最大似然法速度谱估计的改进

本文分析了现行的最大似然法速度谱估计的基本运算过程。结果表明,各记录道间的幅度差异将严重降低方法的分辨率,对此,文中提出两种改进方法,并用人工合成记录方式进行了方法的可行性试验。     

应用混合极值理论及最大似然法估计东南沿海各地震区的地震危险性

将东南沿海地区划分为７个地震区带，利用历史及现代地震资料，动用混合极值理论及最大似然法分析了各个地震区带的地震危险性，并采用预测检验的方法确定了各个地震区带的危险阈值，对各地震区未来两年的中小地震及未来５年的中强地震的危险性分别给出了定量估计。     

基于最大似然法的亚洲地震人口损失预测

亚洲是全球地震活动,特别是浅源地震活动最活跃的地区之一,由于亚洲大多数国家属于发展中国家,抗御地震的能力偏低,导致地震灾害十分严重。本文采用最大似然法,据亚洲9个国家历史上因各次地震死亡的人口资料,计算得到了各国不同时期因地震造成不同死亡度的概率曲线;另外,由各国每10年的人口统计资料,拟合得到各国人口的增长曲线。将历史上因各次强震的死亡人数归一到2010年人口的死亡数字,并以此数据给出了各国在考虑了人口增长情况下的因震人口损失预测结果。     

最大似然谱估计方法及其在磁震关系中的应用

最大似然谱估计方法及其在磁震关系中的应用曾小苹１）林云芳１）赵跃辰１）赵明１）续春荣２）于明鑫３）汪江田４）王居云５）１）中国北京１０００８１国家地震局地球物理研究所２）中国北京１０００８５国家地震局地壳应力研究所３）中国辽宁大连１１６０３３辽宁省...     

震级-频度关系中b值的极大似然法估计及其影响因素分析

b值在地震活动性研究和地震危险性分析中起着十分重要的作用,通常拟合b值的方法有最小二乘法(Least Squares Method)和极大似然法(Maximum Likelihood Estimation)。最小二乘法简单易行,得到了广泛的应用。然而很多研究表明该方法存在一定的局限性,极大似然法在特定条件下可以作为最小二乘法的一种可行的替代或补充方法。前人对极大似然法的研究非常繁杂,提出了各种各样的方程式,每个方程式的隐含假设和求解方式各不相同。文中对主要方程式进行了简要的回顾,并按照是否考虑震级的归档效应、是否设定有限最大震级、是否对不同震级档数据取不同的观察时段和是否具有解析解这4个方面,对这些方程式进行了分类和总结。进而对震级的归档效应、震级的测量误差、样本量、震级跨度、最小完整震级和前余震共6个可能影响极大似然法估计b值的因素进行了分析和总结。最后对正确使用这些方程式提出了合理的建议。文中的分析和总结有助于更准确地理解和使用不同的极大似然法估计b值的方程式,以供相关研究者参考。     

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.     

基于最大似然属性和拉普拉斯金字塔的断面波增强方法建立

针对在绕射波和回转波的干扰下,断面波识别度较低的问题,本文结合最大似然属性方法和拉普拉斯金字塔算法,提出了一种有效提高断面波识别度的方法.首先通过最大似然属性对三维数据体进行扫描,并计算数据体采样点之间的相似性,以获得工区内精确断层的位置,进而利用拉普拉斯金字塔算法进行断面波能量增强,即在构造拉普拉斯金字塔的过程中加入映射函数,使断面波能量得到增强,提高了断面波识别度.由实际工区应用证明,本文提出的方法是合理且可行的,该方法为后续确定断层位置及断层展布特征、断层平面组合关系提供依据,更好地实现断层精细解释和断裂系统的有效识别.

     

基于轮廓似然估计的广义极值分布在地震中长期预测中的应用

为描述强震预测的不确定性,在地震预报极值分析模型的参数估计中,引入轮廓似然估计法。对广义极值分布中形状参数和地震重现水平的轮廓似然估计原理及数值算法进行了详细地阐述,并利用构建的广义极值分布模型对东昆仑地震带进行了地震危险性分析。关于形状参数和重现水平的点估计,以及10年以内的重现水平置信区间的估计,轮廓似然估计法与极大似然估计法效果基本相同,但在中长期地震重现水平置信区间的预测中,轮廓似然估计法得到的关于置信水平不对称的置信区间,在强震水平下对预测震级的不确定性表达更准确,预测结果更加有效。     

评估空间—发生率—震级地震预测的基于似然的检验

区域地震似然模型(RELM)工作组的5年实验是设计用来比较预测加州及附近各纬度-经度-震级单元地震发生率的若干有希望的方法。这种预测模式被作为世界范围内其他地震可预测性试验的蓝本,因此考虑如何评估这种预测的性能是很重要的。最近采用的两个试验都基于给定预测情况下观测到的地震分布的概率,一个测试比较了空间-发生率-震级单元的观测值和预测值,另一个测试仅仅比较了预测的发生率和观测地震的数目。在本文中,我们讨论了目前关于发生率预测的微小的缺陷,我们建议采用另外两个测试分别进行空间-发生率-震级预测的空间和震级分量的预测。为了更好地说明问题,我们考虑了区域地震似然模型预测和进行区域地震似然模型实验的前半期观测到的地震分布。我们得出空间—发生率—震级预测好像是和观测地震的分布相一致,尽管空间预测和观测地震的空间分布是不一致的,我们建议这些新的测试应该被用于提供更详细的地震预测评估。我们也讨论了每个基于似然测试的统计学功效以及基于似然测试的结果的稳定性(相对于地震目录的不确定性)。     

基于流变体模型的波恩近似方程地震正演模拟

常规τ值法假设应力松弛时间与应变延迟时间近似相等, 造成了常Q模型拟合精度低. 本文利用精确的广义流变体模型Q值计算公式, 研究改进的τ值法求解常Q模型参数. 根据地震波散射理论, 推导了基于广义流变体模型的黏滞性介质一阶波恩近似方程, 结合位移-速度关系得到了含卷积完全匹配层边界条件的黏滞性介质应力-速度方程的一阶波恩近似表达式. 通过数值实验验证并对比了黏滞性介质中全波波动方程、 一阶波恩近似方程以及单程波波动方程的波场特征, 讨论了基于流变体模型的黏滞性介质一阶波恩近似方程对速度扰动和Q扰动的适应性, 以及对旅行时和振幅精度的影响.      

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.     

DEPTH ESTIMATION OF MAGNETIC SOURCES BY MEANS OF FOURIER AMPLITUDE SPECTRA*

The Fourier transform of a square-shaped section of a magnetic survey, digitized in a square grid, forms a rectangular matrix of coefficients which can be condensed to a series of average amplitudes dependent only on their frequency and no longer on the direction of the respective partial waves. These average amplitudes together represent a spectrum which–when plotted in a semilogarithmic coordinate system (log amplitude versus frequency)–often shows straight segments which decrease with increasing frequency. By continuing the given field downwards these straight segments become horizontal at a certain depth, the so-called “white depth”. This white depth may be used as a first estimate for the depth of magnetic sources producing the respective part of the field. It is shown that the sources which correspond to such use of the white depth can be expected to be “randomly distributed with some positive autocorrelation”. As an example for such a depth estimation the interpretation of the aeromagnetic survey of NW-Germany by a relief in 8–16 km depth is given. The relief divides the subsurface in an upper nonmagnetic layer and a lower layer with magnetization M= 2 Am^?1.     

THE MAXIMUM LIKELIHOOD ESTIMATION OF b-VALUE IN MAGNITUDE-FREQUENCY RELATION AND ANALYSIS OF ITS INFLUENCING FACTORS

b-value in the magnitude-frequency(G-R)relationship plays a vital role in seismicity research and seismic hazard analysis, and the most commonly used techniques to simulate it are least square approach and maximum likelihood method. Least square method is simple and easy to apply, therefore widely used in China. However, many researches show that there exist some limits in least square estimation of b-value. Earthquakes with different magnitudes are not equally weighted in this method, and larger events have higher weights, so b-value is vulnerable to the fluctuation of several big earthquakes; meanwhile, least square method needs to divide magnitude intervals artificially. With a small sample size, data points could be not enough if the magnitude interval is too wide, and events in a magnitude interval may be lacking if it is divided to be too narrow. Especially for incremental G-R relationship, it is possible that N(M_i)equals 0 in an interval with large magnitude, so log(N(M_i))loses meaning and has to be ignored, resulting in a low b-value. Therefore, under certain conditions, maximum likelihood method is recommended as an effective substitution or supplementary for least square estimation of b-value. Among numerous previous researches on maximum likelihood estimation of b-value, lots of equations have been provided, based on varied implicit assumptions and different ways of solution. A brief overview is first presented for these equations, and classification and summary are provided based on whether taking account of the effect of binned magnitude, with finite maximum magnitude, using unequal observation periods for different magnitude intervals, and with analytic solution or not. Following this, a total of 6 influential factors are analyzed, such as binning magnitude, measurement errors of magnitude, sample size, magnitude span, minimum completeness magnitude and fore- and aftershocks. At last, reasonable suggestions are provided for using those equations properly. The equations of Aki(1965), Utsu(1965), Page(1968)and Kijko and Smit(2012)are based on assumption that magnitudes are continuous random variables, and have no corrections for this, so these equations are not recommended here. For simplicity, the equations of Utsu(1966)or Tinti and Mulargia(1987)can be used, but magnitude span should be greater than 2.5 due to without finite maximum magnitude in the formulas. For researchers having capability to write code and calculate numerically, Weichert(1980)or Bender(1983)'s algorithm could be utilized. Especially when it is required to apply data with different observation periods for varied magnitudes, the formula of Weichert(1980)is recommended. This study contributes to more accurately understand and use different formulas of estimating b-value by maximum likelihood technique, which can be used as reference for peers.     

用最大似然法进行波场分解和震相识别

本文以介质中弹性波场的传播特征和多元统计分析为基础,从数学上进行严格的推导,得到了模型与资料拟合的最大似然判据,以检验地震波列中是否存在某种特殊波型的能量。利用概率滤波可得分解后的地震图,从图中可以直接得到震相到时。用此方法处理P波资料,效果较好。对于剪切波资料,有时处理结果不十分理想。这可能是由于径向分量和横向分量之间的线性相关性造成的。对于因介质各向异性而形成的分裂剪切波,用此方法得到的S波到时为快S波到时。此方法对于单台三分向记录资料的处理是十分有效的。     

用波速层析成像方法提高储层横向预测精度

以数值模拟方法为基础，考察了反射地震层析成像技术对油气储层波速横向检测的效果，然后用渤海油田的地震资料进行了实用试验．对数值模拟结果和实际数据的试验结果进行了分析与评价，认为油气勘探中的反射地震资料具有地震射线近似垂直分布的特点，适合用反射地震层析成像技术进行目标层横向非均匀性检测．     

用波速层析成像方法提高储层横向预测精度

以数值模拟方法为基础,考察了反射地震层析成像技术对油气储层波速横向检测的效果,然后用渤海油田的地震资料进行了实用试验．对数值模拟结果和实际数据的试验结果进行了分析与评价,认为油气勘探中的反射地震资料具有地震射线近似垂直分布的特点,适合用反射地震层析成像技术进行目标层横向非均匀性检测．     

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.     

P-P波及P-SV波叠前深度偏移速度模型建立方法

针对多波叠前深度偏移速度模型的建立问题,提出在CDP道集上利用互换原理组成伪地集作为叠前偏移速度分析的数据道集,先用叠前时间偏移方法求取层间互不影响的等效偏移速度模型,再用餐前深度偏移方法逐层求取层速度模型．对各层的速度质量、整个速度模型层位结构及速度横向变化,采用人机交互方式进行监控,并在速度叠代中引入全局寻优的遗传算法,使整个速度模型建立过程具有稳定、可靠和可视化的优点．经理论和实际资料处理结果证明,本方法是行之有效的．