The high‐frequency limit of usable response spectral ordinates from filtered analogue and digital strong‐motion accelerograms

The range of response frequencies for which spectral ordinates obtained from accelerograms may be considered reliable is limited by several factors, primary among them being the effects of filters that are routinely applied to remove noise from the records. Considerable attention has been focused on the low‐frequency limit of the usable spectral ordinates because of various engineering applications requiring long‐period spectral accelerations or displacements but only recently have rational approaches to selecting the high‐frequency limit been proposed. Since there are applications for which the high‐frequency spectral ordinates are important, the approaches to this issue presented in the recent studies are reviewed and their application to the ground‐motion database from Europe and the Middle East is explored. On the basis of the results of these analyses, it is concluded that a large proportion of this dataset can be used to provide reliable estimates of response spectral ordinates at much shorter periods than may have previously been considered feasible. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of long‐period filter cut‐off on elastic spectral displacements

The effect of the long‐period filter cut‐off, T_c, on elastic spectral displacements is investigated using a strong ground‐motion database from Europe and the Middle East. The relation between the filter and oscillator responses is considered to observe the influence of T_c for both analogue and digital records, and the variations with site classification, magnitude, filter order and viscous damping. Robust statistics are derived using the re‐processed European data to generalize the effects of the long‐period filter cut‐off on maximum oscillator deformation demands as a function of these seismological and structural features. Statistics with a 95% confidence interval are derived to suggest usable period ranges for spectral displacement computations as a function of T_c. The results indicate that the maximum period at which spectral displacements can be confidently calculated depend strongly on the site class, magnitude and filter order. The period range where reliable long‐period information can be extracted from digital accelerograms is twice that of analogue records. Copyright © 2006 John Wiley & Sons, Ltd.     

Prediction of elastic displacement response spectra in Europe and the Middle East

Empirical equations are presented for the prediction of displacement response ordinates for damping ratios of 2, 5, 10, 20 and 30% of critical and for response periods up to 4s, using 532 accelerograms from the strong‐motion databank from Europe and the Middle East. The records were all re‐processed and only employed for regressions at periods within the usable range, defined as a fraction of the filter cut‐off and depending on the instrument type (digital or analogue), earthquake magnitude and site class. The equations can be applied to predict the geometric mean displacement and pseudo‐acceleration spectra for earthquakes with moment magnitudes ( M ) between 5 and 7.6, and for distances up to 100km. The equations also include style‐of‐faulting and site class as explanatory variables. The predictions obtained from these new equations suggest that earlier European equations for spectral displacements underestimate the ordinates at longer periods as a result of severe filtering and the use of the spectral ordinates at periods too close to the filter cut‐off. The results also confirm that the period defining the start of the constant displacement plateau in the Eurocode 8 (EC8) spectrum is excessively short at 2s. The results not only show that the scaling factor defined in EC8 for estimating the spectral ordinates at damping ratios different from 5% of critical are a good general approximation, but also that this scaling varies with magnitude and distance (reflecting the influence of duration) and also displays a mild dependence on response period. Copyright © 2007 John Wiley & Sons, Ltd.     

What is a Poor Quality Strong-Motion Record?

Some accelerograms are affected by non-standard recording and digitization problems that mean they are often not used in strong-motion studies. These non-standard problems cannot be corrected by the standard processing techniques that remove low and high-frequency noise from the time-history. Records from analogue instruments are more prone to these problems but even records from digital instruments, which are becoming increasingly common, can be affected by such errors. Since all strong-motion data is valuable it is important to know whether any useful information can be obtained from accelerograms that are affected by such problems. This article examines whether strong-motion records from analogue instruments that are missing their initial part due to late triggering of the instrument and also strong-motion records from digital instruments with low A/D converter resolution can be used for response spectral studies. It is found, by simulating such errors on high-quality strong-motion records, that good response spectral ordinates can be obtained from such `poor-quality' records within the period range of most engineering interest. This revised version was published online in July 2006 with corrections to the Cover Date.     

Broadband (0.05 to 20 s) prediction of displacement response spectra based on worldwide digital records

A new set of empirical equations for prediction of displacement response spectral ordinates from 20 Hz to T = 20 s is illustrated. The coefficients of the equations were obtained by regressing a dataset based on 1,155 tri-axial digital and 9 analog accelerometer records from 60 earthquakes worldwide. Long period disturbances in the accelerograms were evaluated and removed using a very recent method, aimed at preserving the long-period spectral content of the records. Analysis of variance has disclosed only little evidence for regional dependence of ground motions, while a carefully conducted evaluation of site effects resulted in clearly differentiated spectral amplification bands associated to the main ground types B, C, and D of Eurocode 8. Spectral ordinates for vibration periods >5 s were found to scale with magnitude quite consistently with theoretical scaling from Brune’s model. On the other hand, comparison of results with those yielded by recent prediction models in Europe and the United States (NGA), indicated that the latter may not be uniformly reliable at long periods. The proposed empirical equations are easily implemented in computer programs for seismic hazard assessment, being characterized by a simple functional form and a restricted number of predictor variables. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

数字化噪声对强震记录的影响及其消除方法

本文详细地分析了强震加速度记录的数字化噪声。分析表明:数字化噪声由数字化设备的系统误差和操作者的随机读数误差迭加而成,随机数字化误差是具有各态历经性质的,其振幅按高斯规律分布的平稳随机过程,在其频谱组成中,长周期分量占明显的优势,因此将对二次积分加速度记录的位移曲线产生严重的影响。 研究表明:随机数字化噪声位移主要分布在周期大于25秒的频段,对加速度记录来说,分布在周期小于25秒的频段内,其随机噪声是相当小的(假定记录纸速为1厘米/秒)。因此,利用数字滤波技术,可以除去数字化加速度记录中的大部份随机数字化噪声。 作为实例,对一个典型的强震加速度记录进行了滤波,给出了低噪声的加速度记录和由此算出的位移曲线,且和未经滤波的相应记录及其位移进行了比较。      

强震记录的采样与插值研究

本文从频域和时域两方面对强震记录的采样和插值过程进行了研究。研究中将采样与插值当作一个信号转换系统,通过数值计算,求得和各种常用的采样和插值过程相对应的传递函数。通过对传递函数的进一步研究表明:采样和插值方式对强震记录数据处理的结果有重要的影响,发现采样过程相当于一个低通滤波器,可以滤除信号中的某些高频信息,而插值过程犹如一个高频噪声源,会在数字记录中引入某些伪高频分量。分析结果还表明:在相同的采样密度下,不等距采样方式具有较高的精度,而等间距采样方式能给出更宽的平坦的频率特性曲线;抛物线插值给出的传递函数结果要比线性插值的结果更精确,这对恢复数字信号中的高频成分具有重要的意义。     

SMART-1台阵记录的长周期反应谱特性

利用台湾SMART－1台阵的数字强震仪加速度记录分析了同类场地上的地震动长周期分量特性，结果表明：同一次地震震中距基本相同的同类场地加速度反应谱短周期部分有较明显的差别，长周期部分则基本相同；震级和震中距对短周期反应谱影响明显，对长周期反应谱也有一定影响。最后将SMART－1台阳场地的平均谱与新的建筑抗震设计规范修订稿中提出的设计反应谱作了比较。     

An approach to digitize analog form of accelerograms recorded at Tarbela—Pakistan

Pakistan has a long history of seismological activity. The devastation caused by Kashmir earthquake has been administered all over the world. In Pakistan first seismological network, consisting of analog accelerograms and seismographs, was setup in early 1969 at Tarbela, where the largest water reservoir of the country is located. An approach to convert analog ground motion records into digital form is explained using a simple technique. The digitized data was compared with the original analog record and found in good agreement. The data has been used to plot response spectra. The digitized data will be available for seismic response analysis of structures and seismic risk analysis of the region.     

基于L1范数正则化的强震动加速度记录基线漂移识别方法

本文提出了一种基于L₁范数正则化的基线校正新方法,即以拟合速度时程误差最小为目标,以基线漂移本身尽可能小为约束条件,经过凸优化多次迭代自动求解出满足条件的基线漂移,避免了人为选取基线漂移分段次数和基线漂移起止时刻的主观干扰;随后利用该方法对多组加入了基线漂移噪声模型的强震动加速度记录进行验证。结果表明:本文方法对于识别和处理单段式、两段式和多段式的基线漂移噪声具有普适性,能敏锐地捕捉到速度时程发生漂移的趋势（斜率变化）,无需预先设定加速度基线漂移模型也可有效地识别出多种基线漂移噪声的起止位置和漂移程度;地震记录事前部分对本文方法处理结果影响较大,当记录事前部分足够长时（如20 s）,识别基线漂移噪声的准确性较高,位移时程可以较好地与原始位移匹配;而对于发生漂移的速度时程,本文方法可以不受地震事前部分长短的干扰,甚至在加速度记录出现明显丢头现象时,也能很好地实现峰值速度和整个速度时程的恢复。      

Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information

Scalar and vector intensity measures are developed for the efficient estimation of limit‐state capacities through incremental dynamic analysis (IDA) by exploiting the elastic spectral shape of individual records. IDA is a powerful analysis method that involves subjecting a structural model to several ground motion records, each scaled to multiple levels of intensity (measured by the intensity measure or IM), thus producing curves of structural response parameterized by the IM on top of which limit‐states can be defined and corresponding capacities can be calculated. When traditional IMs are used, such as the peak ground acceleration or the first‐mode spectral acceleration, the IM‐values of the capacities can display large record‐to‐record variability, forcing the use of many records to achieve reliable results. By using single optimal spectral values as well as vectors and scalar combinations of them on three multistorey buildings significant dispersion reductions are realized. Furthermore, IDA is extended to vector IMs, resulting in intricate fractile IDA surfaces. The results reveal the most influential spectral regions/periods for each limit‐state and building, illustrating the evolution of such periods as the seismic intensity and the structural response increase towards global collapse. The ordinates of the elastic spectrum and the spectral shape of each individual record are found to significantly influence the seismic performance and they are shown to provide promising candidates for highly efficient IMs. Copyright © 2005 John Wiley & Sons, Ltd.     

地震动永久位移对结构地震反应影响

本文推导了基于位移激励计算单自由度体系拟速度谱公式,通过构造的脉冲位移时程对公式精度进行了验证;之后利用小波变换去除强震记录噪声而保留地震动永久位移,再基于去趋势项方法和滤波方法去除永久位移后,计算拟速度谱。算例结果表明:短周期段内,不保留永久位移的位移激励拟速度谱值与保留永久位移的位移激励拟速度谱值相差很小;中长周期段内,不保留永久位移的位移激励拟速度谱值总体上小于保留永久位移的位移激励拟速度谱值,且不保留永久位移时,滤波方法引起的拟速度谱降幅大于去趋势项方法所引起的拟速度谱降幅。因此,基于位移激励计算中长周期结构的地震反应时,应保留地震动永久位移,或基于去趋势项方法去除永久位移。     

Nonlinear response estimates of RC frames using linear analysis of SDOF systems

An approximate‐simple method for nonlinear response estimates of reinforced concrete frames subjected to near‐field and far‐field records is presented in this paper. The approximate method is based on equivalent single‐degree‐of‐freedom and linear multi‐degree‐of‐freedom models. In this procedure, the nonlinear maximum roof displacement is estimated using an effective period factor and elastic response spectrum with an equivalent damping. The effective period factor was proposed for far‐field and near‐field ground motion records. For regions of high seismicity, the maximum roof displacement can be estimated by applying an effective period factor of 2.3 and 2.1 for near‐field and far‐field records, respectively, and 9% damped displacement response spectrum. For regions of moderate seismicity, a lower effective period factor of 1.9 and 1.8, for near‐field and far‐field records, respectively, can be applied to estimate the maximum roof displacement. A relationship between linear and nonlinear response of multi‐degree‐of‐freedom systems was also proposed to obtain estimates of the maximum inter‐story drift of nonlinear responding reinforced concrete frames. In addition, the effects of number of ground motion records used in the analyses on the scatters of results were investigated. The required number of ground motions to produce a reliable response was proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

Extending ground-motion prediction equations for spectral accelerations to higher response frequencies

Ground-motion prediction equations (GMPEs) for spectral accelerations have traditionally focused on the range of response periods most closely associated with the dynamic characteristics of buildings. Providing predictions only in this period range (from 0.1 to 2 or 3 s) has also accommodated the assumed limitations on the usable period range resulting from the processing of accelerograms. There are, however, engineering applications for which estimates of spectral ordinates are required at shorter response periods. Recent work has demonstrated that high-frequency spectral ordinates are relatively insensitive to record processing, contrary to previous assumptions. In the light of this finding, additional regressions are performed to extend a recent pan-European GMPE to higher response frequencies. This model and others that also include coefficients for spectral ordinates at several high response frequencies are used to explore options for interpolating coefficients for equations that do not provide good coverage in this range. The challenges and uncertainties associated with such interpolations are discussed. The paper concludes that a set of standard response frequencies could be usefully established for future GMPEs.     

基于强震记录估算同震位移的研究进展及方法

通过对强震加速度记录估算同震位移技术自20世纪40年代以来国内外研究成果的总结,系统地阐述了通过近断层加速度记录计算同震位移的相关理论、方法的发展历程和成就。首先简述了基于强震记录估算同震位移的意义和普遍存在的漂移现象,然后总结了从模拟记录到数字记录两个阶段计算同震位移所取得的成果,接着归纳了为解决漂移现象所采取的3种基于时程拟合的方法和2种基于小波分析的方法,最后对基于数字强震仪记录估算同震位移的未来研究进行了展望。     

Wavelet‐based simulation of spectrum‐compatible aftershock accelerograms

In damage‐based seismic design it is desirable to account for the ability of aftershocks to cause further damage to an already damaged structure due to the main shock. Availability of recorded or simulated aftershock accelerograms is a critical component in the non‐linear time‐history analyses required for this purpose, and simulation of realistic accelerograms is therefore going to be the need of the profession for a long time to come. This paper attempts wavelet‐based simulation of aftershock accelerograms for two scenarios. In the first scenario, recorded main shock and aftershock accelerograms are available along with the pseudo‐spectral acceleration (PSA) spectrum of the anticipated main shock motion, and an accelerogram has been simulated for the anticipated aftershock motion such that it incorporates temporal features of the recorded aftershock accelerogram. In the second scenario, a recorded main shock accelerogram is available along with the PSA spectrum of the anticipated main shock motion and PSA spectrum and strong motion duration of the anticipated aftershock motion. Here, the accelerogram for the anticipated aftershock motion has been simulated assuming that temporal features of the main shock accelerogram are replicated in the aftershock accelerograms at the same site. The proposed algorithms have been illustrated with the help of the main shock and aftershock accelerograms recorded for the 1999 Chi–Chi earthquake. It has been shown that the proposed algorithm for the second scenario leads to useful results even when the main shock and aftershock accelerograms do not share the same temporal features, as long as strong motion duration of the anticipated aftershock motion is properly estimated. Copyright © 2008 John Wiley & Sons, Ltd.     

利用近场加速度记录确定近震震源参数的研究

本文对利用强震近场加速度记录确定时,空、强三个完整的震源参数。文中给出一种利用计算机自动识别地震记录的Ｐ波初动到时和Ｓ波震相到的算法。根据新近发表的Ｗｏｏｄ－Ａｎｄｅｒｓｏｎ地震仪器的最新参数,修牍正唐山地区量规函数。利用唐 山数字震观测台阵得到的近场加速度数据,计算了１０次地震的震源位置和震级,并对定位误差进行了综合分析,将强震台网测定的震源参数与地震台     

A stochastic ground motion model with separable temporal and spectral nonstationarities

A fully nonstationary stochastic model for strong earthquake ground motion is developed. The model employs filtering of a discretized white‐noise process. Nonstationarity is achieved by modulating the intensity and varying the filter properties in time. The formulation has the important advantage of separating the temporal and spectral nonstationary characteristics of the process, thereby allowing flexibility and ease in modeling and parameter estimation. The model is fitted to target ground motions by matching a set of statistical characteristics, including the mean‐square intensity, the cumulative mean number of zero‐level up‐crossings and a measure of the bandwidth, all expressed as functions of time. Post‐processing by a second filter assures zero residual velocity and displacement, and improves the match to response spectral ordinates for long periods. Copyright © 2008 John Wiley & Sons, Ltd.