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.     

地震记录小波域高阶相关叠加技术

水平叠加技术能够有效地压制随机噪声和多次波,但是对于由于相邻道的噪声表现出相关性和一致性而产生的某些相干干扰,常规的叠加技术容易产生假的同相轴,难以取得较高的信噪比.基于小波理论和高阶统计理论本文提出了小波域高阶相关叠加技术(HOCS),其基本原理是将经动静校正的CMP道集变换到小波域,然后在小波域求取高阶相关系数,进而加权叠加.数值实验和实际资料计算的结果表明,此方法比常规叠加更能够有效地提高信噪比,剔除常规加权叠加无法抑制的某些相关噪声.     

A new direction for shallow refraction seismology: integrating amplitudes and traveltimes with the refraction convolution section

The refraction convolution section (RCS) is a new method for imaging shallow seismic refraction data. It is a simple and efficient approach to full‐trace processing which generates a time cross‐section similar to the familiar reflection cross‐section. The RCS advances the interpretation of shallow seismic refraction data through the inclusion of time structure and amplitudes within a single presentation. The RCS is generated by the convolution of forward and reverse shot records. The convolution operation effectively adds the first‐arrival traveltimes of each pair of forward and reverse traces and produces a measure of the depth to the refracting interface in units of time which is equivalent to the time‐depth function of the generalized reciprocal method (GRM). Convolution also multiplies the amplitudes of first‐arrival signals. To a good approximation, this operation compensates for the large effects of geometrical spreading, with the result that the convolved amplitude is essentially proportional to the square of the head coefficient. The signal‐to‐noise (S/N) ratios of the RCS show much less variation than those on the original shot records. The head coefficient is approximately proportional to the ratio of the specific acoustic impedances in the upper layer and in the refractor. The convolved amplitudes or the equivalent shot amplitude products can be useful in resolving ambiguities in the determination of wave speeds. The RCS can also include a separation between each pair of forward and reverse traces in order to accommodate the offset distance in a manner similar to the XY spacing of the GRM. The use of finite XY values improves the resolution of lateral variations in both amplitudes and time‐depths. The use of amplitudes with 3D data effectively improves the spatial resolution of wave speeds by almost an order of magnitude. Amplitudes provide a measure of refractor wave speeds at each detector, whereas the analysis of traveltimes provides a measure over several detectors, commonly a minimum of six. The ratio of amplitudes obtained with different shot azimuths provides a detailed qualitative measure of azimuthal anisotropy and, in turn, of rock fabric. The RCS facilitates the stacking of refraction data in a manner similar to the common‐midpoint methods of reflection seismology. It can significantly improve S/N ratios.Most of the data processing with the RCS, as with the GRM, is carried out in the time domain, rather than in the depth domain. This is a significant advantage because the realities of undetected layers, incomplete sampling of the detected layers and inappropriate sampling in the horizontal rather than the vertical direction result in traveltime data that are neither a complete, an accurate nor a representative portrayal of the wave‐speed stratification. The RCS facilitates the advancement of shallow refraction seismology through the application of current seismic reflection acquisition, processing and interpretation technology.     

On the retrieval of moment tensors from borehole data

The complete moment tensors of seismic sources in homogeneous or vertically inhomogeneous isotropic structures cannot be retrieved using receivers deployed in one vertical borehole. The complete moment tensors can be retrieved from amplitudes of P‐waves, provided that receivers are deployed in at least three boreholes. Using amplitudes of P‐ and S‐waves, two boreholes are, in principle, sufficient. Similar rules also apply to transversely isotropic media with a vertical axis of symmetry. In the case of limited observations, the inversion can be stabilized by imposing the zero‐trace constraint on the moment tensors. However, this constraint is valid only if applied to observations of shear faulting on planar faults in isotropic media, which produces double‐couple mechanisms. For shear faulting on non‐planar faults, for tensile faulting, and for shear faulting in anisotropic media, the zero‐trace constraint is no longer valid and can distort the retrieved moment tensor and bias the fault‐plane solution. Numerical modelling simulating the inversion of the double‐couple mechanism from real data reveals that the errors in the double‐couple and non‐double‐couple percentages of the moment tensors rapidly decrease with increase in the number of boreholes used. For noisy P‐ and S‐wave amplitudes with noise of 15% of the top amplitude at each channel and for a velocity model biased by 10%, the errors in the double‐couple percentage attain 25, 13 and 6% when inverting for the double‐couple mechanism from one, two and three boreholes.     

THE PERFORMANCE OF OPTIMUM STACKING FILTERS IN SUPPRESSING UNCORRELATED NOISE*

Optimum stacking filters based on estimates of trace signal-to-uncorrelated noise ratios are assessed and compared in performance with conventional straight stacking. It is shown that for the trace durations and signal bandwidths normally encountered in seismic reflection data the errors in estimating signal/noise ratios largely counteract the theoretical advantages of the optimum filter. The more specific the filter (e.g. the more frequency components included in its design) the more this is true. Even for a simple weighted stack independent of frequency, the performance is likely to be better than a straight (equal weights) stack only for relatively high signal/noise ratios, when the performance is not critical anyway.     

A SEMBLANCE-GUIDED MEDIAN FILTER1

Reiter , E.C., Toksoz , M.N. and Purdy , G.M. 1992. A semblance-guided median filter. Geophysical Prospecting 41 , 15–41. A slowness selective median filter based on information from a local set of traces is described and implemented. The filter is constructed in two steps, the first being an estimation of a preferred slowness and the second, the selection of a median or trimmed mean value to replace the original data point. A symmetric window of traces defining the filter aperture is selected about each trace to be filtered and the filter applied repeatedly to each time point. The preferred slowness is determined by scanning a range of linear moveouts within the user-specified slowness passband. Semblance is computed for each trial slowness and the preferred slowness selected from the peak semblance value. Data points collected along this preferred slowness are then sorted from lowest to highest and in the case of a pure median filter, the middle point(s) selected to replace the original data point. The output of the filter is therefore quite insensitive to large amplitude noise bursts, retaining the well-known beneficial properties of a traditional 1D median filter. Energy which is either incoherent over the filter aperture or lies outside the slowness passband, may be additionally suppressed by weighting the filter output by the measured peak semblance. This approach may be used as a velocity filter to estimate coherent signal within a specified slowness passband and reject coherent energy outside this range. For applications of this type, other velocity estimators may be used in place of our semblance measure to provide improved velocity estimation and better filter performance. The filter aperture may also be extended to provide increased velocity estimation, but will result in additional lateral smearing of signal. We show that, in addition to a velocity filter, our approach may be used to improve signal-to-noise ratios in noisy data. The median filter tends to suppress the amplitude of random background noise and semblance weighting may be used to reduce the amplitude of background noise further while enhancing coherent signal. We apply our method to vertical seismic profile data to separate upgoing and downgoing wavefields, and also to large-offset ocean bottom hydrophone data to enhance weak refracted and post-critically reflected energy.     

A procedure to reduce side lobes of reflection wavelets: A contribution to low frequency information

Side lobes of the wavelets arise from the lack of low frequency content in a reflection wavelet. They tend to increase the time span of an individual reflection event and interfere with the other primary reflections or side lobes. Furthermore, their trace-by-trace consistency may produce pseudo-reflections and may cause misinterpretations of the side lobes as weak reflections.A procedure in order to improve the low frequency content of the seismic traces by suppressing the side lobe amplitudes based on the complex trace envelope is proposed. Using the average energies of the seismic trace and its envelope, the polarity table of the trace is obtained and used to correct the phase of the envelope. The resultant trace is termed “side lobe reduced (SLR) trace”. The method can be applied to the stack or migrated seismic data by a trace-by-trace basis. The only required parameter of the method is the moving average operator length which is used to calculate average energies of the input traces. In general, shorter operator lengths yield better results when the dominant frequency of the input increases.Results from synthetics and real seismic data sets show that the procedure improves the low frequency components of the input trace and side lobes in the output SLR trace are significantly suppressed. The method may be considered as a seismic amplitude attribute, which aids the interpreter to obtain the true seismic signature of the geological formations by removing the side lobes of the wavelet and restoring the low frequency components if the lower frequencies of deeper reflections are of primary concern.     

WEIGHTED VERTICAL STACKING IN CRUSTAL SEISMIC REFLECTION STUDIES ON THE CANADIAN SHIELD*

Seismic reflection methods are being developed at the University of Manitoba to aid in determining fine crustal structure in the Precambrian of Manitoba and northwestern Ontario. Present-day environmental concern as well as mineshaft conditions necessitate the detonation of several smaller charges repeated, say, I times and followed by ‘vertical’ stacking. To obtain the familiar √I improvement in signal-to-noise (S:N) amplitude ratio applying the straight-sum (SS) method, one assumes, among other things, that both S:N ratio and signal variance are the same on all traces. Dropping these assumptions, as we must for our data, it becomes necessary to apply weighting coefficients to optimize the S:N ratio of the stacked trace. We still assume the signal shapes to be the same for repeated shots, so for the jth trace on the record of the ith shot we model the time series as: t_ij=a_i (s_j+n_ij); where a_i is a scaling factor. The proper weights w_i are then shown to be proportional to σ_si/σ²_ni where σ² is variance, or to γ_i/a_i where γ_i is S:N power ratio. Applying the weighted-stack (WS) method gives S:N amplitude ratios which are, on average, 55% of the optimal ratios expected from WS theory compared with only 24% for the SS method. The 45% shortfall in WS performance is ascribed mainly to trace-alignment (or time-delay) errors. Varying noise levels on individual traces, slight dissimilarity of signal shape, and correlated noise may also contribute to a lesser extent (in decreasing order of significance). This WS method appears to strike a good practical balance between S:N improvement and processing efficiency.     

共转换点道集S变换谱相似性的多波地震数据横波波场提取技术

横波速度动校正后的共转换点(CCP)道集内,同时刻的各道横波信号S变换(ST)谱与其叠加道ST谱具有相似关系.因此,可基于这种相似关系设计自适应滤波器来提取多波地震数据中的横波波场.首先对共中心点(CMP)道集应用纵波速度动校正并在各道减去叠加道来去除数据中的纵波波场;然后在CCP道集应用横波速度动校正,将地震道振幅水平调整至叠加道振幅水平并做S变换,以叠加道ST谱为参考对地震道ST谱进行自适应滤波,去除数据中的残余纵波和噪声;最后,将滤波结果的振幅水平恢复至滤波前振幅水平.理论和实际数据试算表明,本文方法可有效提取多波地震数据中的横波波场,为多波多分量横波数据处理提供新思路.     

共接收点倾斜叠加波动方程偏移

共接收点倾斜叠加波动方程偏移,本质上是一种叠前偏移方法.每给定一个斜率P,对经过叠前（动校正前）常规处理的地震记录中的各共接收点道集,沿直线t=τ+px进行倾斜叠加,就形成一个共接收点倾斜叠加剖面.对之进行波动方程偏移,该偏移剖面将代表地下真实构造.对一系列的p,我们可以得到一系列这样的偏移剖面.对它们作共接收点叠加,偏移叠加剖面的信噪比将超过水平叠加剖面.本文导出了在均匀、水平层状及非均匀介质条件下的共接收点倾斜叠加波动方程偏移算法.     

振幅衰减特性在地震与爆破识别中的应用

基于小震级地震与爆破事件,从快速识别要求出发,分析了P波初动振幅AI和P波最大振幅AP分别与S波最大振幅AS的幅值比判据及其对事件的识别能力．考虑到传播路径对地震与爆破各振幅的影响,选用合理的振幅随距离衰减公式,分别研究了P波、 S波各振幅随震中距的衰减特征,结果显示爆破振幅衰减比地震快; 在100 km处进行衰减校正后重新计算P波与S波幅值比,得到经过衰减校正后的幅值比AI/AS正确识别率从84%提高到98%,AP/AS正确识别率从92%提高到100%,表明经衰减校正后的幅值比判据可以更好地应用于小震级地震与爆破的识别中．      

Geomechanical property estimation of unconventional reservoirs using seismic data and rock physics

An extension of a previously developed rock physics model is made that quantifies the relationship between the ductile fraction of a brittle/ductile binary mixture and the isotropic seismic reflection response. By making a weak scattering (Born) approximation and plane wave (eikonal) approximation, with a subsequent ordering according to the angles of incidence, singular value decomposition analyses are performed to understand the stack weightings, number of stacks, and the type of stacks that will optimally estimate two fundamental rock physics parameters – the ductile fraction and the compaction and/or diagenesis. It is concluded that the full PP stack, i.e., sum of all PP offset traces, and the “full” PS stack, i.e., linear weighted sum of PS offset traces, are the two optimal stacks needed to estimate the two rock physics parameters. They dominate over both the second‐order amplitude variation offset “gradient” stack, which is a quadratically weighted sum of PP offset traces that is effectively the far offset traces minus the near offset traces, and the higher order fourth order PP stack (even at large angles of incidence). Using this result and model‐based Bayesian inversion, the seismic detectability of the ductile fraction (shown by others to be the important rock property for the geomechanical response of unconventional reservoir fracking) is demonstrated on a model characteristic of the Marcellus shale play.     

L'EGALISATION SPECTRALE: UN MOYEN D'AMELIORER LA QUALITE DES DONNEES SISMIQUES*

In land seismic surveys spectrum equalization can increase the quality of seismic data in a selected frequency band. The power of lower frequencies in the spectrum of input traces is generally greater than that of higher frequencies, particularly in land seismic surveys because of ground roll. In order to improve the quality of seismic data it is necessary to raise the energy of higher frequencies to the same level as that of lower frequencies, without alteration of the phases. The first step of the method is to compute the amplitude spectrum of each input trace to determine a weighting function which is then applied to the amplitude spectrum in order to balance it. The function is the inverse of the short wavelength variation of the amplitude spectrum. The short wavelength variation can be obtained by interpolation between average values of the modulus of the amplitude spectrum computed in narrow bands within a selected band of frequencies. Another way of obtaining the short wavelength variation is to apply a low-pass filter to the amplitude spectrum. The calculations are readily performed in the frequency domain by the Fourier transform. Spectrum equalization is automatically adjusted to each trace and does not modify the average amplitude in the time domain. However, as the frequency band and energy of the ground roll both vary according to the distance from the shot, spectrum equalization tends to make the spectrum of output traces independent of the offset distance. The use of spectrum equalization before any two-dimensional filtering improves ground roll elimination. Continuity and resolution of horizons are also increased by spectrum equalization before CDP stack. Several examples of applications of spectrum equalization to seismic land and marine surveys are shown.     

用人工神经网络实现地震记录中的废道自动切除

切除废道（即道编辑）的工作是地震信号处理中重要而又工作量巨大的一步.本文提出了一种用人工神经网络实现的自动切除方法,所用的神经网络模型为新奇滤波器模型,方法简单实用,切除效果令人满意.文中介绍了方法的原理并给出了几个实验结果.     

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.     

频谱代换无拉伸动校正方法研究

动校正拉伸是地震资料处理的一个基本问题,解决拉伸问题的处理方法是切除.现代地震数据大多为长排列采集,动校正拉伸更为严重.依据褶积模型和Fourier变换的基本性质,本文给出频谱代换无拉伸动校正方法.算法实现就是将CMP道集变换到频率域,取参考道的相位谱替换其它偏移距道的相位,同时保持其振幅谱不变,再做Fourier反变换就得到动校正后的地震剖面.通过其实现过程可知该方法不需要地下介质的速度信息,算法可完全自动实现,且具有较高的计算效率.频谱代换无拉伸动校正可适用于任何偏移距的地震资料,而且还可有效保持地震资料的AVO效应.理论模拟数据及其叠加结果显示频谱代换法的有效性和实用性,同时该方法具有较强的抗随机噪音能力.     

SIGNAL-TO-NOISE RATIO ENHANCEMENT IN SEISMIC MULTIFOLD DATA USING BAYESIAN STATISTICS*

Bayesian statistics are applied to the problem of signal-to-noise ratio enhancement from a common-midpoint gather. By maximizing the a posteriori probability distribution of the gather with respect to the minimum-offset trace and suppressing multiples via a semblance criterion, a statistically biased stack is formed with signal-to-noise ratio comparable to that of the usual stack while preserving the resolution and registration of the original noisy trace. Application of the algorithm to real data reveals geologically significant features which are indistinct in the standard stacked section.     

Tracking the amplitude versus offset (AVO) by using orthogonal polynomials1

Inversion for S-wave velocities from the amplitude variation with offset of P-wave data is far from being a standard routine in the seismic processing sequence. However, the need for tracking the amplitude versus offset (AVO) occurs in several situations, for example in order to estimate the zero-offset amplitude, to reveal areas with particular AVO characteristics, or to compress the AVO so that it is more easily obtainable at a later stage of the seismic processing. Furthermore, weak reflections can occasionally, due to the effect of the angle-dependent reflectivity, have a polarity-shift with offset, resulting in a very poor, or even vanishing, stack response. In such cases, the reflection event has to be represented by some other property than its mean amplitude or stack value. We outline how the AVO of seismic data may be extracted and classified by the use of orthogonal polynomials. The main advantage of this method compared to a general polynomial fit is that the AVO may be classified by a unique Spectrum of polynomial coefficients. This is in analogy to Fourier coefficients where the orthogonal basis is harmonic functions. The set of orthogonal polynomials is constructed entirely from the set of offset coordinates, and these polyno-mials are defined only on the offset window considered. Compared to a Fourier transform, this is a major advantage since there is no effect of a limited spatial bandwidth. The AVO of normal-moveout corrected data may be represented by a data gather where the orthogonal polynomial coefficients are given as time traces with each trace revealing a certain AVO characteristic. For instance, the stack is proportional to the zeroth-order coefficient, the mean gradient is given by the firstorder coefficient, while the second-order coefficient indicates whether the AVO increases and then decreases, or vice versa.     

基于非稳态多项式拟合的地震噪声衰减方法研究(英文)

基于非稳态多项式拟合理论,针对地震数据中同相轴振幅变化这一特征,我们提出了一种地震噪声衰减的新方法。非稳态多项式拟合系数是时变的,通过整形正则化约束多项式拟和系数的光滑性,自适应的估计地震数据的相干分量。基于动校正后的共中心点道集(CMP)中地震信号的相干性,利用非稳态多项式拟合估计有效信号,从而衰减随机噪声。对于线性相干噪声,如地滚波,首先利用径向道变换(RadialTraceTransform,RTT)将地震数据变换到时间一视速度域,在时间—视速度域利用非稳态多项式拟合估计出相干噪声,然后减去相干噪声。该方法可以有效的估计振幅变化的相干分量,不需要相干分量振幅为常量的假设。模拟和实际资料处理结果表明,与传统的稳态多项式拟合和低切滤波相比,该方法可以更为有效的衰减地震噪声,同时保真了地震有效信号。     

Geophone-seabed coupling effect and its correction

By summing geophone and hydrophone data with opposite polarity responses to water layer reverberation, the ocean bottom cable dual-sensor acquisition technique can effectively eliminate reverberation, broaden the frequency bandwidth, and improve both the resolution and fidelity of the seismic data. It is thus widely used in industry. However, it is difficult to ensure good coupling of the geophones with the seabed because of the impact of ocean flow, seafloor topography, and field operations; therefore, geophone data are seriously affected by the transfer function of the geophone-seabed coupling system. As a result, geophone data frequently have low signal-to-noise ratios (S/N), which causes large differences in amplitude, frequency, and phases between geophone and hydrophone data that severely affect dual-sensor summation. In contrast, the hydrophone detects changes in brine pressure and has no coupling issues with the seabed; thus, hydrophone data always have good S/N. First, in this paper, the mathematical expression of the transfer function between geophone and seabed is presented. Second, the transfer function of the geophone-seabed is estimated using hydrophone data as reference traces, and finally, the coupling correction based on the estimated transfer function is implemented. Using this processing, the amplitude and phase differences between geophone and hydrophone data are removed, and the S/N of the geophone data are improved. Synthetic and real data examples then show that our method is feasible and practical.