Simulation and generation of spectrum-compatible ground motions based on wavelet packet method

This paper deals with the problem of generating spectrum-compatible artificial accelerograms for seismic dynamic analysis of engineering projects. A wavelet-packet-based, two-step procedure for the issue is proposed. The first step is to generate acceleration time history that could account for temporal and frequency non-stationarities of recorded ground motions. The second step is to decompose it into a desired number of wavelet packet vectors with high frequency resolution and non-overlapping frequency contents. Then each wavelet packet vector is scaled suitably and iteratively for the response spectrum of the simulated accelerogram to fit a specified design spectrum. The advantages of this procedure are that it can simulate user-specified acceleration time history with only 6 input parameters and the adjusted accelerogram has similar characteristics to the recorded one. The proposed procedure has been illustrated by simulating and modifying acceleration time history that are compatible with two different design spectrums for nuclear power plants. In addition, iterative efficiency of the method is investigated by simulating and adjusting acceleration time history for 100 successive times. The maximum relative error of the 76 period control points can reach 6% or below. Results show that the proposed method is effective and practical to generate and find spectrum-compatible ground motions with both stochastic and deterministic aspects.     

Wavelet-based generation of spatially correlated accelerograms

For the seismic analysis of complex or nonlinear extended structures, it is useful to generate a set of properly correlated earthquake accelerograms that are consistent with a specified seismic hazard. A new simulation approach is presented in this paper for the generation of ensembles of spatially correlated accelerograms such that the simulated motions are consistent with (i) a parent accelerogram in the sense of temporal variations in frequency content, (ii) a design spectrum in the mean sense, and (iii) with a given instantaneous coherency structure. The formulation is based on the extension of stochastic decomposition technique to wavelet domain via the method of spectral factorization. A complex variant of the modified Littlewood-Paley wavelet function is proposed for the wavelet-based representation of earthquake accelerograms, such that this explicitly brings out the phase information of the signal, besides being able to decompose it into component time-histories having energy in non-overlapping frequency bands. The proposed approach is illustrated by generating ensembles of accelerograms at four stations.     

Common problems in automatic digitization of strong motion accelerograms

Common problems encountered in automatic digitization of strong motion accelerograms, recorded on film, are presented and discussed. These include synchronization of the time scale for the three components of motion, non-uniform film speed, trace following in case of scratches or trace crossings, distortions from high contrast preprocessing of the scanned image, and trace “rotation” resulting from rotated position of the scanned film record. Procedures for correcting or eliminating these problems are suggested. The image processing hardware has developed so much during the past 20 years, that at present it exceeds the technical requirements for processing strong motion accelerograms. The problems described in this paper result from lack of training of the operators and lack of quality control in the process, which still seems to be esoteric and highly specialized. This situation may have been caused by the low demand by the engineering profession for high quality and large volume of strong motion data.     

小波分析法在海拉尔地震台前兆数据处理中的应用研究

应用小波变换法可对不同频率成分进行分解的特性,选取d b4小波基函数,尺度为1～8阶,对海拉尔地震台前兆资料进行分析研究.结果表明,应用小波变换方法可较容易地识别和剔除气压、场地环境干扰等影响海拉尔地震台伸缩仪观测资料精度的诸多因素,气压和场地环境干扰在小波细节分解d3～d6部分异常显著;小波变换法对同震效应的识别、提...     

基于小波变换的拟合规范反应谱多维地震动模拟

本文提出一种基于小波变换的拟合规范反应谱的多维地震动模拟算法。首先将规范反应谱推广到三维相关设计反应谱,然后将已有的三维地震动加速度时间历程曲线分解为一系列不同频段上的地震动分量,调整每一个地震动分量的幅值使其在相应的频率范围内拟合设计反应谱,最后经过调整后的地震动分量进行重构得到更新的地震动时间历程曲线。将该时间历程曲线的反应谱与目标反应谱进行比较,重复该过程直到误差位于特定的范围内。该方法可以保留原始地震动的局部时-频特性,为多维地震动的模拟提供了一种新的方法。     

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。     

A note on the useable dynamic range of accelerographs recording translation

Since the late 1970s, the dynamic range and resolution of strong motion digital recorders have leaped from 65 to 135 dB, opening new possibilities for advanced data processing and interpretation. One of these new possibilities is the calculation of permanent displacement of the ground or of structures, associated with faulting or with non-linear response. Proposals on how permanent displacements could be recovered from recorded strong motion have been published since 1976. The analysis in this paper concludes that permanent displacements of the ground and of structures in the near-field can be calculated provided all six components of strong motion (three translations and three rotations) have been recorded, and the records are corrected for transducer rotation, misalignment and cross-axis sensitivity.     

极移十年尺度波动的多分辨率重建及其统计特性

极移的频谱分布包含ｆ０、ｆ（－１）和ｆ（－２）分量,研究各个分量的统计特征及其产生机制在天文地球动力学的研究中有着十分重要的地位．本文利用小波分析的正交分解的特点,将地球极移按幂律谱进行分解,提出了核函数的概念,并对校函数的特性进行了分析．结果表明：ｆ（－１）过程的核函数的平均变化周期４３８天,最大变化周期５２５天,最小３４５天,ｆ（－２）过程的核函数的平均变化周期４２６天,最大变化周期４９５天,最小３６０天．ｆ０过程与太阳黑子的变化有很强的相关性,ｆ（－１）和ｆ（－２）分量与太阳活动无关．     

极移十年尺度波动的多分辨率重建及其统计特性

极移的频谱分布包含ｆ０、ｆ（－１）和ｆ（－２）分量,研究各个分量的统计特征及其产生机制在天文地球动力学的研究中有着十分重要的地位．本文利用小波分析的正交分解的特点,将地球极移按幂律谱进行分解,提出了核函数的概念,并对校函数的特性进行了分析．结果表明：ｆ（－１）过程的核函数的平均变化周期４３８天,最大变化周期５２５天,最小３４５天,ｆ（－２）过程的核函数的平均变化周期４２６天,最大变化周期４９５天,最小３６０天．ｆ０过程与太阳黑子的变化有很强的相关性,ｆ（－１）和ｆ（－２）分量与太阳活动无关．     

The effect of energy concentration of earthquake ground motions on the nonlinear response of RC structures

Usually different nonlinear time responses due to earthquake ground motion are distinguished by non-localized spectra, such as the response or power spectra. However, these spectra are often not able to explain the large discrepancy among structural responses caused by different earthquake records. The local spectrum, obtained by the wavelet transform, shows the energy distribution in the time-frequency domain, and helps to understand the very different structural responses. By changing the energy distribution in time of several earthquake records, the effect of energy concentration on the structural nonlinear response is demonstrated. This paper proposes the use of the characteristic peak ground acceleration, which is the peak of the signal constructed by only a few special wavelet components of an earthquake record, to quantify the difference between earthquake records, since this measure indicates the magnitude of the energy concentrated around the fundamental period of a structure.     

Effect of tilt on strong motion data processing

In the near-field of an earthquake the effects of the rotational components of ground motion may not be negligible compared to the effects of translational motions. Analyses of the equations of motion of horizontal and vertical pendulums show that horizontal sensors are sensitive not only to translational motion but also to tilts. Ignoring this tilt sensitivity may produce unreliable results, especially in calculations of permanent displacements and long-period calculations. In contrast to horizontal sensors, vertical sensors do not have these limitations, since they are less sensitive to tilts. In general, only six-component systems measuring rotations and accelerations, or three-component systems similar to systems used in inertial navigation assuring purely translational motion of accelerometers can be used to calculate residual displacements.     

消除强震加速度记录数字化误差的方法和处理软件

本文详细地分析了用数字化仪和激光扫描仪对模拟加速度记录进行数字化时所产生的误差及消除这些误差的方法，并开发了相关处理软件。数字化误差由数字化设备的系统误差和读数员在操作过程中的随机误差迭加而成，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。利用激光扫描仪做强震记录数字化，工作效率很高。本文给出了激光扫描仪分析处理软件和消除数字化噪声实例。     

An explanation of the large PGA value of 2013 Ms7.0 Lushan earthquake at 51BXD station through topographic analysis

In Ms7.0 Lushan earthquake, a large amount of strong ground motion recordings were collected. In this paper, we analyze the recordings carefully. The abnor- mality of ground motion recordings is identified through a log linear regression. In the station of 51BXD, the PGA value has exceeded 1 g, which is the biggest peak ground acceleration （PGA） value obtained from all recordings in this earthquake. The log linear relation shows the PGA value in this station is abnormally large. As this station is located on the footage of a hill, the topographic amplifi- cation factor is explored in order to explain this abnor- mality. Through 3D numerical modeling using spectral element method with transmitting boundary conditions, the amplification factor is quantized. In this station, the topo- graphic amplification is highly polarized in the direction of East-West which agrees with the empirical recordings. This research result suggests us in future directionality of topographic amplification should be considered in the aseismic design.     

基于小波的地闪首次回击辐射场的多重分形分析

利用2002年夏季青海野外观测慢天线电场变化仪资料,应用小波变换模极大方法对地闪首次回击辐射场的检测及多重分形谱特征进行了分析.发现小波分解在小尺度上的时间变异系数在回击主脉冲峰处（回击点）呈现明显的尖峰,据此可对回击点进行快速可靠的检测;地闪回击辐射场多重分形谱可用推广的多重分形二项倍增串级公式比较精确地拟合,最小标度指数及谱宽度平均分别为-0.11和1.5,是重要的回击特征参数,而小波及多重分形应是闪电信号处理的重要工具.     

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.     

Amplitude and frequency characteristics of the 2001 Southern Peru, M w = 8.4 earthquake records

The Departments of Civil Engineering and Geophysics of the University of Chile, together with international institutions, deployed strong-motion stations in the northern Chile seismic gap. These instruments recorded the June 23, 2001 M _w = 8.4 earthquake that occurred in Southern Peru. This earthquake exhibited at stiff deep soil sites in northern Chile, relatively large maximum accelerations although the recording stations are located more than 400 km away from the epicentral region and 200 km from the southern edge of the rupture. Typical accelerations at these distances are in the order of 0.30 g, consIDerably larger than those expected from recently presented attenuation formulae. Frequency and Wavelet Decomposition of the signals are presented from which the evolution of the amplitude, as a function of selected frequency bands, is analyzed. Typical Central Frequency varies from 3 to 4.8 Hz for horizontal records and 4.5 to 9.5 Hz for vertical records. Ninety five percent of the record energy is concentrated below 11 Hz. Evolution of energy for bands higher than the average record frequency is relatively smooth, and for low frequency, the energy shows abrupt changes as a function of time. The sudden changes are associated to dominant large amplitude motions observed in most of the records. The high frequency content of the motion observed for this earthquake is correlated with the heterogeneities of the interplate contact. To statically characterize the energy evolution with time a smooth three-parameter envelope adjusted for each frequency band is used, therefore, comparison is possible and results could be applied for synthesis studies.     

唐山丰南M4.1级地震强震记录分析

2010年4月9日唐山丰南发生M4.1级地震,津冀地区共有36个强震台站获取到强震记录,记录的最大加速度为58.92cm/s2,通过对比强震记录的峰值,发现该地震竖向峰值比水平向大,在三个分量上加速度傅氏谱谱型以多峰为主。通过对强震记录频谱特征进行分析,得出随着震中距的增大,反应谱高频成分衰减快于低频成分,竖向与水平向加速度比值与常规认为的1/2—2/3差别较大。通过对本次强震动记录反应谱标定并结合唐山地区3.5级以上地震记录,获得唐山地区土层场地反应谱谱型参数。     

中国重力异常的小波变换与多尺度分析

阐述了小波变换及多尺度分析方法的原理，利用二维小波多尺度分析方法对中国布格重力异常进行了分解，并从其中划分出有意义的剩余异常．模型结果证明方法有效．由于本文方法可以将重力异常分解成各种几何尺度意义下的不同成分，这为重力解释和研究地壳的结构提供更多更新的依据．     

中国重力异常的小波变换与多尺度分析

阐述了小波变换及多尺度分析方法的原理,利用二维小波多尺度分析方法对中国布格重力异常进行了分解,并从其中划分出有意义的剩余异常．模型结果证明方法有效．由于本文方法可以将重力异常分解成各种几何尺度意义下的不同成分,这为重力解释和研究地壳的结构提供更多更新的依据．     

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.