A time varying AR coefficient model for modelling and simulating earthquake ground motion

A smoothness priors-time varying autoregressive (AR) coefficient model method for the modelling of earthquake ground motion is shown. The method yields the instantaneous smoothed values of the AR coefficients and the instantaneous smoothed values of the innovations variance. These results in turn yield estimates of the instantaneous spectral density, the time varying covariance function and a simulation model for the ground motion data. An example of the application of the method to the analysis of an accelogram from the February 1971 San Fernando, California earthquake is shown.     

基于AR模型的相干函数有效频段范围的确定

目前人们在进行地震动相干函数模型参数的拟合时,选取的频段范围存在很大差异,而确定有效的频段范围对相干函数模型拟合结果的合理性很重要。本文利用AR模型(Autoregressive Model,自回归模型)计算地震动的功率谱,提出了根据功率谱"信噪比(SNR)"确定相干函数有效频段范围的方法。本文的信噪比中的"噪",专指AR模型中的激励白噪声,用于衡量AR模型中某一频率地震动功率谱与激励白噪声功率谱之间的比例。定义信噪比SNR=0时对应的频率为有效频段的最高频率,大于最高频率的频率成分,被当作是地震波中的随机成分,可以不考虑地震动的相关性。采用这一方法,对SMART-1第45次地震记录的不同台站间距下的地震波进行了功率谱估计,根据信噪比确定出了有效频段范围,并计算了相应的相干函数,结果表明此方法是可行的。     

基于工程应用的频率时变模型研究

对美国NGA数据库中的3551组地震记录按场地条件、震级、震中距进行了分组,采用一维连续小波变换得到每条记录的小波功率谱。研究任意时间处小波功率谱最大值所对应的主频率,并对每个地震动分组内的主频率值做一定时间窗内的均方根处理,分别采用线性函数、指数函数和指数三角函数模型来拟合得到的主频率随时间变化的曲线,最后分析了场地条件、震级和震中距对频率时变曲线的影响,并给出了每个分组内水平向和竖直向地震动主频率随时间变化的模型参数。结果表明:地震动主频率随时间的增大逐渐减小,但是竖直向要比水平向衰减得快一些。     

基于均生函数的数学预测模型在地震中期预报中的应用

利用均生函数数学建模方法拟合地震的震级或能量序列,进行地震中期趋势预测。由于引入了“双评分准则”,即在拟俣时考虑了数量预报和趋势预报的平衡问题,选取合适的调整系数,从而提高了地震中期趋势预测的准确率。另外采用了分级拟合的思路,利用残差序列逐级提高拟合的精度和速度。利用该方法对中国大陆地区未来１～３年的地震活动趋势进行了预测。     

Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics

A method for generating an ensemble of orthogonal horizontal ground motion components with correlated parameters for specified earthquake and site characteristics is presented. The method employs a parameterized stochastic model that is based on a time‐modulated filtered white‐noise process with the filter having time‐varying characteristics. Whereas the input white‐noise excitation describes the stochastic nature of the ground motion, the forms of the modulating function and the filter and their parameters characterize the evolutionary intensity and nonstationary frequency content of the ground motion. The stochastic model is fitted to a database of recorded horizontal ground motion component pairs that are rotated into their principal axes, a set of orthogonal axes along which the components are statistically uncorrelated. Model parameters are identified for each ground motion component in the database. Using these data, predictive equations are developed for the model parameters in terms of earthquake and site characteristics and correlation coefficients between parameters of the two components are estimated. Given a design scenario specified in terms of earthquake and site characteristics, the results of this study allow one to generate realizations of correlated model parameters and use them along with simulated white‐noise processes to generate synthetic pairs of horizontal ground motion components along the principal axes. The proposed simulation method does not require any seed recorded ground motion and is ideal for use in performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulation of earthquake ground motions using autoregressive moving average (ARMA) models

Parsimonious representations of recorded earthquake acceleration time series are obtained by fitting stationary autoregressive moving average models after a variance-stabilizing transformation. Simulated acceleration series are then constructed by generating realizations from the fitted stationary models and applying the reverse transformation. As demonstrated on three components of a typical series, the response spectra for the observed and simulated series show good agreement for periods of less than eight seconds. Further, the model parameters for the three components are very similar, suggesting a consistency which could be useful for identifying site-specific characteristics.     

Analysis of three-dimensional strong ground motions along principal axes,San Fernando earthquake

An orthogonal set of principal axes is defined for earthquake ground motions. These principal axes are obtained such that the corresponding variances of motion have maximum, minimum and intermediate values and the covariances equal zero. This indicates that the corresponding components of motion along the principal axes are uncorrelated with respect to each other. Since real earthquake accelerograms are assumed to be reasonably well represented by Gaussian random processes, the three components of motion along the principal axes are statistically independent of each other. Using these principal axes and applying the moving-window technique to the ground accelerograms recorded during the San Fernando earthquake of 9 February 1971, time-dependent characteristics of three-dimensional ground motions along principal axes are determined. Results of the analysis indicate significant correlation between directions of principal axes and directions from the recording stations to the fault slip zone. It is concluded that three components of ground motion can be generated stochastically with statistical independence being maintained, provided they are assumed to be directed along principal axes.     

新型随机地震动模型

在研究结构的随机地震反应时，要用大量的符合场地条件的地震记录作为输入数据。但强震历史记录却不是每个地区都有的，因此根据符合场地条件的现有地震记录建立随机地震动模型具有重要意义。本文利用中国抗震规范2001版修正选取的样本波作为目标波，考虑了幅值和频率的双重非平稳性，建立了新型随机地震动模型——改进的时变ARMA模型随机地震动模型。通过使用残差的卡方检验法，对多种非平稳ARMA模型生成的模拟波进行检验；同时又比较丁模拟波与目标波的功率谱密度图和反应谱图。结果证明：此法能够更精确地反映不同场地条件地震动的频谱和幅值的真实内容，从而建立符合目标场地条件的更为有效的模拟地震动，为相关研究与工程设计架起一座桥梁。     

2013年芦山MS7.0地震序列参数的早期 特征: 传染型余震序列模型计算结果

为考察2013年4月20日芦山M_S7.0地震震后序列参数的早期特征, 利用“传染型余震序列”(ETAS)模型和最大似然法进行了参数估计. 设定截止震级M_c=M_L2.0, 拟合时段为震后0.31—24.12天, 计算获得α=1.89, p=1.22, 同时利用最大似然法估计获得b=0.72. 与中国大陆地区其它中强震的余震序列参数的比较表明, 芦山M_S7.0地震序列参数表现为触发次级余震的能力较弱和序列衰减速率较快的特征, 反映出余震区相对较高的应力水平. 为检测结果的稳定性, 设定不同的截止震级M_c以及不同的拟合截止时间, 分别进行参数拟合和参数标准差估计. 结果表明, M_c的选取对α值影响明显, 对p值影响则较小. 此外, 震后10天内获得的参数拟合结果随时间变化较为明显, 而其后各参数变化总体较为平稳.      

地震波动强度变化的数学建模分析与仿真

传统利用灰色关联分析方法对地震波动强度变化进行数学建模分析与仿真时,对地震波动强度变化的数列进行仿真分析时,忽略了地震波动强度的时间属性对结果的影响,导致分析结果准确性较低。本论述提出新的地震波动强度变化数学建模分析与仿真方法,通过地震波动强度序列的经验分布确定门限自回归模型的门限值,依据该门限值、AIC最小准则以及最小残差平方等方法获取地震波动强度序列的门限自回归模型,分析自回归模型的极限环和振荡的属性特点,得到地震波动强度变化的初步数值模拟结果。本论述构建了基于均生函数的地震波动强度序列的数学模型,通过均生函数数学建模方法拟合地震波动强度时间序列,依据时间序列基于双评分准则选取拟合周期,实现地震波动强度的数值仿真。实验结果表明,所提方法对地震波动强度变化模型具有较高的准确性和稳定性。     

Simulation of three-dimensional strong ground motions along principal axes,San Fernando earthquake

Power spectral density which describes frequency content is considered one of the most significant properties to be taken into account when generating ground motions through the use of stochastic processes. Using a smoothed and normalized Fourier amplitude spectrum, frequency content for components of motion along a set of principal axes is estimated. Fourier amplitude spectra obtained by this moving-window technique are presented which show the time dependency of frequency content for motions produced by the San Fernando earthquake of 9 February 1971. A mathematical model to simulate ground motion processes is proposed for which both the intensity and frequency content are non-stationary. Using this mathematical model with parameter characteristics along principal axes similar to those of the motions recorded during the San Fernando earthquake, three-dimensional ground motions are synthetically generated. The properties of the simulated motions show general characteristics similar to the characteristics observed in real accelerograms. The suggested model is considered adequate for engineering purposes.     

利用1996年丽江地震序列反演震区应力状态

本文以1996年丽江M_S7.0地震为例,以地震目录和强震震源模型为输入参数,将力学计算与统计分析相结合,反演计算了1986～1996年间丽江震区2.5°×3.0°空间范围内的地壳应力状态.结果表明,丽江地区应力场最大主应力为近南北向,方位角为355°,最小主应力方位角为241°,二者倾角为近水平,应力形因子为0.398,最大主应力大小约为53 MPa,远小于完整岩石的强度.该方法可获得地壳深部绝对应力大小、有效摩擦系数,反演获得的震区地壳深部应力状态的方向性特征与震源机制解结果基本一致;该研究表明地震活动的空间分布可以为我们提供有关强震孕震的地壳深部应力状态信息.这些结果对了解震区应力场具有理论上和实践上的意义.     

唐山地震序列的应力释放调整过程

本文搜集了1976年7月28日至1979年12月31日期间唐山地震序列中所有M_s≥4.0地震的初动资料。这些资料来自于68个地震台的记录图和其它14个地震台的数据。其中,167次地震得到可靠的断层面解。对这些断层面解的分析表明,震源区介质中的应力经历了一个由震前紧张平衡态,经主震后的极不稳定态,逐渐向松驰平衡态演变的释放调整过程;对于余震区的不同部分,该过程存在着细节上的差异。两种平衡态下应力主轴的空间取向基本相同,这意味着制约唐山地区构造应力场的周围环境因素没有因发生唐山地震而改变。因此,该地区的构造运动将有继承性,而地震活动将会间歇性地重现。     

Annual streamflow modelling with asymmetric distribution function

Classical autoregressive models (AR) have been used for forecasting streamflow data in spite of restrictive assumptions, such as the normality assumption for innovations. The main reason for making this assumption is the difficulties faced in finding model parameters for non‐normal distribution functions. However, the modified maximum likelihood (MML) procedure used for estimating autoregressive model parameters assumes a non‐normally distributed residual series. The aim in this study is to compare the performance of the AR(1) model with asymmetric innovations with that of the classical autoregressive model for hydrological annual data. The models considered are applied to annual streamflow data obtained from two streamflow gauging stations in K?z?l?rmak Basin, Turkey. Copyright © 2008 John Wiley & Sons, Ltd.     

基于机器学习的地震动特征提取与模拟以2021年云南漾濞6.4级地震为例

随着地震动数据数量的增长和质量的提高,将基于数据驱动的机器学习方法应用到地震动模拟中有重要意义。以2021年5月21日云南漾濞M_S6.4地震为例,利用主成分析方法从前震及余震地震动记录中提取特征母波时程,将地震动三要素作为模拟误差约束,在求解母波的线性组合系数时使用多目标优化算法寻优,最终找到帕累托最优解作为模拟目标台站记录时的组合系数,得到模拟地震动时程。结果表明:主成分析法在对实际地震动记录进行特征提取后,得到的特征母波时程可以在一定程度上保留原始数据的主要信息;考虑幅值、频谱和持时这三要素的角度去控制模拟误差,可以使得模拟的地震动时程更加接近真实记录。提出的基于特征提取的地震动模拟方法可以为基于小震数据合成大震地震动提供参考。     

基于新《电力设施抗震设计规范》的地震动随机模型参数研究

根据新《电力设施抗震设计规范》(GB50260-2013)对随机地震动功率谱参数的取值进行分析。介绍新《电力设施抗震设计规范》中设计反应谱,推导设计谱到功率谱的转换过程。选取常用的Clough-Penzien修正过滤白噪声模型作为拟合函数,通过功率谱参数拟合,得到不同场地类别、不同抗震设防烈度下的地震动模型参数。该研究成果可为电力工程抗震设计分析提供参考。     

随机地震动场多点激励下大跨度桥梁地震反应分析方法

地震输入问题一直是工程结构抗震研究关注的焦点。对大跨度桥梁结构，考虑随机地震动场的多点激励而进行地震反应分析较为合理。本文结合大跨度桥梁抗震设计，系统地介绍了随机地震动场的模型以及随机地震动场多点激励下大跨度桥梁地震反应分析的方法。     

Seismic hazard assessment of Western Coastal Province of Saudi Arabia:deterministic approach

Seismic hazard assessment is carried out by utilizing deterministic approach to evaluate the maximum expected earthquake ground motions along the Western Coastal Province of Saudi Arabia. The analysis is accomplished by incorporating seismotectonic source model,determination of earthquake magnitude(Mmax), set of appropriate ground motion predictive equations(GMPE), and logic tree sequence. The logic tree sequence is built up to assign weight to ground motion scaling relationships. Contour maps of ground acceleration are generated at different spectral periods. These maps show that the largest ground motion values are emerged in northern and southern regions of the western coastal province in Saudi Arabia in comparison with the central region.     

基于COSMIC掩星数据探测汶川 MS8.0地震震前电离层异常

获取COSMIC掩星2级数据, 基于球谐函数使用最小二乘拟合法计算模型值, 为2008年5月12日汶川M_S8.0地震前电离层电子密度变化提供背景依据. 同时应用主成分分析法研究最大电子密度, 得到各主成分所占能量百分比随时间的变化. 研究结果发现, 震前在震中邻近区域出现电离层扰动增强现象, 且随高度不同存在一定差异, 主要集中在F₂层300—450 km. 主成分分析结果显示, 4月15日—29日19:00—24:00(地方时)第三主成分能量百分比显著增加. 上述结果表明, 震前电离层存在异常扰动现象. 这一研究结果有助于加强地震电离层耦合机理方面的研究.