沿深度方向地震动相干函数影响因素分析

基于KiK-net台网强震记录,探讨震级、震中距、场地类别及测点高差等对沿深度方向相干函数的影响规律。结果表明:①水平分量的相干函数值随频率变化规律相同,竖向与水平分量间的差异较大;相干函数值随频率和测点高差的增加而减小;Ⅲ类场地较之Ⅰ,Ⅱ类场地,所记录的相干函数值随频率增加而衰减的速度更快。②近场(R≤300 km)相干函数值大于远场(R300 km);震级对相干函数的影响规律不明显;不同场地记录沿深度方向地震动相干性不同,建议选用王招招模型描述Ⅲ类场地地震动相干性,Harichandran模型描述Ⅰ,Ⅱ类场地地震动相干性。③基于日本"3·11"地震记录拟合得到了按震中距分段的相干函数模型参数值。     

地震动空间相干函数的极限性质

基于弹性理论中旋转与平移之间的微分关系，研究了当空间两点间距离趋于零时地震动空间相干函数的极限性质．结果表明，为满足这一微分关系，在建立小范围地震动随机场模型时，空间相干函数的选择必须满足一定的函数特征，不能完全凭经验统计方法来验定其函数形式．同时指出，基于随机地震动场估计旋转地震动分量功率谱密度的关键，是精确地确定地震动空间相干函数关于空间坐标的二阶导数．      

大跨曲线桥多点激励下的地震响应分析

用相位谱表征地震动频率的非平稳特性,用相干函数表征地震动空间变化的不相干效应,采用随频率变化的等效相速度代替随意给定的视波速表征地震动的行波效应,生成了具有强度和频率非平稳特性的多点地震动。将这种考虑时间和空间变化的地震动在水平方向作用于5跨高墩连续刚构曲线桥桥墩基础处,计算了墩顶位移及墩底内力,分析了大跨曲线桥多点输入中不相干效应和行波效应对结构响应的影响。结果表明考虑地震动空间变化特性的墩顶位移峰值多数显著大于一致激励。相干性显著增大了激励方向墩底的动内力,但对拟静力位移差动产生的内力有时增大有时减小,两者叠加后的总内力峰值多数大于一致激励。     

参数和非参数方法计算相干函数的比较

地震动空间相干函数计算主要两类方法,一是采用谱窗方法对功率谱和互功率谱进行平滑的非参数方法,另一类是采用K-T(Kainai-Tajimi)谱拟合功率谱和互功率谱的参数方法。本文选取了SMART-1台阵第5次和第45次地震的水平分量加速度记录,采用AR(Auto-Regressive)自回归模型的参数方法,计算了不同台站间距的相干系数,并选用Loh相干函数模型,对两种方法的相干系数进行拟合,分别得到了拟合参数和标准差。结果表明:(1)基于AR自回归模型方法得到的拟合标准差小于非参数法;(2)非参数法和参数法的相干系数有明显差别;(3)随着间距的增大,基于非参数法的相干系数随着频率增大而变小的程度放缓,而基于参数法的相干系数明显反映出相干系数符合随着频率增大而变小,同时也随距离的增大而减小的共识。     

基于能量的相干函数有效频段范围的选取

目前的地震动空间相干函数模型中频率的适用范围存在很大差别。本文利用地震动功率谱所表征的地震动能量在各频段内分布的相对关系,从功率谱-能量的角度,引入能量比的概念,即某一频段范围的功率谱与总功率谱的比值,提出了确定一种相干函数模型有效频段范围的方法。选取了SMART-1台阵第5、33、40和45号地震的水平分量加速度记录进行了对比分析,发现:当频率范围为0～5 Hz时,能量比达到95%以上;当频率范围为0～8 Hz时,频段内的能量已达到总能量的99%左右。因此,建议在进行相干函数模型中参数拟合时,可采用能量比达到95%～99%时对应的频率作为最大频率,从而减少高频成分对拟合结果的影响。     

台站间距d的分布对地震动空间相干函数的影响

对地震动空间相干函数进行拟合时,常常遇到台站间距离d偏少的问题。对不同距离台站对的不足对相干函数模型拟合参数的影响进行了对比分析。选取了SMART-1台阵第45号地震的水平分量加速度作为分析数据,计算了d等于200 m,1 000 m和2 000 m等3个台站间距的空间相干系数,并对3个距离的所有计算值进行了拟合,得到了第一组拟合参数;另外又增加计算了d等于400 m,800 m和1 200 m等3个台站间距的空间相干系数,并对所有6个距离的计算值进行了拟合,得到了第二组拟合参数。结果表明,第二组拟合参数的离散性优于第一组拟合参数,且根据第二组拟合参数计算得到的相干系数曲线更合理。因此建议,当采用统计方法获得地震动空间相干函数时,应尽量多地考虑不同距离台站对的强震记录。     

地震动空间相干函数模型中拟合参数的修正

采用SMART-1台阵第5次和第45次地震的水平向分量加速度记录,首先计算了不同间距台站对的地震动空间相干函数;然后讨论了台站距离对相干函数拟合结果的影响,即某一特定距离的相干函数与所有不同距离的相干函数的拟合结果存在明显差异。为减小这一差异,提出了一种对各个不同距离的相干函数拟合参数进行二次回归的方法,并选用Loh相干函数模型进行了验证,最后给出了基于Loh相干函数模型的拟合参数的修正结果。结果表明本文提出的修正方法将大大提高相干函数模型中参数的拟合精度。      

基于小波变换的地震动时-频特性研究

对美国NGA,采用一维连续小波变换得到每条记录的小波功率谱。研究了任意时间处小波功率谱最大值所对应的主频率。结果表明:地震动主频率随时间的增大逐渐减小;竖向地震动分量的主频比水平向分量随时间减小更快。分别采用线性函数模型、指数函数模型和指数三角函数模型,分析了场地、震级和震中距对主频变化曲线的影响,拟合了主频率在不同场地条件、震级、震中距等情况下随时间的变化曲线,水平向和竖向的频率时变曲线整体上都是随时间递减的,且竖向衰减得更快些,大多数情况下竖向记录的高频成分比水平向记录的相应成分要多。     

地面运动最大幅值,到时的差动特性

利用ＳＭＡＲＴ－１台阵３次地震的水平分量加速度记录统计了局部场地上地震动加速度最大幅值，到时的变化特性，统计结果表明：在局部场地上，地震动加速度的最幅值随大幅值 随土层厚度和测点坐标的变化是显著的，而到时变化仅依赖于测点坐标。     

基岩地震动的一个相干函数模型-走滑断层情形h

目前研究地震动空间变化的主要方法是利用密集台阵（如SMART1台阵等）的强震观测记录进行统计分析，由于地震动观测资料的不足，因而缺少基岩及不同场地类别地震动相干函数模型. 本文利用数值方法了模拟理论地震图，进而研究采用震源位错模型的基岩随机地震动的空间变化规律，并考虑震源破裂速度、子源个数、震源深度和介质传播速度等因素的影响. 其具体思路为:首先对应于每个样本，用有限差分数值模拟方法计算弹性半空间近场地震动场，而后对所有样本的计算结果进行统计，给出了一个走滑断层情形下的近场基岩表面及沿基岩竖直方向水平分量地震动的相干函数模型.      

Coherency analysis of accelerograms recorded by the UPSAR array during the 2004 Parkfield earthquake

Spatial variability of near‐fault strong motions recorded by the US Geological Survey Parkfield Seismograph Array (UPSAR) during the 2004 Parkfield (California) earthquake is investigated. Behavior of the lagged coherency for two horizontal and the vertical components is analyzed by separately examining the decay of coherency with frequency and distance. Assumptions, approximations, and challenges that are involved in estimation of the coherency from recorded data are presented in detail. Comparison of the UPSAR coherency estimates with coherency models that are commonly used in engineering practice sheds light on the advantages and limitations of different approaches to modeling the coherency, as well as on similarities and differences in the spatial variability exhibited by seismic ground motion arrays at different sites. Copyright © 2013 John Wiley & Sons, Ltd.     

A COHERENCY MODEL FOR SPATIALLY VARYING GROUND MOTIONS

A theoretical model for the coherency function describing spatial variability of earthquake ground motions is developed. The model consists of three components characterizing three distinct effects of spatial variability, namely, the incoherence effect that arises from scattering of waves in the heterogeneous medium of the ground and their differential superpositioning when arriving from an extended source, the wave-passage effect that arises from difference in the arrival times of waves at different stations, and the site-response effect that arises from difference in the local soil conditions at different stations. Attenuation of waves, which also gives rise to spatial variability, is shown to have little influence on the coherency function. It is shown that the incoherence component of the coherency function is a real-valued, non-negative, decaying function of frequency and interstation distance, whereas the wave-passage and site-response components are complex functions of unit modulus that characterize the phasing of the wave components. A parametric study reveals that the site-response effect can be more significant for short- or medium-span structures situated in regions with rapidly varying local soil conditions, whereas the wave-passage effect can be more significant for long-span, flexible structures.     

Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.     

Modeling of soil heterogeneity and its effects on seismic response of multi-support structures

This paper addresses the analytical evaluation of soil lateral heterogeneity effects,especially the random fluctuations of the soil layer's predominant frequency,on the spatial coherency of ground motion and the seismic response of multi-support structures.A coherency probabilistic model is proposed.In this model,the spatial variation of motion is attributed to wave passage effects,effects of loss of coherence in the bedrock motion and particularly site response effects(based on the assumption of vertically propagating shear-waves through a horizontal layer with random characteristics).The results indicate that soil lateral heterogeneity effects tend to cause diminution of the values of the total coherency function.This diminution is not limited to the vicinity of the mean resonant frequency of the layer,but reaches considerably high frequencies even for relatively low values of coefficient of variation(CV of 5 to 15%).Therefore,the trend of the total coherency function(exponential decay) can be influenced significantly by site effects.Finally,the proposed coherency model is applied for two different support seismic excitations.Study results indicate that the greater the soil heterogeneity,the larger are the dynamic displacements and shear forces in the columns of the oscillator(i.e.,support structure).Furthermore,these two components of the response are influenced differently by soil heterogeneity effects.     

Nonlinear processes in earthquake foci

The results of laboratory experiments on biaxially compressed physical models of a seismic source are presented, discussed and interpreted in terms of nonlinear dynamics; the relation is shown between the degree of seismic pulse coherency (expressed through the amplitude frequency spectra development) and energy (or magnitude) in a series of model experiments. It has been ascertained that the degree of radiated waves coherency plays a more important role concerning the seismic energy release than the size (radius) of the seismic source.The relations among individual source parameters obtained in the laboratory were tested by the analysis of three series of seismograms of aftershocks which followed the 1988 Spitak earthquake (two series) and the 1975 Oroville earthquake (one series). The fundamental effect observed in the laboratory, i.e., the growth of pulse coherency with increasing stress concentration in the focal region (reflected in growing earthquake magnitude), was clearly manifested in all three earthquake aftershock series.Due to derivation by a comparison of the above results, obtained on the basis of nonlinear dynamics with the classical source models by Brune, Madariaga and others, it seems to be namely the self-organizing of the structure itself caused by the increasing stress field in the seismic source, which can answer the question concerning the degree of energy cumulation in the earthquake focus at a given moment.     

Spatial coherency analysis of seismic ground motions from a rock site dense array implemented during the Kefalonia 2014 aftershock sequence

The objective of studies presented in this paper is to analyse the spatial incoherency of seismic ground motions using signals from a velocimeter dense array located on a rock site, recording the aftershock sequence of the two M6 Kefalonia earthquakes that occurred in January/February 2014 (Kefalonia island, Greece). The analyses are carried out with both horizontal and vertical components of velocigrams for small separation distances of stations (<100 m). The coherencies of seismic ground motions identified from strong motion windows are compared with those identified from coda parts of signals. It is realized that there is no significant difference between the coherencies estimated from those two parts of signals. The influence of earthquake event number on the result of coherencies and the dispersions of coherencies estimated from different earthquake events are presented. Finally, coherencies estimated from the dense array are compared with several coherency models proposed and widely used in the literature. The possibility of modifying some parameters of those existing coherency models to fit with in situ coherencies are discussed and presented. Copyright © 2017 John Wiley & Sons, Ltd.     

基于高阶统计量的相干体算法在地震中深层构造解释中应用

利用高阶统计量所具有的可抑制高斯噪声和比常规的自相关函数包含更多信息的优点,并结合地震解释的实际问题,本文采用四阶矩函数代替互相关函数进行相干计算,对第一代相干体算法进行了改进,发展了基于高阶统计量的相干体算法.该方法不仅计算速度快,而且抑制噪声能力强.通过与传统相干算法实际应用对比,该算法有效地突出了地层的高连续性特征,有利于层位追踪和断层解释,尤其利于中深层构造解释.     

CHARACTERISTICS OF TORSIONAL GROUND MOTIONS

Due to the inherent difficulty in directly recording the rotational ground motions, torsional ground motions have to be estimated from the recorded spatially varying translational motions. In this paper, an empirical coherency function, which is based on the recorded motions at the SMART-1 array, is suggested to model the spatial variation of translational motions. Then, the torsional ground motion power spectral density function is derived. It depends on the translational motion power spectral density function and the coherency function. Both the empirical coherency function and the torsional motion power spectral density function are verified by the recorded motions at the SMART-1 array. The response spectra of the torsional motions are also estimated. Discussion on the relations between the torsional motion response spectrum and the corresponding translational motion response spectrum is made. Numerical results presented can be used to estimate the torsional ground motion power spectral density function and response spectrum.     

Influence of irregular topography and random soil properties on coherency loss of spatial seismic ground motions

Coherency functions are used to describe the spatial variation of seismic ground motions at multiple supports of long span structures. Many coherency function models have been proposed based on theoretical derivation or measured spatial ground motion time histories at dense seismographic arrays. Most of them are suitable for modelling spatial ground motions on flat‐lying alluvial sites. It has been found that these coherency functions are not appropriate for modelling spatial variations of ground motions at sites with irregular topography (Struct. Saf. 1991; 10 (1):1–13). This paper investigates the influence of layered irregular sites and random soil properties on coherency functions of spatial ground motions on ground surface. Ground motion time histories at different locations on ground surface of the irregular site are generated based on the combined spectral representation method and one‐dimensional wave propagation theory. Random soil properties, including shear modulus, density and damping ratio of each layer, are assumed to follow normal distributions, and are modelled by the independent one‐dimensional random fields in the vertical direction. Monte‐Carlo simulations are employed to model the effect of random variations of soil properties on the simulated surface ground motion time histories. The coherency function is estimated from the simulated ground motion time histories. Numerical examples are presented to illustrate the proposed method. Numerical results show that coherency function directly relates to the spectral ratio of two local sites, and the influence of randomly varying soil properties at a canyon site on coherency functions of spatial surface ground motions cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.     

Spatial variation of seismic motion induced by propagation of body waves

Spatial variation of earthquake ground motion is an important phenomenon that cannot be ignored in the design and safety of strategic structures. Several models have been developed to describe this variation using statistical, mathematical or physical approaches. The latter approach is not specific to an event. A recent contribution, which uses such an approach and called complete stochastic deamplification approach (CSDA), was developed [1]. The aim of this paper is to analyze the spatial variation of earthquake motion induced by the propagation of body waves using the CSDA. Coherency functions are evaluated for the cases of SH–SV–P waves propagating through stratified soil. Results obtained show that the variation of the coherency function is not the same for vertical and horizontal components and that the motion is more coherent at depth than at the free surface. In fact, we found that the rate of decrease with frequency and distance is not the same if P–SV waves propagate through stratified soil.