A brief theory and computing of seismic ground rotations for structural analyses

The seismic ground rotations are important with respect to spatial structural models, which are sensitive to the wave propagation. The rotational ground motion can lead to significant increasing of structural response, instability and unusual damages of buildings. Currently, the seismic analyses often take into account the rocking and torsion motions separately using artificial accelerograms. We present an exact analytical method, proposed by Nazarov [15] for computing of three rotational accelerograms simultaneously from given translational records. The method is based on spectral representation in the form of Fourier amplitude spectra of seismic waves, corresponding to the given three-component translational accelerogram. The composition, directions and properties of seismic waves are previously determined in the form of a generalized wave model of ground motion. It is supposed that seismic ground motion can be composed by superposition of P, SV, SH- and surface waves. As an example, the dynamic response analysis of 25-story building is presented. Here recorded (low-frequency) and artificial (high-frequency) accelerograms were used; each of them includes three translational and three rotational components. In this structural analysis, we have clarified primarily conditions under which rotational ground motion should be taken into account. Next, we have calculated three rotational components of seismic ground motion. Then they were taken as additional seismic loads components for further seismic analysis of the building. Note, soil–structure interaction (SSI) is not considered in this study. For computing, we use the special software for structural analyses and accelerogram processing (FEA Software STARK ES and Odyssey software, Eurosoft Co., Russia). It was developed and is used in engineering practice in the Central Research Institute of Building Constructions (TsNIISK, Moscow, Russia).     

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.     

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.     

Wavelet-based generation of spectrum-compatible time-histories

This paper deals with the well-known problem of generating spectrum-compatible synthetic accelerograms for the linear and non-linear time-history analyses of structural systems. A wavelet-based procedure has been used to decompose a recorded accelerogram into a desired number of time-histories with non-overlapping frequency contents, and then each of the time-histories has been suitably scaled for matching of the response spectrum of the revised accelerogram with a specified design spectrum. The key idea behind this iterative procedure is to modify a recorded accelerogram such that the temporal variations in its frequency content are retained in the synthesized accelerogram. The proposed procedure has been illustrated by modifying five recorded accelerograms of widely different characteristics such that those are compatible with the same USNRC design spectrum.     

The use of optimization to construct critical accelerograms for given structures and sites

In this paper a methodology has been presented for constructing the most critical accelerogram from among a be class of candidate accelerograms for a given site and structure. This most critical accelerogram could be used to assess seismic resistance of a structure with a high level of confidence. Specifically, the method superimposes accelerograms recorded at similar sites to create the candidate accelerograms, then uses optimization and approximation techniques find the most critical accelerogram. The most critical accelerogram is defined as the one which maximizes damage is structure, as computed by non-linear dynamic structural analysis, as well as satisfies constraints on ground parameters to ensure credibility. The damage has been defined as cumulative inelastic energy dissipation or sure of interstorey drifts. The method is applied to ten examples in the paper.     

Simulation of artificial earthquakes

A procedure is developed for the simulation of artificial earthquake accelerograms, The time variation of amplitude and frequency content is preserved in the simulation procedure. Sixteen artificial earthquake accelerograms are simulated and compared with a target accelerogram. The time variation of amplitude and frequency content for 26 historical earthquake accelerograms is characterized.     

强震加速度记录的数据处理方法

本文用数值积分法,对RDZ1-12-66型自动触发电流计记录式强震仪的幅频响应失真进行校正。并采用高通数字滤波的方法,修正加速度图的零线.为此编制了计算机程序,绘制了修正后的加速度、速度和位移时程曲线.计算了修正前后加速度图的傅氏谱。同时,对这些结果加以讨论。 修正后的加速度图,精确地表示了仪器基本频带在0.09HZ和25HZ之间的绝对地面加速度。      

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.     

BUILDING DUCTILITY DEMAND: INTERPLATE VERSUS INTRAPLATE EARTHQUAKES

The inelastic seismic response behaviour for a range of simplified single-degree-of-freedom models has been analysed using 180 random phase angle synthetic accelerograms with different frequency contents and different durations and 105 real accelerograms collected from different regions worldwide. Results from the analyses have identified that the frequency content of the excitation can greatly influence the ductility demand ratio due to inelastic amplification effects. Consequently, results derived from intraplate earthquake records (typically of higher frequency content) were generally different to those from interplate records. However, the commonly used El Centro accelerogram has significantly lower ductility demand in the low period range than the average of records with similar elastic response spectral shape. Apart from this, there was little evidence to suggest any inherent differences in the inelastic response behaviour of buildings from intraplate and interplate earthquakes which possessed similar frequency content. Thus, the average ductility demand ratios from future earthquakes in an area can be predicted by interpolation of the results presented in this paper assuming the elastic response spectrum has been defined. Ductility demand ratios derived from the synthetic accelerograms and the real accelerograms with similar frequency content have been shown to be consistent. However, results from synthetic records derived for the idealised code design spectra (such as the Uniform Building Code and the Australian Standard AS1170.4) indicate a significantly higher ductility demand in the long period range.     

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。      

Time–frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition

In this paper, the adaptive chirplet decomposition combined with the Wigner-Ville transform and the empirical mode decomposition combined with the Hilbert transform are employed to process various non-stationary signals (strong ground motions and structural responses). The efficacy of these two adaptive techniques for capturing the temporal evolution of the frequency content of specific seismic signals is assessed. In this respect, two near-field and two far-field seismic accelerograms are analyzed. Further, a similar analysis is performed for records pertaining to the response of a 20-story steel frame benchmark building excited by one of the four accelerograms scaled by appropriate factors to simulate undamaged and severely damaged conditions for the structure. It is shown that the derived joint time–frequency representations of the response time histories capture quite effectively the influence of non-linearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event; in this context, tracing the mean instantaneous frequency of records of critical structural responses is adopted.The study suggests, overall, that the aforementioned techniques are quite viable tools for detecting and monitoring damage to constructed facilities exposed to seismic excitations.     

A prediction model for frequency spectrum of blast‐induced seismic wave in viscoelastic medium

A prediction model for frequency spectrum of blast‐induced seismic waves is established. The effect of explosive sources is considered in this model. Our model implies that the frequency spectrum of blast‐induced seismic wave is mainly influenced by the initial pressure and the adiabatic exponent of explosives. The dominant frequency increases with the decreasing of initial pressure or the increasing of adiabatic exponent. In addition, this prediction model is verified by the experiment. The error of the dominant frequency is 4%–6%. It is indicated that the proposed model in this paper can reasonably predict the frequency spectrum of blast‐induced seismic waves, and then, we can provide a better frequency spectrum by optimizing the explosion source.     

Generation of accelerograms compatible with design specifications using information theory

This paper deals with the generation of seismic accelerograms which are compatible with a given response spectrum and other design specifications. The time sampling of the stochastic accelerogram yields a time series represented by a random vector in high dimension. The probability density function of this random vector is constructed using the maximum entropy (MaxEnt) principle under constraints defined by the available information (design specifications). In this paper, an adapted algorithm is proposed to identify the Lagrange multipliers introduced in the MaxEnt principle to take into account the constraints. This algorithm is based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Itô stochastic differential equation in order to estimate the integrals in high dimension of the problem. The constraints related to a seismic accelerogram are developed explicitly. This methodology is validated through an application for which the available information is related to the variance of each component of the random vector representing the accelerogram, statistics on the response spectrum, on the peak ground acceleration, on the cumulative absolute velocity and on the end-values for the velocity and for the displacement.     

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。     

The study of the radiation characteristics and propagation of seismic waves in the North Caucasus by modeling the accelerograms of the recorded earthquakes

For evaluating the parameters of the vibrations of the Earth’s surface in the case of strong earthquakes, which are possible in the future, the regular patterns of the emission and propagation of seismic waves in the North Caucasus regions are investigated. The regional parameters of emission and propagation of seismic waves are evaluated by solution of the inverse problems of stochastic modeling of the accelerograms of the earthquakes, recorded by the seismic station in Sochi. The horizontal components of the strongest earthquakes (M _w ～ 3.9?5.6), that occurred in 2002–2006 within a radius of ～300 km from the seismic station, with source depths up to 60 km are modeled. For calculations of accelerograms, estimates of the quality are used, obtained earlier for this region in the form: Q(f) ～ 80 ～ f ^0.9. The parameter settings are carried out, which determine the shapes of the source spectra, the amplification of the seismic waves in the Earth’s crust, the weakening of the waves at high frequencies (κ), the parameters that determine the shape and duration of accelerograms, etc. Sufficiently good agreement of the calculated and recorded accelerograms is obtained, the regional characteristics of emission and propagation of seismic waves, which can be used for prediction of the parameters of strong motions in the North Caucasus, are evaluated; however, in the future these characteristics should be studied in more detail.     

Windowless Q-factor tomography by the instantaneous frequency

The estimation of the Q factor of rocks by seismic surveys is a powerful tool for reservoir characterization, as it helps detecting possible fractures and saturating fluids. Seismic tomography allows building 3D macro-models for the Q factor, using methods as the spectral ratio and the frequency shift. Both these algorithms require windowing the seismic signal accurately in the time domain; however, this process can hardly follow the continuous variations of the wavelet length as a function of offset and propagation effects, and it is biased by the interpreter choice. In this paper, we highlight some drawback of signal windowing in the frequency-shift method, and introduce a tomographic approach to estimate the Q factor using the complex attributes of the seismic trace. We show that such approach is particularly needed when the dispersion is broadening the waveforms of signals with a long wave-path. Our method still requires an interpretative event picking, but no other parameters as the time window length and its possible smoothing options. We validate the new method with synthetic and real data examples, involving the joint tomographic inversion of direct and reflected signals. We show that a calibration of the frequency-shift method is needed to improve the estimation of the absolute Q factor, otherwise only relative contrasts are obtained.     

Dispersion calculation method based on S-transform and coordinate rotation for Love channel waves with two components

Dispersion analysis is an important part of in-seam seismic data processing, and the calculation accuracy of the dispersion curve directly influences pickup errors of channel wave travel time. To extract an accurate channel wave dispersion curve from in-seam seismic two-component signals, we proposed a time–frequency analysis method based on single-trace signal processing; in addition, we formulated a dispersion calculation equation, based on S-transform, with a freely adjusted filter window width. To unify the azimuth of seismic wave propagation received by a two-component geophone, the original in-seam seismic data undergoes coordinate rotation. The rotation angle can be calculated based on P-wave characteristics, with high energy in the wave propagation direction and weak energy in the vertical direction. With this angle acquisition, a two-component signal can be converted to horizontal and vertical directions. Because Love channel waves have a particle vibration track perpendicular to the wave propagation direction, the signal in the horizontal and vertical directions is mainly Love channel waves. More accurate dispersion characters of Love channel waves can be extracted after the coordinate rotation of two-component signals.     

Selecting time windows of seismic phases and noise for engineering seismology applications: a versatile methodology and algorithm

Seismic signal windowing is the preliminary step for many analysis procedures in engineering seismology (standard spectral ratio, quality factor, general inversion techniques, etc.). Moreover a noise window is often necessary for the data quality control through the signal-to-noise verification. Selecting the noise window can be challenging when large heterogeneous datasets are considered, especially when they include short pre-event noise signals. This study proposes a fully automatic and configurable (i.e., with default parameters that can also be user-defined) algorithm to windowing the noise and the P, S, coda and full signal once the P-wave (T _P ) and S-wave (T _S ) first arrivals are known. An application example is given on a KiK-net dataset. A Matlab language implementation of this algorithm is proposed as an online resource.     

基于褶积原理和改进广义S变换的震动波衰减补偿试验研究

为了恢复震动波能量在传播过程中产生的衰减损耗,提出基于褶积原理求取品质因子Q的方法与改进广义S变换相结合的反Q滤波法。通过震动波衰减补偿模型试验,对试验数据进行改进广义S变换的时频特性分析,得出了信号的能量分布情况以及时间频率对应关系;采用基于褶积原理求取品质因子的方法,得到时变Q值;对试验数据进行反Q滤波处理,使震动波能量得到了补偿。结果表明本文提出的反Q滤波法提高了对震动波能量衰减补偿的效果,拓宽了地震资料的频带,提高了地震资料分辨率,有利于进行高分辨率地震勘探、深部信号增强和油气藏预测工作的开展。     

Real-time 3-D space numerical shake prediction for earthquake early warning

In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake prediction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.