Extracting rotational components of earthquake ground motion using data recorded at multiple stations

Rotational components of earthquake ground motion have not been considered for seismic analysis, design and performance assessment because recordings of these components are unavailable. A number of procedures have been proposed to extract rotational components of ground motion from translational time series recorded at multiple, closely spaced recording stations. In this paper, a new procedure that is capable of capturing higher frequency content in rotational time‐series is presented. The frequencies at which numerical errors are introduced in the solution, which are a function of apparent wave velocity and array dimension, are identified. Results are presented for the proposed procedure, the widely accepted geodetic method, and a single‐station procedure developed by the authors, all using data recorded at the Lotung array in Taiwan. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

特殊长周期地震动的参数特征研究

近断层脉冲型地震动和远场软土层场地类谐和地震动是两类特殊的长周期地震动,当前的规范均很少对这两类地震作用进行具体的规定。研究了近断层脉冲型和远场类谐和地震动的幅值、幅值比（V／A,D／V）、傅里叶幅值谱和反应谱的差别,分析了相位角和作用循环周期数对简单脉冲的影响,并用于解释两类特殊地震动的工程特征。以集集地震动为数据基础,分析了两类长周期地震动的傅里叶谱和反应谱特征;将平均加速度和位移规准反应谱分别与规范设计谱进行了比较。建议设计谱在长周期段考虑近断层作用和软土场地面波效应的影响。     

The effects of torsional ground motion on thin cylindric shell structures

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地震动空间变化随机描述及相干函数模型研究进展

本研究主要讨论地震动空间变化的随机描述.首先给出了基于密集地震台阵记录估计相干函数的方法,并对计算中需要关注的问题给出了相应的解释;然后对现有的经验和半经验相干函数模型的建立进行了详细的梳理,并对模型在工程应用中的适用性、有效性和局限性进行了讨论;最后通过对比分析不同相干函数模型对场址地震动空间相关性的模拟结果,对相干函数模型的选择提出了建议.     

场地条件对地震动相干函数的影响

本通过弹性半空间内位错源的数值解法研究了曲岩地震动相干函数，采用有限元方法分析了一些典型场地的地表地震动相干函数，两的对比结果表明：复杂场地对地震动相干函数的影响强烈。     

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.     

Methods for estimating rotational components of seismic ground motion and their numerical comparisons*

Rotational components play an important role in natural earthquake research, engineering seismic investigation, building monitoring, seismic exploration and other fields. Traditional researches mainly focus on three translational components, but less on rotational ones. As the precision of rotational sensing techniques has increased, many scholars have paid more attention to the seismic rotational motions. Because the rotational observations are not very popular before and now, approximately converting the translational components into rotational components is utilized in rotation analysis. Based on numerical six-component seismic data with the finite difference method, we compare three different conversion methods, the travelling-wave, frequency-domain and the difference method, to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.     

多点地震动合成简化方法研究

本文在前人研究的基础上给出了一种合成考虑空间相关性多点地震动时程的方法,该方法通过对互功率谱密度矩阵简化,只需要对迟滞相干函数矩阵分解,不需要对互功率谱矩阵进行Cholesky分解,避免了算数矩阵运算,提高了合成的效率。用该方法编制了相应的程序,给出了合成的算例。     

考虑岩土介质随机特性的工程场地地震动相干函数研究

将随机结构正交展开理论和随机振动分析的虚拟激励原理运用于场地波动有限元分析，形成了一种可以考虑岩土介质随机特性对工程场地地震动相干函数影响的分析方法。实例分析表明，非严格均匀分布的随机介质场地对场地表面的迟滞相干函数值有重要影响，这种影响可由场地的随机影响因子来衡量，在进行工程场地地震动随机场研究时应当考虑场地介质随机特性的影响。     

Experimental analysis of seismic torsional ground motion recorded by the LSST‐Lotung array

The purpose of this study was to perform an experimental analysis of the amplitude of full‐scale spatial variability of seismic motions with regard to earthquake engineering. The LSST‐Lotung array in Taiwan provides a good set of records for this type of study. Of interest are the free‐field torsional seismic components induced by the spatial variability of seismic motions. In this study, three events have been considered: LSST‐06, LSST‐07 and LSST‐16. In time domain analysis, the experimental results obtained show that when the separation distance increases, the induced torsion decreases, and the normalized differential motion parameter increases. Also, the results show that the stronger the event, in terms of maximum PGA, the larger the induced torsional amplitude and the smaller the induced normalized differential motion parameter. Copyright © 2002 John Wiley & Sons, Ltd.     

Measurement of six degree-of-freedom ground motion by using eight accelerometers

A new integrated measuring system with eight force-balance accelerometers is proposed to obtain a direct measurement of six degree-of freedom （DOF） ground motions, including three rotational and three actual translational acceleration components without gyroscopes. In the proposed measuring system, the relationship between the output from eight force-balance accelerometer and the six DOF motion of the measuring system under an earthquake are described by differential equations. These equations are derived from the positions and directions of the eight force-balance accelerometers in the measuring system. The third-order Runge-Kutta algorithm is used to guarantee the accuracy of the numerical calculation. All the algorithms used to compute the six DOF components of the ground motion are implemented in a real-time in Digital Signal Processor （DSP）. The distortion of the measured results caused by position and direction errors of the accelerometers in the measuring system are reduced by multiplying a compensation coefficient C to the output and subtracting static zero drift from the measured results, respectively.     

Semi-empirical estimation of ground motion using observed records at a site in Shikoku, Japan

A semi-empirical approach using fore- or after-shockrecords as Green's functions is applicable to thesimulation of strong ground motion, however suchrecords are obviously not available for predictionpurposes. Thus we have predicted ground motion fora hypothetical large earthquake from other minorevents by adopting a distance correction based ongeometrical spreading. Another difficulty inprediction is fault modeling. Surface traces weresimplified as fault models 27, 46, 55, and 77 km inlength. Further, the actual fault rupture may beinhomogeneous, so an asperity distribution isassumed. This asperity model assumes thatdislocation and stress drop are double than theaverage values. Although, the near field term isneglected in our simulation, no significantdifference was seen in the motions estimated byindividual models for periods up to 2.0 seconds. This indicates that the dependence of source size issmall for strong motion, perhaps as a result of therandom summation of high-frequency phases.     

Selection and ranking of ground motion models for seismic hazard analysis in the Pyrenees

The issue addressed in this paper is the objective selection of appropriate ground motion models for seismic hazard assessment in the Pyrenees. The method of Scherbaum et al. (2004a) is applied in order to rank eight published ground motion models relevant to intraplate or to low deformation rate contexts. This method is based on a transparent and data-driven process which quantifies the model fit and also measures how well the underlying model assumptions are met. The method is applied to 15 accelerometric records obtained in the Pyrenees for events of local magnitude between 4.8 and 5.1, corresponding to moment magnitudes ranging from 3.7 to 3.9. Only stations at rock sites are considered. A total of 720 spectral amplitudes are used to rank the selected ground motion models. Some control parameters of these models, such as magnitude and distance definitions, may vary from one model to the other. It is thus important to correct the selected models for their difference with respect to the magnitude and distance definitions used for the Pyrenean data. Our analysis shows that, with these corrections, some of the ground motion models successfully fit the data. These are the Lussou et al. (2001) and the Berge-Thierry et al. (2003) models. According to the selected ground motion models, a possible scenario of a magnitude 6 event is proposed; it predicts response spectra accelerations of 0.08–0.1 g at 1 Hz at a hypocentral distance of 10 km.     

基于分解方法的脉冲型地震动非弹性反应谱分析

本文旨在分析脉冲型地震动中不同频率的地震动分量对于原始地震动幅值及其非弹性反应谱的影响.首先以近期12次大地震的53条典型脉冲型地震动为数据基础, 基于多尺度分解方法获取脉冲型地震动中的高频分量和低频分量.为与传统方法对比, 本文获取了能够表征地震动脉冲特性的卓越分量及滤除卓越分量的剩余分量.然后对比分析原始地震动和4种地震动分量的幅值特征和非弹性反应谱的特性, 以讨论地震动分量对原始地震动幅值参数及其非弹性反应谱的影响.最后结合简谐地震动模型和地震动分量的性质, 讨论脉冲型地震动非弹性反应谱诸多特征的产生原因.分析发现, 低频分量不仅是控制脉冲型地震动速度和位移幅值的主要因素, 其对原始地震动的加速度幅值也具有不可忽略的影响.低频分量也是导致脉冲型地震动非弹性位移比谱偏大以及强度折减系数谱偏小的直接原因, 从而造成结构在脉冲型地震动作用下需要具有更大的非弹性位移以及更高的强度需求.     

基岩地震动的一个相干函数模型--倾滑断层情形

本文研究了基岩随机地震动的空间变化规律，考虑了震源破裂速度、子源个数、震源深度和介质传播速度等因素的影响。对应于每个样本，用数值模拟方法计算了采用震源位错模型的弹性半空间近场地震动场，最后通过统计方法给出了一个倾滑断层情形下的近场基岩地震动的相干函数模型。这一方法可以补充常用的统计方法因观测资料有限而导致的欠缺。     

Torsional response of symmetric buildings to incoherent and phase‐delayed earthquake ground motion

This paper studies the effect of coherency loss and wave passage on the seismic torsional response of three‐dimensional, multi‐storey, multi‐span, symmetric, linear elastic buildings. A model calibrated against statistical analyses of ground motion records in Mexico City is used for the coherency function. The structural response is assessed in terms of shear forces in structural elements. Incoherence and wave passage effects are found to be significant only for columns in the ground level of stiff systems. The increase of column shears in the ground level is much higher for soft than for firm soil conditions. For the torsionally stiff systems considered, it is found that incoherent and phase‐delayed ground motions do not induce a significant rotational response of the structure. The use of a code eccentricity to account for torsion due to ground motion spatial variation is assessed. On firm soil, the use of a base shear along with an accidental eccentricity results in highly overestimated shear forces; however, for soft soil conditions, code formulations may result in underestimated shear forces. Copyright © 2003 John Wiley & Sons, Ltd.     

A coherency function model of ground motion at base rock corresponding to strike-slip fault

IntroductionEarthquakedamagesurveyandresearchresultshavedemonstratedthatspatialdistributiondifferenceofgroundmotionisoneoftheimportantreasonswhichcausedlongstructure(eglongspanbridge,undergroundpipe)destroy.Thathowtoprovideareasonableinputofgroundmotionfieldforaseismicdesignoflongstructureisaurgentprobleminearthquakeengineeringfield.Atpresent,themethodtostudyspatialvariationofgroundmotionsisadoptingstatisticanalysisbasedondensearrayrecordssuchasSMART-1array,etc,togetcoherencyfunctionofground…     

工程场地地震动相干函数的数值模拟

在确定性波动有限元分析基础上,结合随机振动分析的虚拟激励原理,可以形成工程场地随机波动分析方法。该方法将随机输入下的波动分析问题转换为多个虚拟激励下的确定性波动分析组合问题,从而可以方便地获得场地波动观测量之间的谱密度矩阵,进而计算给出工程场地的地震动相干函数。本文阐述了随机波动分析的基本原理,提出了该方法的正确性验证标准。将建议方法分别应用于具有一致随机激励与非一致随机激励的复杂工程场地的地震动相干函数分析之中,讨论了受局部场地条件影响的地震动相干函数的若干特征。