Stochastic simulation of regionalized ground motions using wavelet packets and cokriging analysis

Performance‐based earthquake engineering often requires ground‐motion time‐history analyses to be performed, but very often, ground motions are not recorded at the location being analyzed. The present study is among the first attempt to stochastically simulate spatially distributed ground motions over a region using wavelet packets and cokriging analysis. First, we characterize the time and frequency properties of ground motions using the wavelet packet analysis. The spatial cross‐correlations of wavelet packet parameters are determined through geostatistical analysis of regionalized ground‐motion data from the Northridge and Chi‐Chi earthquakes. It is observed that the spatial cross‐correlations of wavelet packet parameters are closely related to regional site conditions. Furthermore, using the developed spatial cross‐correlation model and the cokriging technique, wavelet packet parameters at unmeasured locations can be best estimated, and regionalized ground‐motion time histories can be synthesized. Case studies and blind tests using data from the Northridge and Chi‐Chi earthquakes demonstrate that the simulated ground motions generally agree well with the actual recorded data. The proposed method can be used to stochastically simulate regionalized ground motions for time‐history analyses of distributed infrastructure and has important applications in regional‐scale hazard analysis and loss estimation. Copyright © 2014 John Wiley & Sons, Ltd.     

A spatial cross‐correlation model of spectral accelerations at multiple periods

Many seismic loss problems (such as disruption of distributed infrastructure and losses to portfolios of structures) are dependent upon the regional distribution of ground‐motion intensity, rather than intensity at only a single site. Quantifying ground‐motion over a spatially‐distributed region therefore requires information on the correlation between the ground‐motion intensities at different sites during a single event. The focus of the present study is to assess the spatial correlation between ground‐motion spectral accelerations at different periods. Ground motions from eight well‐recorded earthquakes were used to study the spatial correlations. On the basis of obtained empirical correlation estimates, we propose a geostatistics‐based method to formulate a predictive model that is suitable for simulation of spectral accelerations at multiple sites and multiple periods, in the case of crustal earthquakes in active seismic regions. While the calibration of this model and investigation of its implications were somewhat complex, the model itself is very simple to use for making correlation predictions. A user only needs to evaluate a simple equation relying on three sets of coefficients provided here to compute a correlation coefficient for spectral values at two periods and at a specified separation distance. These results may then be used in evaluating the seismic risk of portfolios of structures with differing fundamental periods. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling spatially correlated spectral accelerations at multiple periods using principal component analysis and geostatistics

Regional seismic risk assessments and quantification of portfolio losses often require simulation of spatially distributed ground motions at multiple intensity measures. For a given earthquake, distributed ground motions are characterized by spatial correlation and correlation between different intensity measures, known as cross‐correlation. This study proposes a new spatial cross‐correlation model for within‐event spectral acceleration residuals that uses a combination of principal component analysis (PCA) and geostatistics. Records from 45 earthquakes are used to investigate earthquake‐to‐earthquake trends in application of PCA to spectral acceleration residuals. Based on the findings, PCA is used to determine coefficients that linearly transform cross‐correlated residuals to independent principal components. Nested semivariogram models are then fit to empirical semivariograms to quantify the spatial correlation of principal components. The resultant PCA spatial cross‐correlation model is shown to be accurate and computationally efficient. A step‐by‐step procedure and an example are presented to illustrate the use of the predictive model for rapid simulation of spatially cross‐correlated spectral accelerations at multiple periods.     

Efficient sampling and data reduction techniques for probabilistic seismic lifeline risk assessment

Probabilistic seismic risk assessment for spatially distributed lifelines is less straightforward than for individual structures. While procedures such as the ‘PEER framework’ have been developed for risk assessment of individual structures, these are not easily applicable to distributed lifeline systems, due to difficulties in describing ground‐motion intensity (e.g. spectral acceleration) over a region (in contrast to ground‐motion intensity at a single site, which is easily quantified using Probabilistic Seismic Hazard Analysis), and since the link between the ground‐motion intensities and lifeline performance is usually not available in closed form. As a result, Monte Carlo simulation (MCS) and its variants are well suited for characterizing ground motions and computing resulting losses to lifelines. This paper proposes a simulation‐based framework for developing a small but stochastically representative catalog of earthquake ground‐motion intensity maps that can be used for lifeline risk assessment. In this framework, Importance Sampling is used to preferentially sample ‘important’ ground‐motion intensity maps, and K‐Means Clustering is used to identify and combine redundant maps in order to obtain a small catalog. The effects of sampling and clustering are accounted for through a weighting on each remaining map, so that the resulting catalog is still a probabilistically correct representation. The feasibility of the proposed simulation framework is illustrated by using it to assess the seismic risk of a simplified model of the San Francisco Bay Area transportation network. A catalog of just 150 intensity maps is generated to represent hazard at 1038 sites from 10 regional fault segments causing earthquakes with magnitudes between five and eight. The risk estimates obtained using these maps are consistent with those obtained using conventional MCS utilizing many orders of magnitudes more ground‐motion intensity maps. Therefore, the proposed technique can be used to drastically reduce the computational expense of a simulation‐based risk assessment, without compromising the accuracy of the risk estimates. This will facilitate computationally intensive risk analysis of systems such as transportation networks. Finally, the study shows that the uncertainties in the ground‐motion intensities and the spatial correlations between ground‐motion intensities at various sites must be modeled in order to obtain unbiased estimates of lifeline risk. Copyright © 2010 John Wiley & Sons, Ltd.     

A predictive model for Arias intensity at multiple sites and consideration of spatial correlations

Arias intensity, I_a, has been identified as an efficient intensity measure for the estimation of earthquake‐induced losses. In this paper, a new model for the prediction of Arias intensity, which incorporates nonlinear site response through the use of the average shear‐wave velocity and a heteroskedastic variance structure, is proposed. In order to estimate the effects of ground motions on spatially‐distributed systems, it is important to take into account the spatial correlation of the intensity measure. However, existing loss‐estimation models, which use I_a as an input, do not take this aspect of the ground motion into account. Therefore, the potential to model the spatial correlation of Arias intensity is also investigated. The empirical predictive model is developed using recordings from the Pacific Earthquake Engineering Research Center Next Generation of Attenuation database whereas the model for spatial correlation makes use of the well‐recorded events from this database, that is the Northridge and Chi‐Chi earthquakes. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Site dependence of far-source ground motions during the Wenchuan earthquake

This paper aimed to examine the site dependence and evaluate the methods for site analysis of far-source ground motions. This was achieved through the examination of frequency content estimated by different methods based on strong ground motions recorded at twelve far-source stations in Shandong province during the Wenchuan earthquake. The stations were located in sites with soil profiles ranging from code classes Ⅰ to Ⅲ. Approaches used included the Fourier amplitude spectrum (FAS), the earthquake response spectrum (ERS), the spectral ratio between the horizontal and the vertical components (H/V), the spectral ratio between the spectra at the site and at a reference site (SRRS), and coda wave analysis (CWA). Results showed that major periods of these ground motions obtained by FAS, ERS and H/V ratio methods were all evidently larger than site dominant periods; the periods were also different from each other and mainly reflected the frequency content of long period components. Prominent periods obtained by the SRRS approach neither illuminated the long period aspect nor efficiently determined site features of the motions. The CWA resulted in a period close to site period for stations with good quality recordings. The results obtained in this study will be useful for the evaluation of far-source effect in constructing seismic design spectra and in selecting methods for ground motion site analysis.     

Characteristics of earthquake ground motions and the H/V of microtremors in the southwestern part of Taiwan

The relationships between the spectral characteristics of earthquake ground motions and those of micro‐tremors are investigated using the observed data from a dense strong‐motion network consisting of 108 stations in the Yun‐Li, Chia‐Yi and Tai‐Nan areas in southwestern Taiwan. Many high‐quality recordings, including those of the 921 Chi‐Chi earthquake (M_w=7.6), the 1022 Chia‐Yi mainshock (M_L=6.4), the 1022 major aftershock (M_L=6.0), as well as some weak motion events are selected to evaluate site responses. Microtremor measurements are also performed at most ground motion stations. With many stations in the area located on an alluvium structure, however, it is difficult to find good reference stations on rock sites, which therefore necessitates the calculation of single‐station H/V ratios. The predominant frequencies obtained from H/V ratios are consistent with those from spectral ratios. The site characteristics between the strong and weak events are different, however. This implies that a nonlinear effect probably occurred with the strong‐motion events. The main peak in the H/V spectra of the microtremors is in good agreement with the first peak obtained from the spectra of earthquake ground motions. It is reasonable to claim that the main peak reflects the deep underground structure. On the basis of the H/V ratios of the microtremors, it is concluded that the lower predominant frequencies appear in the plain area, while the higher values are near the mountainous region. Copyright © 2002 John Wiley & Sons, Ltd.     

2020年7月12日唐山古冶5.1级地震揭示的北京城区地震动场地效应分析

局部场地条件对地震动特性影响显著,深厚的软弱覆盖层引起的地震动场地效应会显著放大中长周期反应谱。采用谱比法,对2020年7月12日唐山古冶5.1级地震中获得的部分强震动记录进行统计,发现在本次地震中北京城区的地震动场地效应显著,深厚覆盖层明显放大了加速度反应谱,在T=1.2 s左右反应谱放大倍数可达4.0,说明北京地区的场地和盆地效应使得远场地震动的中长周期成分显著放大。此外,发现参考基岩场地记录是否与土层场地处遭受的基岩地震动一致,仍然是制约统计结果可靠性的关键因素。      

Ground motion characteristics of the Chi‐Chi earthquake of 21 September 1999

The purpose of this paper is to investigate the ground motion characteristics of the Chi‐Chi earthquake (21 September 1999) as well as the interpretation of structural damage due to this earthquake. Over 300 strong motion records were collected from the strong motion network of Taiwan for this earthquake. A lot of near‐field ground motion data were collected. They provide valuable information on the study of ground motion characteristics of pulse‐like near‐field ground motions as well as fault displacement. This study includes: attenuation of ground motion both in PGA and spectral amplitude, principal direction, elastic and inelastic response analysis of a SDOF system subjected to near‐field ground motion collected from this event. The distribution of spectral acceleration and spectral velocity along the Chelungpu fault is discussed. Based on the mode decomposition method the intrinsic mode function of ground acceleration of this earthquake is examined. A long‐period wave with large amplitude was observed in most of the near‐source ground acceleration. The seismic demand from the recorded near‐field ground motion is also investigated with an evaluation of seismic design criteria of Taiwan Building Code. Copyright © 2000 John Wiley & Sons, Ltd.     

Spatial correlations of ground motion for non-ergodic seismic hazard analysis

Traditional probabilistic seismic hazard analysis (PSHA) uses ground-motion models that are based on the ergodic assumption, which means that the distribution of ground motions over time at a given site is the same as their spatial distribution over different sites. Evaluations of ground-motion data sets with multiple measurements at a given site and multiple earthquakes in a given region have shown that the ergodic assumption is not appropriate as there are strong systematic region-specific source terms and site-specific path and site terms that are spatially correlated. We model these correlations using a spatial Gaussian process model. Different correlations functions are employed, both stationary and non-stationary, and the results are compared in terms of their predictive power. Spatial correlations of residuals are investigated on a Taiwanese strong-motion data set, and ground motions are collected at the ANZA, CA array. Source effects are spatially correlated, but provide a much stronger benefit in terms of prediction for the ANZA data set than for the Taiwanese data set. We find that systematic path effects are best modeled by a non-stationary covariance function that is dependent on source-to-site distance and magnitude. The correlation structure estimated from Californian data can be transferred to Taiwan if one carefully accounts for differences in magnitudes. About 50% of aleatory variance can be explained by accounting for spatial correlation.     

Prediction of site factors by a non‐parametric approach

The problem addressed in this paper is the estimation of the (de)amplification of ground motion at soil sites (compared to rock sites) as a function of the intensity of the ground motion. A non‐parametric empirical approach, called the Conditional Average Estimator (CAE) method, has been used, which is different from all existing approaches. Site factors (SFs) for sites characterized with V_s30 between 180 and 360 m/s were predicted for the peak ground acceleration (PGA) and the spectral accelerations by using a combined database of recorded ground motions. Based on the results of the study, site factors for PGA and selected spectral accelerations are proposed, separately for weaker and stronger ground motions. Comparisons are made with the SFs used in two standards (Eurocode 8 and ASCE 7‐10) and with SFs proposed in the literature, including four Next Generation Attenuation (NGA) ground‐motion prediction equations. The study reveals that (i) SFs depend strongly on the ground‐motion intensity. In the case of stronger ground motions, they decrease with increasing acceleration. (ii) The SFs predicted in this study agree reasonably well with the existing SFs in the case of weak ground motion. For higher intensities of ground motion, they are generally smaller than the existing ones. Copyright © 2014 John Wiley & Sons, Ltd.     

Empirical correlations between cumulative absolute velocity and spectral accelerations from NGA ground motion database

Considering multiple ground motion intensity measures is important in seismic hazard analysis and ground motion selection process. Using the NGA strong motion database and recently developed ground-motion prediction models, empirical correlations are developed between cumulative absolute velocity (CAV) and spectral accelerations (Sa) at periods from 0.01 to 10 s. The CAV–Sa correlations at long periods are significantly influenced by rupture distance due to modification of the frequency content and duration of the acceleration time history through travel path. Similarly, the presence of strong velocity pulses in near-source ground motions also affects the correlations at moderate to long periods. On the other hand, the correlations are not particularly sensitive to the earthquake magnitude, orientation of the ground-motion recordings, selection of ground-motion prediction models and local site conditions. Piecewise linear fitting equations are provided to quantify the correlations for various cases. The application of the CAV–Sa correlations in ground motion selection process is also discussed.     

汶川地震远场地震动场地相关性与分析方法评价

为考查远场地震动的场地相关性并评价一些场地特性分析方法的适用性,采用不同方法对汶川地震山东省12个远场台站的强震记录进行了分析.选取台站分别位于按建筑抗震设计规范(CBC)场地划分中的Ⅰ—Ⅲ类场地上.地震动记录的分析方法包括傅里叶幅值谱法,地震反应谱法,水平与竖向谱比率法,参考点谱比率法,以及尾波分析等.结果表明,按傅里叶幅值谱法,地震反应谱法,水平与竖向谱比法计算得到的卓越周期均远大于台站场地的卓越周期,不同方法得到的结果之间也有较大差别,且主要反映长周期地震动的卓越频率;参考点谱比率法的结果未反映地震动的卓越周期,也与场地的卓越周期差别较大;对完整记录尾波分析所得的结果比较接近场地的卓越周期.希望本文能为考虑远场地震作用时设计谱的建立,以及场地特性估计时地震动分析方法的选取提供参考依据.     

Influence of spatial correlation of strong ground motion on uncertainty in earthquake loss estimation

In addition to the mean values of possible loss during an earthquake, parameters of the probability distribution function for the loss to a portfolio (e.g. fractiles and standard deviation) are very important. Recent studies have shown that the proper treatment of ground‐motion variability and, particularly, the correlation of ground motion are essential for the estimation of the seismic hazard, damage and loss for distributed portfolios. In this study, we compared the effects of variations in the between‐earthquake correlation and in the site‐to‐site correlation on seismic loss and damage estimations for the extended objects (hypothetical portfolio) and critical elements (e.g. bridges) of a network. A scenario earthquake approach and a portfolio containing a set of hypothetical building and bridges were used for the purpose. We showed that the relative influences of the types of correlation on characteristics of loss distribution and the probability of damage are not equal. In some cases, when the median values of loss distribution or the probability that at least one critical element of a lifeline will be damaged are considered and when the spatial correlation of ground motion is used, the possible variations in the between‐earthquake correlation may be neglected. The shape of the site‐to‐site correlation function (i.e. the rate of decrease of the coefficient of spatial correlation with separation distance) seems also to be important when modelling spatially correlated ground‐motion fields. Copyright © 2010 John Wiley & Sons, Ltd.     

Ground motion directionality in the 2010–2011 Canterbury earthquakes

This paper examines the observed directionality of ground motions in the Christchurch urban area during the 2010–2011 Canterbury, New Zealand earthquakes. A dataset of ground motions recorded at 20 strong motion stations over 10 different earthquake events is utilized to examine the ratios of various response spectral directionality definitions and the orientation of the maximum direction. Because the majority of previous related studies have utilized overlapping ground motion datasets from the NGA database, the results of this study provide a largely independent assessment of these ground motion aspects. It is found that the directionality ratio between the maximum (100th percentile) and 50th percentile orientation‐independent spectral acceleration is similar to that obtained from recent studies. Ground motions from the 4 September 2010 Darfield earthquake are shown to exhibit strong directionality for source‐to‐site distances up to R_rup = 30 km, notably further than results from a previous study, which suggests that such effects are generally limited to R_rup < 5 km. The adopted dataset also offers the unique potential to consider site‐specific effects on directionality ratios and maximum direction orientations; however, in both cases, site‐specific effects are found not to be significant in the observed empirical results. Copyright © 2014 John Wiley & Sons, Ltd.     

基于实测记录分析场地因素对海底地震动特性影响

目前基于海底实测记录的分析发现海底与陆地地震动特性存在明显差异,但难以进一步确定海底地震动特性的影响因素。在以往研究的基础上对比同次地震中相邻海底台站间地震动特性的差异,并分析造成差异的原因。以日本K-NET地震台网中6个海底强震台站及其相邻不同场地条件陆地台站监测的8次强震记录为研究对象,通过分析强震记录的峰值加速度、水平放大系数谱、竖向与水平反应谱的比谱等,对比分析不同海底台站地震动的特性,以及海底台站与相邻不同场地条件陆地台站地震动特性的差别。研究发现：（1）海底与陆地竖向地震动存在明显差异;（2）不同海底台站间地震动特性亦存在较大差异和明显的规律性,海底场地条件、地形等场地因素对海底地震动特性的影响较大;（3）海底水平向地震动反应谱的特征周期较大,谱特性介于陆地中硬土与软土场地间。     

Correlation in spectral accelerations for earthquakes in Europe

The shape of a uniform hazard spectrum has been criticized to be unrealistic for a site where the spectral ordinates of the uniform hazard spectrum at different periods are governed by different scenario events and conservative for long‐return‐period earthquake shaking. The conditional mean spectrum considering epsilon (CMS‐ε) takes into account the correlation of spectral demands (represented by values of ε) at different periods, to address these issues. This paper proposes new prediction models for the correlation coefficient of ε(T₁) and ε(T₂), a key component for developing a CMS, using Pan‐European earthquake records from a European ground motion database. Epsilon (ε) for each record is computed using the 2005 Ambraseys ground‐motion prediction equation. The model can be used to develop CMS for European sites, and it can be incorporated in the European seismic standards. Copyright © 2012 John Wiley & Sons, Ltd.     

1-D and 2-D analyses of weak motion data in Fraser Delta from 1966 Duvall earthquake

The 1996 Duvall earthquake in Washington State triggered ground motion stations in the Fraser Delta, British Columbia, located on varying depths of Holocene and Pleistocene soils to a maximum depth of 800 m and one station on bedrock. Recorded ground motions were used to examine the applicability of 1-D and 2-D site response analyses for amplification studies in the Delta. 1-D response analysis gave a good indication of the period of peak response. Response spectra computed by 1-D analysis did not compare well with recorded spectra except at very deep sites. The use of 2-D analyses to include buried topography generally improved the predictions of site response spectra at the shallow sites. However, for the shallow earth sites, the recorded motions showed a strong spectral response at short periods in the range of 0.1–0.25 s. Neither 1-D nor 2-D analysis predicted this response.