu Dhabi to (+ 0.45 ± 0.25)% for the sand-shale section in Alaska, a positive sign meaning that the higher frequencies travelled faster. Except for Alaska the calibration surveys were made with a wall-clamp geophone, and for these areas amplitude measurements were made. After suitable corrections estimates of the absorption parameter Q were obtained. These varied from 20 to 200 with mean values of 63 for Libya, 70 for Abu Dhabi and 88 for the North Sea (excluding the Tertiary). If, as is usually assumed, the absorption mechanism is linear and is described by a Q which is independent of frequency, then these values would necessarily imply dispersion of several percent. As instanced above no such dispersion was observed. It is possible that the expected dispersion was compensated for by invasion of the mud filtrate into the borehole walls, but it is more likely that the absorption mechanism was substantially non-linear.     

ASPECTS OF VERTICAL SEISMIC RESOLUTION*

It is proposed that the vertical resolving power of a seismic signal is controlled by three aspects: the width of the central lobe, the side lobe ratio, and the side-tail oscillations. A comparative study of zero-phase signals covering the same frequency range shows that improvement of any one of these aspects inevitably leads to deterioration of one of the other aspects. An analytical simulation model is proposed of zero-phase signals free from side-tail oscillations, in which both the width of the central lobe and the side lobe ratio are adjustable. Analysis of the spectra of this model shows that, while the high frequency content of the spectrum is essential for obtaining a small width of the central lobe, the low frequency content of the spectrum plays an essential part in causing a low value of the side lobe ratio.     

LIMITS OF STRUCTURAL INVERSION OF SEISMIC HORIZONS*

Time horizons can be depth-migrated when interval velocities are known; on the other hand, the velocity distribution can be found when traveltimes and NMO velocities at zero offset are known (wavefront curvatures; Shah 1973). Using these concepts, exact recursive inversion formulae for the calculation of interval velocities are given. The assumption of rectilinear raypath propagation within each layer is made; interval velocities and curvatures of the interfaces between layers can be found if traveltimes together with their gradients and curvatures and very precise V_NMO velocities at zero offset are known. However, the available stacking velocity is a numerical quantity which has no direct physical significance; its deviation from zero offset NMO velocity is examined in terms of horizon curvatures, cable length and lateral velocity inhomogeneities. A method has been derived to estimate the geological depth model by searching, iteratively, for the best solution that minimizes the difference between stacking velocities from the real data and from the structural model. Results show the limits and capabilities of the approach; perhaps, owing to the low resolution of conventional velocity analyses, a simplified version of the given formulae would be more robust.