Long period Fourier amplitude spectra of strong motion acceleration

The empirical equations for scaling Fourier amplitude spectra in the frequency band from ~0·1 to 25 Hz can be extrapolated to describe the long period strong motion amplitudes. The results of this extrapolation can agree with (1) the seismological and field estimates of permanent ground displacement (near field), and with (2) the independent estimates of seismic moment and the observed frequencies of far field Fourier spectrum amplitudes.     

Empirical model for estimating Fourier amplitude spectra of ground acceleration in Taiwan region

A collection of ground‐motion recordings (1070 acceleration records) of moderate (5.1⩽M_L⩽6.5) earthquakes obtained during the execution of the Taiwan Strong Motion Instrumentation Program (TSMIP) since 1991 was used to study source scaling model and attenuation relations for a wide range of earthquake magnitudes and distances and to verify the models developed recently for the Taiwan region. The results of the analysis reveal that the acceleration spectra of the most significant part of the records, starting from S‐wave arrival, can be modelled accurately using the Brune's ω‐squared source model with magnitude‐dependent stress parameter Δσ, that should be determined using the recently proposed regional relationships between magnitude (M_L) and seismic moment (M₀) and between M₀ and Δσ. The anelastic attenuation Q of spectral amplitudes with distance may be described as Q=225 ƒ^1.1 both for deep (depth more than 35 km) and shallow earthquakes. The source scaling and attenuation models allow a satisfactory prediction of the peak ground acceleration for magnitudes 5.1⩽M⩽6.5 and distances up to about 200 km in the Taiwan region, and may be useful for seismic hazard assessment. Copyright © 2000 John Wiley & Sons, Ltd.     

Pseudo relative velocity spectra of earthquake ground motion at high frequencies

The currently available empirical scaling laws for estimation of spectral amplitudes are limited to periods longer than 0–04 s. However, for design of equipment and stiff structures on multiple and distant supports, exposed to strong shaking near faults where peak accelerations can exceed 1g, specification of design ground motions at higher frequencies is required. This paper presents a method for extrapolation of pseudo-relative velocity spectral amplitudes of strong earthquake shaking to short periods (0–01 < T < 0–04 sec). The extrapolated spectra can be used as a physical basis for defining design spectral amplitudes in this higher-frequency range. The analysis in this paper implies that for typical strong motion accelerations, particularly on sedimentary sites in California, the peak ground accelerations are projected to be unaffected by frequencies higher than those recorded. Consequently, in California, the high-frequency pseudo-acceleration spectra can be approximated from the recorded absolute peak accelerations.     

Exact computation of input‐energy spectra from Fourier amplitude spectra

A theoretically exact relation is presented between the Fourier amplitude spectrum and the elastic input‐energy spectrum. This energy spectrum is computed from the Fourier acceleration amplitude spectrum and the real part of the relative velocity transfer function of the single‐degree‐of‐freedom elastic oscillator. Some accelerometric records collected worldwide are used to prove the solution. It is shown that the relation presented in this work opens the door for a better understanding of the relationship between the input‐energy spectrum and other seismological variables, such as magnitude and focal distance. Copyright © 2003 John Wiley & Sons, Ltd.     

Q and high-frequency strong motion spectra

Empirical scaling equations for Fourier amplitude spectra of strong ground motion are used to describe A₀ and τ in the assumed (high-frequency) shape of strong motion amplitudes: FS(_φ) = A₀e-^πτφ. The res of computed A₀ and τ with other related estimates of spectral amplitudes; (2) smooth decay of strong motion spectral amplitudes up to φ = 25 Hz, without an abrupt low-pass filtering of high frequecies; and (3) good agreement with other estimates of the regionally specific attenuation of high-frequncy seismic waves.As the recorded strong earthquake shaking in the western United States typically samples only the shallow (10 km) and local (100km) characteristics of wave attenuation, the processed strong motion accelerograms can be used as the most direct means of describing the nature of the high-frequency attenuation of the entire strong motion signal for use in earthquake engineering applications. Seismological body wave, Lg and coda wave estimates of Q sample different volumes of the crust surrounding the station, and involve different paths of the waves. These differences must be carefully documented and understood before the results can be used in earthquake engineering characterization of strong motion amplitudes.     

近断层地震动加速度峰值衰减规律的研究

提出了近断层地面运动的衰减模型,对全球范围内6．0≤Mw≤7．6且震源深度均小于20km的636条地震动加速度峰值进行了统计分析,确定了本文研究的近断层区域为断层距25km,利用此范围内的440条记录进行了近断层加速度衰减规律的研究。水平地震记录分为硬土和软土两种场地类型,竖向地震记录只考虑土层场地,利用最小二乘法进行数据拟合分析,得到PGA随断层距和震源深度变化在不同震级处形成的衰减曲面,分析了近断层处水平、竖向的PGA以及竖向与水平PGA之比(V／H)的衰减规律。     

Evolution of accelerographs, data processing, strong motion arrays and amplitude and spatial resolution in recording strong earthquake motion

This paper presents a review of the advances in strong motion recording since the early 1930s, based mostly on the experiences in the United States. A particular emphasis is placed on the amplitude and spatial resolution of recording, which both must be ‘adequate’ to capture the nature of strong earthquake ground motion and response of structures. The first strong motion accelerographs had optical recording system, dynamic range of about 50 dB and useful life longer than 30 years. Digital strong motion accelerographs started to become available in the late 1970s. Their dynamic range has been increasing progressively, and at present is about 135 dB. Most models have had useful life shorter than 5–10 years. One benefit from a high dynamic range is early trigger and anticipated ability to compute permanent displacements. Another benefit is higher sensitivity and hence a possibility to record smaller amplitude motions (aftershocks, smaller local earthquakes and distant large earthquakes), which would augment significantly the strong motion databases. The present trend of upgrading existing and adding new stations with high dynamic range accelerographs has lead to deployment of relatively small number of new stations (the new high dynamic range digital instruments are 2–3 times more expensive than the old analog instruments or new digital instruments with dynamic range of 60 dB or less). Consequently, the spatial resolution of recording, both of ground motion and structural response, has increased only slowly during the past 20 years, by at most a factor of two. A major (and necessary) future increase in the spatial resolution of recording will require orders of magnitude larger funding, for purchase of new instruments, their maintenance, and for data retrieval, processing, management and dissemination. This will become possible only with an order of magnitude cheaper and ‘maintenance-free’ strong motion accelerographs. In view of the rapid growth of computer technology this does not seem to be (and should not be) out of our reach.     

Preliminary empirical model for scaling fourier amplitude spectra of strong ground acceleration in terms of modified mercalli intensity and recording site conditions

This paper presents an empirical model for scaling Fourier amplitude spectra of ground acceleration during strong earthquake shaking in terms of the reported Modified Mercalli Intensity (MMI) and the simplified characteristics of the geologic environment at the recording station. This analysis shows that (i) for the intermediate and high-frequency motions the spectral amplitudes approximately double for every level of the MMI; that (ii) the uncertainties associated with estimation of Fourier spectral amplitudes in terms of MMI are not greater than the uncertainties associated with similar estimation in terms of earthquake magnitude and epicentral distance; that (iii) the high frequency spectral amplitudes tend to be greater on basement rock sites relative to alluvium sites, with this trend being reversed for the low-frequency spectral amplitudes; and that (iv) the spectral amplitudes of very high-frequency vertical shaking are equal to or higher than the corresponding spectral amplitudes for horizontal shaking.     

Evaluation of models for Fourier amplitude spectra for the Taiwan region

In the Taiwan region, the empirical spectral models for estimating ground-motion parameters were obtained recently on the basis of recordings of small to moderate (5.0≤M_L≤6.5) earthquakes. A large collection of acceleration records from the M_L=7.3 Chi-Chi earthquake (21 September, 1999) makes it possible to test the applicability of the established relationships in the case of larger events. The comparison of ground-motion parameters (Fourier amplitude spectra, peak accelerations and response spectra), which were calculated using the models, and the observed data demonstrates that the models could provide an accurate prediction for the case of the Chi-Chi earthquake and the largest aftershocks. However, there are some peculiarities in the ground-motion frequency content and attenuation that, most probably, are caused by the features of the rupture process of the large shallow earthquake source.     

A stochastic model of the Fourier phase of strong ground motion

ＡｓｔｏｃｈａｓｔｉｃｍｏｄｅｌｏｆｔｈｅＦｏｕｒｉｅｒｐｈａｓｅｏｆｓｔｒｏｎ　ｇｒｏｕｎｄｍｏｔｉｏｎＺｈｅｎ－ＰｅｎｇＬＩＡＯ；（廖振鹏）ａｎｄＸｉｎｇＪＩＮ（金星）（ＩｎｓｔｉｔｕｔｅｏｆＥｎｇｉｎｅｅｒｉｎｇＭｅｃｈａｎｉｃｓ，ＳｔａｔｅＳ...     

水工建筑物强震动加速度记录的分析处理

从工程应用角度详细介绍水工强震动加速度记录正确处理分析的方法与原理.主要介绍了震源的评估原理,强震动加速度记录预处理过程中单位换算、奇异点剔除、基线校正、滤波除噪等步骤的方法原理,后处理分析中一次、二次积分、谱分析原理.阐述了利用强震动加速度记录进行震害快速评估原理.文中以二滩拱坝强震监测台阵监测到的一次强震加速度记录的处理过程为例,以图表形式直接明了地强调指出了强震动加速度记录处理中容易发生错误的过程,并提出相应的处理方法.     

基于快速傅里叶变换的地震波加速度构成及其幅频特性研究

根据2008年汶川M_S8.0地震广元曾家台(GYZJ)的强震记录,运用Matlab软件对东西向55—75 s的加速度时程进行快速傅里叶变换,得到有限复傅里叶系数,从而将离散的加速度记录转化为加速度随时间变化的函数表达式. 该表达式中包含了50组不同频率的正弦波和余弦波,由此确定了地震波加速度的主要构成. 经回归分析可知, 函数计算值与原始记录的相关系数R为0.9,拟合程度良好; 利用SeismoSignal软件对地震波加速度时程进行谱分析,结果表明在原来的波中频率约为2.8 Hz的谐振分量振幅最大且0—10 Hz这一频段的波最为丰富. 这一结果与函数表达式中频率与振幅的分布基本吻合, 为深入研究汶川地震的动力特性及其对山体动力效应的分析提供了重要的理论依据,具有广阔的应用前景.     

基于随机Fourier谱的地震动合成研究

本文基于与物理随机模型相对应的随机Fourier谱,通过对地震动非平稳性及其所受影响机制的分析,建立了非平稳地震动合成的新方法。通过引入基本相位差谱,并将初始相角视为随机变量,以相位差谱的分布特性、随机地震动的统计特征以及对结构随机反应的影响为原则,利用计算机程序生成相位差谱,提出了基于随机Fourier谱的合成地震动方法。同时,利用快速FFT技术提高合成精度。根据本文提出的合成方法获得的地震动具有非平稳特性,将为后续研究工作提供合理的地震动加速度时程。     

Analysis of strong earthquake ground motion for prediction of response spectra

Prediction of response spectra for earthquake engineering purposes is considered from a new point of view based on the dislocation theory of earthquakes. It is shown that the traditional scaling of response spectra by the predicted peak acceleration should be limited to the high-frequency end of the spectrum, and that the peak acceleration in the near field is not strongly correlated with earthquake magnitude. The amplitude of the long-period end of response spectrum at source to station distances greater than about 10 source dimensions should be scaled with seismic moment, while for distances less than about one source dimension this amplitude should be proportional to the permanent ground displacement. To reconcile the existing extensive data on seismicity of active regions based on magnitude scale, it is shown that magnitude can be used to determine approximately the seismic moment.     

地震动滞回能量谱衰减规律研究

本文选用美国西部California州15次较大地震中的266条强地震动记录,利用衰减关系建立了滞回能量谱,分析了场地条件、延性系数、震级及距离等参数对滞回能量谱的影响。研究发现,场地条件对滞回能量谱影响很大,随着场地变软,滞回能量谱变大,与A B类场地相比,C类场地的滞回能量谱平均要高出70％左右,D类场地则要高出170％左右。随着延性系数的增大,滞回能量谱有增大的趋势,尤其是当延性系数由2变到4或6时更为明显,但当延性系数增加到一定程度时,滞回能量谱的差别不大,延性系数为4和6时的滞回能量谱差别不大,甚至在周期较大时,延性系数为6的滞回能量谱反而小于延性系数为4时的滞回能量谱。另外,研究结果表明,大的震级和小的距离对结构产生比较大的滞回能量需求。利用本文结果,可以估计未来地震中结构物所遭受滞回能量的大小。     

Determination of noise spectra from strong motion data recorded in Greece

A large number of strong ground motions inGreece have been recorded by analogaccelerographs. The processing of analogstrong motion recordings and conversion toa digital form introduces noise in thesignal, due to the digitization andprocessing whichsignificantly affects the record. In thepresent paper a unified processing anddetermination of digitization andprocessing noise for the Greek strongmotion records is presented. Moreover,appropriate relations are proposed for thelower cut-off frequency with respect tothe epicentral distance and earthquakemagnitude for record filtering.     

地震总输入能量与瞬时输入能量谱的研究

现有的抗震设计理论大多是基于承载力或强度的设计方法,与其相应的反应谱理论最大的缺陷是无法反映地震动持时的影响,而以地震动能量作为设计参数时就能弥补现有抗震理论的不足。本文按照反应谱理论的思路建立了线性单自由度体系的地震动总输入能量谱和瞬时输入能量谱。研究发现,阻尼比为5%时的地震动总输入能量谱和最大瞬时输入能量谱的等价速度谱可以分别用阻尼比为0.5%和10%下的拟速度谱来近似获得;地震波的V/A值大于0.15时,总输入能量谱的Δt谱峰值与地震波的强震持时呈线性增长关系,V/A值小于0.15时,两者间的关系无规律性。最大瞬时输入能量谱的Δt谱峰值基本不受地震波的V/A值与强震持时的影响;输入能量谱(总输入能量谱与最大瞬时输入能量谱)的特征周期随地震波V/A值的增大而增大,根据分析结果本文提出了线性单自由度体系输入能量谱的简化计算方法,方法简便,计算结果偏安全。     

地震动加速度反应谱竖向分量与水平分量的比值

本文采用水平向444条,竖向228条严格按我国抗震设计规范划分场地条件的实际强震记录,计算了不同情况下加速度反应谱竖向分量与水平分量的比值(V／H)的平均值,结果表明：(1)V／H随周期变化明显。在短周期,有1个1．0左右的峰值,在周期0．2～1．0间有1个0．4左右的低谷,在2s以后的长周期,V／H趋近1个0．6左右的常数。(2)V／H值与震中距也有很大关系,在震源附近竖向反应谱与水平向反应谱很接近,V／H均值在周期长于2s时达到了0．9。(3)它与场地条件也有很大关系,短周期处,Ⅰ类场地V／H峰值为0．7,Ⅱ、Ⅲ类场地V／H峰值为1．1,长周期处则随场地类别由Ⅰ,Ⅱ到Ⅲ类,V／H由大到小。建议抗震设计规范修订时应考虑对竖向反应谱的规定予以修正,文中给出了建议方案。     

Characteristics of amplitude and duration for near fault strong ground motion from the 1999 Chi-Chi, Taiwan Earthquake

A great number of free-field ground motion records are obtained during the 1999 Chi-Chi, Taiwan, earthquake. Records from 130 near fault free-field stations within 55 km to the causative fault surface are used as database, and characteristics of earthquake peak ground acceleration, velocity, displacement and duration are analyzed. According to this study, near fault ground motions are strongly affected by distance to fault, fault rupture directivity, site condition, as well as thrust of hanging wall. Compared with empirical strong ground motion attenuation relations used in China, US and Japan, the PGAs and PGVs recorded in this earthquake are not as large as what we have expected for a large earthquake as magnitude 7.6. However, the largest PGV and PGD worldwide were recorded in this event, which are 292 cm/s and 867 cm, respectively. Caused by nonlinear site effects of soil, peaks and corresponding ratios on E-class site were markedly different from those on other sites. Just as observed in historic earthquakes, fault rupture directivity effects caused significant differences between peaks of ground motion of two horizontal components, but took very slight effects on the duration of ground motion. The significant velocity pulses associated with large PGVs and PGDs, as well as large permanent displacements, which may result from the large thrust of the hanging wall, became the outstanding character of this event. Based on this study, we point out that 3D waveform modeling is needed to understand and predict near fault ground motion of large earthquakes.