SEISMIC VELOCITY ESTIMATION*

The accuracy of the two most common arrival time functions used in seismic velocity estimation is investigated. It is shown that the hyperbolic arrival time function is more accurate than the parabolic arrival time function for a horizontally layered elastic medium. An upper bound on the difference between the two arrival time functions is given. A maximum-likehood detector for estimating the arrival time of the signals is given. For the signal-in-noise model that is used the maximum-likelihood detector is equivalent to a least-squares detector which corresponds to using the signal energy as coherency measure. The semblance coefficient corresponds to a normalized least-squares detector. The semblance coefficient is very similar to a filter performance measure that is used in least-squares filter design.     

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.     

MAXIMUM LIKELIHOOD ESTIMATION OF SEISMIC REFLECTION COEFFICIENTS*

A seismic trace is modeled as a moving average (MA) process both in signal and noise: a signal wavelet convolved with a reflection coefficient series plus colored random noise. Seismic reflection coefficients can be estimated from seismic traces using suitable estimation algorithms if the input wavelet is known and vice versa. The maximum likelihood (ML) algorithm is used to estimate the system order and the reflection coefficients. The system order is related to the arrival time of the latest signal in a complex seismic reflection event. The least-squares (LS) method does not provide such information. The ML algorithm makes assumptions only about the Gaussian nature of the noise. It is better suited for seismic applications since the LS method inherits the white noise assumption. The Gauss-Newton (G-N) and Newton-Raphson (N-R) optimization algorithms are used to obtain the ML and the LS estimates. Reflection coefficient estimations are affected by the choice of sampling rate of seismic data. Theoretically, the optimum choice in system identification is the Nyquist rate. Experience with synthetic data confirms the theory. In practice, good estimates of reflection coefficients are possible only up to certain pulse separations (or, equivalently, orders). This is mostly due to numerical problems with the optimization algorithms used and partly due to the limited bandwidth of seismic signals. Good estimates from data simulated using three airgun array pulses recorded with 6–128 Hz filter setting are possible up to about 40.0 ms pulse separations. Successful estimations from pinchout and thin layer simulations and well controlled offshore “bright-spots” are given.     

IDENTIFICATION OF SEISMIC REFLECTIONS USING SINGULAR VALUE DECOMPOSITION*

Singular value decomposition (SVD) is applied to the identification of seismic reflections by using two different models: the impulse response model, where a seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus noise, and the delayed pulse model, where the seismic signal is assumed to consist of a small number of delayed pulses of known shape and with unknown amplitudes and arrival times. SVD clearly shows how least-squares estimation of the reflection coefficients may become unstable, since a division by the singular values is required. Two methods for stabilizing this procedure are investigated. The inverse of the singular values may be replaced by zeros when they are less than a given threshold. This is called the SVD cut-off method. Alternatively, we may use ridge regression which in filter design corresponds to assuming white noise. Statistical methods are used to compute an optimal SVD cut-off level and also to compute an optimal weighting parameter in ridge regression. Numerical studies indicate that the use of SVD cut-off or ridge regression stabilizes the least-squares procedure, but that the results are inferior to maximum-likelihood estimation where the noise is assumed to be filtered white noise. For the delayed pulse model, we use a linearization procedure to iteratively update the estimates of both the reflection amplitudes and the arrival times. In each step, the optimal SVD cut-off method is used. Confidence regions for the estimated reflection amplitudes and arrival times are also computed. Synthetic data examples demonstrate the effectiveness of this method. In a real data example, the maximum-likelihood method assuming an impulse response model is first used to obtain initial estimates of the number of reflections and their amplitudes and traveltimes. Then the iterative procedure is used to obtain improved estimates of the reflection amplitudes and traveltimes.     

基于互信息量的地震信号检测和初至提取方法

本文将现代信息科学中的重要基础理论——信息论引入到地震信号的分析和处理中，提出了一种利用互信息量检测地震信号并进行初至提取的方法，给出了该方法的基本原理和具体算法.计算结果表明，互信息量随滑动窗口移动的变化情况可以明确标示出待测地震信号的存在，通过提取互信息量的突变点或峰值点，能够有效拾取地震波的初至时刻.这种方法还可以特别针对非传统的地震信号，如连续随机信号、随机脉冲序列等进行处理.在这些信号条件下，往往信噪比很低，波形随传播距离发生较大变化，传统的信号检测方法效果不佳，而这种以随机信号检测为基础的互信息量探测方法具有很好的性能，很有发展前景.     

区域震相初至估计

本在地震数据自动化处理中，给出一种基于自回归模型的Akaike information criteria(AIC)算法和信号平均幅值比的混合方法来估计地震信号的初至．用信号的AIC曲线和平均幅值比曲线构造一种叠加曲线，再进行类似于坐标旋转的校正，可以准确估计低信噪比记录中信号的初至，尤其对于震相类型比较复杂的后续震相(如S波、Lg波)的初至估计结果很好．通过对中国数字地震台网乌鲁木齐台记录到的23次天然地震中P波、S波和Lg波的初至估计，与人工分析结果相比，P波初至估计的均方误差为0．71s，后续震相(S波、Lg波)的均方误差为1．64s，优于传统AIC算法的估计结果．     

基于最大似然属性的断层识别方法及应用

断层识别是断块型油气田勘探开发的重要研究内容,尤其是在复杂断块油气田的勘探开发中,准确合理的断层识别是落实油气田构造和确定注采井网的关键因素.方差体、相干体、曲率属性等常规方法在断层识别中发挥着重要作用,但在复杂断裂发育区地震资料品质较差,常规方法分辨率较低从而无法准确识别断层组合关系.基于相似系数改进的似然属性在已知断层倾向和倾角时可以精确表征断层,但由于断层的倾向和倾角是未知的,因此可以采用断层倾向和倾角扫描的方法计算最大似然属性来表征断层.本文对比分析了相似系数和最大似然属性的原理;并将最大似然属性应用于模型正演数据和实际地震数据进行断层识别分析,结果表明,最大似然属性在剖面上更符合断层展布特征,在平面上断层组合关系更加清晰,在断层识别上具有较好的应用效果.     

Automatic cross-well tomography by semblance and differential semblance optimization: theory and gradient computation

A technique for automatic cross-well tomography based on semblance and differential semblance optimization is presented. Given a background velocity, the recorded seismic data traces are back-propagated towards the source, i.e. shifted towards time zero using the modelled traveltime between the source and the receiver and corrected for the geometrical spreading. Therefore each back-propagated trace should be a pulse, close to time zero. The mismatches between the back-propagated traces indicate an error in the velocity model. This error can be measured by stacking the back-propagated traces (semblance optimization) or by computing the norm of the difference between adjacent traces (differential semblance optimization).
It is known from surface seismic reflection tomography that both the semblance and differential semblance functional have good convexity properties, although the differential semblance functional is believed to have a larger basin of attraction (region of convergence) around the true velocity model. In the case of the cross-well transmission tomography described in this paper, similar properties are found for these functionals.
The implementation of this automatic method for cross-well tomography is based on the high-frequency approximation to wave propagation. The wavefronts are constructed using a ray-tracing algorithm. The gradient of the cost function is computed by the adjoint-state technique, which has the same complexity as the computation of the functional. This provides an efficient algorithm to invert cross-well data. The method is applied to a synthetic data set to demonstrate its efficacy.     

2012年印尼8.6级地震应变地震波的Hilbert-Huang时频分析

本文通过端点效应压制的Hilbert-Huang变换, 对大同及沁源台布置的四分量钻孔应变仪记录的印尼8.6级地震激发的应变地震波形进行时频分析, 结果显示印尼8.6级地震的主震和8.2级余震的应变地震波序列各个震相具有不同的时频特征: ① 地震波到达之前的所谓“环境噪声”部分, 瞬时频率低, 瞬时振幅小; ② P波初至时, 高频成分突然增加, 振幅也随即增强; ③ S波到达时, 频率有所降低而振幅剧烈上升; ④ 面波到达时, 振幅进一步剧烈上升达到整个序列的极大值; ⑤ 尾波部分振幅逐渐降低, 但与噪声部分相比频率依然偏高, 振幅依然偏大。 本文也将应变地震波与地震仪记录的地震波进行对比, 虽然应变地震波与地震波波形和Fourier谱具有极高的相关系数, 但从Hilbert-Huang变换得到的边际谱上看, 应变地震波与地震波有显著的区别, 应变地震波比地震波记录的低频成分相对更多。 通过Hilbert谱, 有助于更好地了解非平稳信号的局部特征, 对于突变信号的地震波, Hilbert-Huang变换是一个较好的时频分析工具。     

MCZT在气枪震源信号频谱分析中的应用

气枪震源信号是短时非平稳信号,采用频谱细化算法能提高频谱分析的准确性。首先进行了改进线性调频Z变换(MCZT)和FFT两种频谱分析算法的误差仿真计算,然后进行气枪震源的水下子波信号和地震波信号的对比计算。结果表明MCZT计算误差较小、计算时间较少,能有效提高气枪震源信号频率和幅度特征提取的准确性,是气枪震源信号频谱特征分析的一个有效方法。     

METHOD FOR DETERMINATION OF VELOCITY AND DEPTH FROM SEISMIC REFLECTION DATA1

The estimation of velocity and depth is an important stage in seismic data processing and interpretation. We present a method for velocity-depth model estimation from unstacked data. This method is formulated as an iterative algorithm producing a model which maximizes some measure of coherency computed along traveltimes generated by tracing rays through the model. In the model the interfaces are represented as cubic splines and it is assumed that the velocity in each layer is constant. The inversion includes the determination of the velocities in all the layers and the location of the spline knots. The process input consists of unstacked seismic data and an initial velocity-depth model. This model is often based on nearby well information and an interpretation of the stacked section. Inversion is performed iteratively layer after layer; during each iteration synthetic travel-time curves are calculated for the interface under consideration. A functional characterizing the main correlation properties of the wavefield is then formed along the synthetic arrival times. It is assumed that the functional reaches a maximum value when the synthetic arrival time curves match the arrival times of the events on the field gathers. The maximum value of the functional is obtained by an effective algorithm of non-linear programming. The present inversion algorithm has the advantages that event picking on the unstacked data is not required and is not based on curve fitting of hyperbolic approximations of the arrival times. The method has been successfully applied to both synthetic and field data.     

Monitoring Seismo-volcanic and Infrasonic Signals at Volcanoes: Mt. Etna Case Study

Volcanoes generate a broad range of seismo-volcanic and infrasonic signals, whose features and variations are often closely related to volcanic activity. The study of these signals is hence very useful in the monitoring and investigation of volcano dynamics. The analysis of seismo-volcanic and infrasonic signals requires specifically developed techniques due to their unique characteristics, which are generally quite distinct compared with tectonic and volcano-tectonic earthquakes. In this work, we describe analysis methods used to detect and locate seismo-volcanic and infrasonic signals at Mt. Etna. Volcanic tremor sources are located using a method based on spatial seismic amplitude distribution, assuming propagation in a homogeneous medium. The tremor source is found by calculating the goodness of the linear regression fit (R ²) of the log-linearized equation of the seismic amplitude decay with distance. The location method for long-period events is based on the joint computation of semblance and R ² values, and the location method of very long-period events is based on the application of radial semblance. Infrasonic events and tremor are located by semblance–brightness- and semblance-based methods, respectively. The techniques described here can also be applied to other volcanoes and do not require particular network geometries (such as arrays) but rather simple sparse networks. Using the source locations of all the considered signals, we were able to reconstruct the shallow plumbing system (above sea level) during 2011.     

Effect of coherent noise on single-station direction of arrival estimation

Polarization analysis of multi-component seismic data is used in both exploration seismology and earthquake seismology. In single-station polarization processing, it is generally assumed that any noise present in the window of analysis is incoherent, i.e., does not correlate between components. This assumption is often violated in practice because several overlapping seismic events may be present in the data. The additional arrival(s) to that of interest can be viewed as coherent noise. This paper quantifies the error because of coherent noise interference. We first give a general theoretical analysis of the problem. A simple mathematical wavelet is then used to obtain a closed-form solution to the principal direction estimated for a transient incident signal superposed with a time-shifted, unequal amplitude version of itself, arriving at an arbitrary angle to the first wavelet. The effects of relative amplitude, arrival angle, and the time delay of the two wavelets on directional estimates are investigated. Even for small differences in angle of arrival, there may be significant error (>10°) in the azimuth estimate.     

基于改进长短时窗比值及优化变分模态分解的微震初至拾取算法

针对低信噪比条件下微震初至拾取准确度低的问题,基于信号幅度变化引入权重因子,对传统长短时窗比值（STA/LTA）算法进行改进,提高初次拾取精度。为了进一步降低拾取误差,对变分模态分解（VMD）算法进行优化,基于互相关系数和排列熵准则自适应确定VMD分解层数,对初次拾取结果前后2—3 s的记录进行优化VMD,并计算分解后各本征模函数（IMF）的峰度赤池信息准则值,得到各IMF的到时,以各IMF的拾取结果及能量比综合加权得到二次拾取到时。仿真实验表明:改进后的STA/LTA在较低信噪比下可降低初次拾取误差约0.01 s以上;相比经验模态分解（EMD)和小波包分解,自适应VMD分解后能再次降低误差,最终与人工拾取结果平均误差在0.023 s以内。实际微震信号初至拾取结果表明,本算法能快速有效地识别初至P波,与人工拾取结果相比误差小,准确率高。      

基于加权K均值聚类的多属性初至拾取方法

为提高初至拾取方法的准确性和自适应能力,将变异系数加权K均值聚类算法引入初至拾取中。首先提取均方根振幅、相邻道相关性、线积分、振幅谱主频等多种地震属性;然后针对地震属性进行加权K均值聚类,自动识别初至所在时窗;最后结合相位校正法,实现时窗内初至波起跳时间的拾取。在此基础上通过实际数据测试,并与长短时窗能量比法、反向传播神经网络方法对比,验证了本文方法的有效性与可行性。结果表明,基于加权K均值聚类的多属性初至拾取方法能较快速、准确地拾取低信噪比数据的初至,并且无需人为判断时窗,从而提高了拾取的自适应能力。      

Depth and morphology of reflectors from the non-linear inversion of arrival-time and waveform semblance data. Part I: method and applications to synthetic data

We propose a two-dimensional, non-linear method for the inversion of reflected/converted traveltimes and waveform semblance designed to obtain the location and morphology of seismic reflectors in a lateral heterogeneous medium and in any source-to-receiver acquisition lay-out. This method uses a scheme of non-linear optimization for the determination of the interface parameters where the calculation of the traveltimes is carried out using a finite-difference solver of the Eikonal equation, assuming an a priori known background velocity model. For the search for the optimal interface model, we used a multiscale approach and the genetic algorithm global optimization technique. During the initial stages of inversion, we used the arrival times of the reflection phase to retrieve the interface model that is defined by a small number of parameters. In the successive steps, the inversion is based on the optimization of the semblance value determined along the calculated traveltime curves. Errors in the final model parameters and the criteria for the choice of the best-fit model are also estimated from the shape of the semblance function in the model parameter space. The method is tested and validated on a synthetic dataset that simulates the acquisition of reflection data in a complex volcanic structure. This study shows that the proposed inversion approach is a valid tool for geophysical investigations in complex geological environments, in order to obtain the morphology and positions of embedded discontinuities.     

Implementation aspects of eigendecomposition‐based high‐resolution velocity spectra

In this paper, we discuss high‐resolution coherence functions for the estimation of the stacking parameters in seismic signal processing. We focus on the Multiple Signal Classification which uses the eigendecomposition of the seismic data to measure the coherence along stacking curves. This algorithm can outperform the traditional semblance in cases of close or interfering reflections, generating a sharper velocity spectrum. Our main contribution is to propose complexity‐reducing strategies for its implementation to make it a feasible alternative to semblance. First, we show how to compute the multiple signal classification spectrum based on the eigendecomposition of the temporal correlation matrix of the seismic data. This matrix has a lower order than the spatial correlation used by other methods, so computing its eigendecomposition is simpler. Then we show how to compute its coherence measure in terms of the signal subspace of seismic data. This further reduces the computational cost as we now have to compute fewer eigenvectors than those required by the noise subspace currently used in the literature. Furthermore, we show how these eigenvectors can be computed with the low‐complexity power method. As a result of these simplifications, we show that the complexity of computing the multiple signal classification velocity spectrum is only about three times greater than semblance. Also, we propose a new normalization function to deal with the high dynamic range of the velocity spectrum. Numerical examples with synthetic and real seismic data indicate that the proposed approach provides stacking parameters with better resolution than conventional semblance, at an affordable computational cost.     

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.     

5月12日汶川8.0级地震强余震观测的电磁同震效应

2008年5月12日汶川8.0级大地震发生后,在武都汉王地震台及其附近地区进行了为期22d的余震序列电磁异常连续监测,观测到多次余震事件的电磁同震现象。通过与汉王强震台的地震记录数据比较发现,同震信号存在于所有的电场和磁场记录分量中,它们与地震波的到达同步,而不是在地震发生的时刻出现。地震发生时的电磁辐射信号似乎在记录数据中有所显示,但是与地震波到达观测点时的电磁信号相比幅度要小得多     

Using the Wiener–Levinson algorithm to suppress ground-roll

In land seismic surveys, the seismic data are mostly contaminated by ground-roll noise, high amplitude and low frequency. Since the ground-roll is coherent with reflections and depends on the source, the spectral band of seismic signal and ground-roll always overlap, which can be clearly seen in the spectral domain. So, separating them in time or frequency domain commonly causes waveform distortions and information missing due to cut-off effects. Therefore, the combination of these factors leads to search for alternative filtering methods or processes. We applied the conventional Wiener–Levinson algorithm to extract ground-roll from the seismic data. Then, subtracting it from the seismic data arithmetically performs the ground-roll suppression. To set up the algorithm, linear or nonlinear sweep signals are used as reference noise trace. The frequencies needed in creating a reference noise trace using analytical sweep signal can be approximately estimated in spectral domain. The application of the proposed method based on redesigning of Wiener–Levinson algorithm differs from the usual frequency filtering techniques since the ground-roll is suppressed without cutting signal spectrum. The method is firstly tested on synthetics and then is applied to a shot data from the field. The result obtained from both synthetics and field data show that the ground-roll suppression in this way causes no waveform distortion and no reduction of frequency bandwidth of the data.