PRINCIPLES AND APPLICATION OF MAXIMUM KURTOSIS PHASE ESTIMATION1

Methods of minimum entropy deconvolution (MED) try to take advantage of the non-Gaussian distribution of primary reflectivities in the design of deconvolution operators. Of these, Wiggins’(1978) original method performs as well as any in practice. However, we present examples to show that it does not provide a reliable means of deconvolving seismic data: its operators are not stable and, instead of whitening the data, they often band-pass filter it severely. The method could be more appropriately called maximum kurtosis deconvolution since the varimax norm it employs is really an estimate of kurtosis. Its poor performance is explained in terms of the relation between the kurtosis of a noisy band-limited seismic trace and the kurtosis of the underlying reflectivity sequence, and between the estimation errors in a maximum kurtosis operator and the data and design parameters. The scheme put forward by Fourmann in 1984, whereby the data are corrected by the phase rotation that maximizes their kurtosis, is a more practical method. This preserves the main attraction of MED, its potential for phase control, and leaves trace whitening and noise control to proven conventional methods. The correction can be determined without actually applying a whole series of phase shifts to the data. The application of the method is illustrated by means of practical and synthetic examples, and summarized by rules derived from theory. In particular, the signal-dominated bandwidth must exceed a threshold for the method to work at all and estimation of the phase correction requires a considerable amount of data. Kurtosis can estimate phase better than other norms that are misleadingly declared to be more efficient by theory based on full-band, noise-free data.     

储层砂岩声波速度预测

本文主要基于Ｇａｓｓｍａｎｎ方程和经验规律，提出了孔隙流体替代和孔隙度改变时对砂央地震波速度变化的估计，以及直接利用岩石矿物和孔隙流体的弹性性质计算砂岩地震波速度方法，利用已知的岩芯，测井或地震数据，运用这此方法，可合理地对储层砂岩地震波速度进行预测。     

ESTIMATION OF THE DEGREE OF POLYNOMIAL FITTED TO GRAVITY ANOMALIES AND ITS APPLICATION1

A method for estimating the degree of polynomial fitted to gravity anomalies to evaluate the regional anomaly is presented. The anomaly can be fitted by polynomials of different degrees with the least-squares method and the optimum degree of the polynomial evaluating this anomaly can be estimated from the point of discontinuity of the gradient on a graph of variance against the polynomial degree. The Bouguer gravity is initially separated by upward continuation to a proper height and then the degree of regional polynomial to fit the Bouguer anomaly can be estimated. Theoretical and field examples show the effectiveness of the method.     

ESTIMATION OF ELASTIC PARAMETERS FROM AVO EFFECTS IN THE TAU-P DOMAIN1

A quantitative AVO algorithm suitable for media with slow lateral parameter variations is developed. The method is based on a target-oriented inversion scheme for estimation of elastic parameters in a locally horizontally stratified medium. The algorithm uses band-limited PP reflection coefficients in the τ-p domain to estimate P- and S-wave velocities, densities and layer thicknesses. To obtain these reflection coefficients, a pre-processing involving the Radon transform and multiple attenuation is necessary. Furthermore, a macromodel for the velocities above the target zone must be found prior to the inversion. Various inversion tests involving synthetic data with white Gaussian noise and modelling errors that are likely to occur in conjunction with real data have been performed. In general, the inversion algorithm is fairly robust, since it is able to reproduce the main features of the reference model: main interface locations and relative contrasts in the three unknown layer parameters are recovered. From a test combining the effect of source directivity, one thin layer and 20% white Gaussian noise, it was found that neglect of the source directivity in the inversion caused the largest errors in the estimates. This indicates that it is very important either to eliminate the source directivity in a preprocessing step, or to take the directivity into account in the present algorithm. Despite these problems it was concluded that the inversion algorithm was able to reproduce the main features of the reference model.     

优化减震距离

本文对中国大陆内部不同时段发生的七级地震和六级地震分别进行统计分析,求得不同震级的优势地震间距,减震距离以及地震间距随时间变化的关系式。提出地震间距的数值分布可用正态概率分布函数描述,并得到含有时间参量的地震间距概率密度函数。此外,根据弹性位错理论,求得一次地震后在减震距离处所产生的位移,进而求出平均位移速率。     

调谐质量阻尼器的优化分析

本文根据双自由度系统的随机反应，推导了设置调谐质量阻尼器的单自由度系统的运动方程，求出了白噪声基底输入时，设置ＴＭＤ的单自由度系统的反应方差与未设置ＴＭＤ的单自由度系统的反应方差之比，并采用模式搜索法对其进行优化方法，得到了ＴＭＤ系统的最佳减振效果以及相应的ＴＭＤ的参数取值，本文的分析表明，ＴＭＤ系统对减小白噪声基底输入的单自由度系统的随机反应是十分有效的。     

POST-CRITICAL WAVELET ESTIMATION AND DECONVOLUTION1

Using synthetic data, it is demonstrated that the amplitude spectra of post-critical plane-wave components are stable and equal to the amplitude spectrum of the input wavelet (critical reflection theorem). Our analysis and physical explanation of the theorem are based only on amplitude versus offset arguments. The stability of the spectra in the post-critical region is directly related to a high amplitude post-critical reflection that dominates the trace in the slant-stack domain. The validity of the theorem for both the acoustic and elastic cases, its assumptions and limitations, are also examined with emphasis on applications for processing seismic reflection data. Based on the theorem, a deterministic procedure is developed (assuming minimum-phase properties) for wavelet estimation and subsequent deconvolution. We call this method Post-critical Deconvolution, which emphasizes reliance on post-critical reflection data. The performance of the method is shown with real data and the results are compared to those obtained with conventional deconvolution techniques.     

地震道非线性最优化反演

在非线性最优化理论的基础上提出了地震道反演的非线性最优化方法,推导出地震道非线性最优化反演所需的梯度向量、Hasse矩阵,并对测井约束反演、反演稳定性等问题进行了探讨.理论模型和实际资料的反演结果表明,这一方法是地震道反演的一种有效手段.     

斯托克司函数逼近及截断误差估计

本文对高度异常及垂线偏差的截断误差进行了估计,导出了高阶截断系数的近似表达式。这些截断系数是振幅逐渐衰减的正弦函数,而且其振幅与斯托克司函数在界圆φ_0处的值密切相关。经分析认为,采用莫洛金斯基的最小平方逼近方法,将可使截断误差的数量级大为降低,值得在实际中采用。为了进一步提高截断系数的收敛速度,建议在最小平方逼近的基础上,附加上界圆φ_0处的边界条件,这样将较单纯的逼近为优。为此提出两种实施的方法:利用拉格朗日的条件极值和利用样条函数逼近。     

斯托克司函数逼近及截断误差估计

本文对高度异常及垂线偏差的截断误差进行了估计,导出了高阶截断系数的近似表达式。这些截断系数是振幅逐渐衰减的正弦函数,而且其振幅与斯托克司函数在界圆φ_0处的值密切相关。经分析认为,采用莫洛金斯基的最小平方逼近方法,将可使截断误差的数量级大为降低,值得在实际中采用。为了进一步提高截断系数的收敛速度,建议在最小平方逼近的基础上,附加上界圆φ_0处的边界条件,这样将较单纯的逼近为优。为此提出两种实施的方法:利用拉格朗日的条件极值和利用样条函数逼近。     

ELASTIC PARAMETER ESTIMATION BY COHERENCY OPTIMIZATION1

We present a method for estimating P- and S-velocities within defined layers (macromodel), using only kinematic properties (i.e. traveltimes) of the wavefield. The method does not require identification of mixed-mode events on prestack or post-stack data. After obtaining a V_p-depth model by coherency inversion, S-velocities are determined by coherency optimization along computed traveltime curves for mixed-mode events on prestack data. Since the method does not involve any dynamic wavefield computations, a simple ray-tracing algorithm is used to solve the forward problem. The simplicity of the scheme, together with the ability to apply it locally, makes it highly suitable for interactive use. Results of this method may be used to detect Poisson's ratio anomalies within or between layers and may serve as an initial model for more complicated elastic inversion algorithms.     

WAVELET ESTIMATION USING THE MULTITAPER METHOD1

An accurate estimate of the seismic wavelet on a seismic section is extremely important for interpretation of fine details on the section and for estimation of acoustic impedance. In the absence of well-control, the recognized best approach to wavelet estimation is to use the technique of multiple coherence analysis to estimate the coherent signal and its amplitude spectrum, and thence construct the seismic wavelet under the minimum-phase assumption. The construction of the minimum-phase wavelet is critically dependent on the decay of the spectrum at the low-frequency end. Traditional methods of cross-spectral estimation, such as frequency smoothing using a Papoulis window, suffer from substantial side-lobe leakage in the areas of the spectrum where there is a large change of power over a relatively small frequency range. The low-frequency end of the seismic spectrum (less than 4 Hz) decays rapidly to zero. Side-lobe leakage causes poor estimates of the low-frequency decay, resulting in degraded wavelet estimates. Thomson's multitaper method of cross-spectral estimation which suffers little from side-lobe leakage is applied here, and compared with the result of using frequency smoothing with the Papoulis window. The multitaper method seems much less prone to estimating spuriously high coherences at very low frequencies. The wavelet estimated by the multitaper approach from the data used here is equivalent to imposing a low-frequency roll-off of some 48 dB/oct (below 3.91 Hz) on the amplitude spectrum. Using Papoulis smoothing the equivalent roll-off is only about 36 dB/oct. Thus the multitaper method gives a low-frequency decay rate of the amplitude spectrum which is some 4 times greater than for Papoulis smoothing. It also gives more consistent results across the section. Furthermore, the wavelet obtained using the multi-taper method and seismic data only (with no reference to well data) has more attractive physical characteristics when compared with a wavelet extracted using well data, than does an estimate using traditional smoothing.     

场地地震地表破裂危险性估计

摘要：地震地表破裂是强地震活动中沿发震断层在地表形成的位移,它是包括震源因素、传播途径因素、场地地质条件因素等多种复杂因素的综合作用产物。地震地表破裂可以定量地加以描述。在假定基岩介质具有各项均匀刚性的前提下,对于一般的场地,地震地表破裂的危险性（概率P）大致可以确定为场地地震危险性（P1）、断层（P2）、场地第四系覆盖层（P3）的函数,即P=3Пi=1Pi.Pi值的确定可以通过多种途径来实现,本文在Pi值的确定过程中,以场地所在潜在震源区震级上限（Mu）为指标,P1=1．5874（Mu-6）-1;P2表示为断层发育状况、活动程度和断层最新活动性质的概率指数,P2=3Пi=1P2i.P3=nПi=1kiwi,wi为分解的第i均质土层（i=1,2,…,n）对地震破裂的衰减系数,ki为破裂通过第i均质土层（i=1,2,…,n）与其下土层临界面的破裂传播折射损耗率。通过上面的计算可以得到一般场地条件下地震地表破裂的危险性估计,这一估计是相对保守的估计。     

ESTIMATION OF THE PRIMARY SEISMIC PULSE *

A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression where j represents trace number on the record, t is time, α_j is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and n_j is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.     

MAXIMUM-LIKELIHOOD ESTIMATION OF SEISMIC IMPULSE RESPONSES*

A seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus a moving average noise process (colored noise). Multiple reflections and reverberations are assumed to be removed from the trace by conventional means. The method of maximum likelihood (ML) is used to estimate the reflection coefficients and the unknown noise parameters. If the reflection coefficients are known from well logs, the seismic pulse and the noise parameters can be estimated. The maximum likelihood estimation problem is reduced to a nonlinear least-squares problem. When the further assumption is made that the noise is white, the method of maximum likelihood is equivalent to the method of least squares (LS). In that case the sampling rate should be chosen approximately equal to the Nyquist rate of the trace. Statistical and numerical properties of the ML- and the LS-estimates are discussed briefly. Synthetic data examples demonstrate that the ML-method gives better resolution and improved numerical stability compared to the LS-method. A real data example shows the ML- and LS-method applied to stacked seismic data. The results are compared with reflection coefficients obtained from well log data.     

地震监测台网的最佳理论设置初探

本文所讨论的问题是在一个平面区域Ｄ内应如何设置地震监视台，使在该区域内任何一点发生地震，在距震源５０公里的圆周内，至少有４个地震台可监视地震情况，而且使区域Ｄ内设置的地震监视台个数最少．这里，首先对Ｄ为一有界闭区域，给出了在Ｄ内设置的地震监视台个数的下界，并且讨论了Ｄ为半径为５０的圆盘时，地震监视台的下确界以及地震台设置的设计方案．进而又讨论了当Ｄ为半径为５０ｋ公里时（ｋ＝２，３，……）时应设置地震台个数的下界．     

二维不均匀场地地震地面运动的估算

通过对某工程场地采用不同的介质参数和不同的人工边界处理方法求得的地面运动的比较，指出，只有应用合理的计算模型才得到正确的计算结果，文章还对在均匀粘弹性半空间内任意划定刚性和滚轴人工边界造成的计算误差作了探讨。     

烈度分布的几何特征和震源参数的估计

本文在考虑环境刚度效应和非匀阻效应的情况下,采用椭圆形震源简化模型,研究了走滑断层的地震烈度几何要素与震源参数之间的关系,初步建立了估计断层有效发震段长度、错动角、应力降和错动距离等参数的等震线法,并结合唐山、通海、炉霍和永善等震例进行了试算     

南北地震带强震复发间隔的估计

通过对南北地震带各主要断裂带历史强震的时空特点研究 ,试图寻找出带内各主要构造带强震的复发和填充特征 ,并在此基础上研究其差异性 ,对未来各带发生强震的危险性作出估计