Study of the correlations between main shocks and aftershocks and aftershock synthesis method

To consider the influence of aftershocks in engineering design, the correlations between main shocks and aftershocks should be examined, and an aftershock simulation method with main shock ground motions needs to be developed. In this study, the data on the sequences of main shock-aftershock ground motions and other related parameters were collected. Using these data, correlations between the magnitude, frequency, duration and energy of the main shock-aftershock ground motions were investigated. The results showed that the magnitude of the aftershock can be larger than that of the main shock. The shapes of the Fourier amplitude spectra of main shocks and aftershocks were similar; however, the predominant frequency and high-frequency components of the aftershock tended to be larger. Considering the magnitude difference between the main shock and the aftershock, the correlation of durations was explored. Additionally, a new concept, the duration ratio, was defined to describe the concentration of seismic energy release, and main shock energy was strongly positively correlated with the energy attenuated during the main shock-aftershock sequence. Finally, based on these results regarding correlation, an aftershock synthesis using recorded main shock ground motions was constructed with the trigonometric series method for seismic design, and some examples are given to analyze the rationality of this synthetic method.

     

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.     

Damage spectra for the mainshock–aftershock sequence-type ground motions

Strong aftershocks have the potential to increase the damage state of the structures due to the damage accumulation. This paper investigates the damage spectra for the mainshock–aftershock sequence-type ground motions with Park–Ang damage index. A method of simulating the mainshock–aftershock sequence-type ground motions is proposed based on the modified form of Bath's law and NGA ground motion prediction equation. The damage spectra are computed using the recorded and simulated sequence-type ground motions, and the effects of period of vibration, strength reduction factor, site condition, seismic sequence, damping ratio and post-yield stiffness on damage spectra are studied statistically. The results indicate that the effect of aftershock on structural damage is significant and recorded sequence-type ground motions may underestimate the damage of long-period structures due to the incompleteness of dataset. A simplified equation is proposed to facilitate the application of damage spectra in the seismic practice for mainshock–aftershock sequence-type ground motions.     

Scaling of response spectrum and duration for aftershocks

Aftershocks have the potential to cause collapse of a structure that has been already damaged by the preceding main shock. Seismic safety of a structure should therefore be ascertained through a damage analysis using the anticipated main shock and few larger-aftershock motions. Simulation of aftershock motions needs characterization of the seismic hazard due to aftershocks, and therefore it will be useful to develop a conditional scaling model that can predict the response spectrum of an anticipated aftershock motion consistent with the design spectrum of the main shock motion anticipated at the same station. In this study an attempt is made to develop a conditional scaling model for the pseudo spectral velocity spectrum via linear regression analysis on the aftershock and main shock recordings for the 1999 Chi–Chi earthquake. It is shown that it may be possible to obtain a simpler and approximate version of the conditional model from an unconditional model. Damage-causing potential of a ground motion also depends on its strong motion duration (SMD) and therefore a conditional scaling model is developed for SMD of the aftershock motion in several narrow frequency-bands. The model is developed for the larger-aftershock motions and it is shown that a reasonable replacement of such a model may be obtainable directly from an unconditional model. Finally, a simple weighted averaging scheme is proposed to obtain the composite SMD from the SMDs for different frequency bands by using the pseudo spectral acceleration spectrum of the motion.     

A probabilistic framework for quantification of aftershock ground‐motion hazard in California: Methodology and parametric study

This paper presents a proposed method of aftershock probabilistic seismic hazard analysis (APSHA) similar to conventional ‘mainshock’ PSHA in that it estimates the likelihoods of ground motion intensity (in terms of peak ground accelerations, spectral accelerations or other ground motion intensity measures) due to aftershocks following a mainshock occurrence. This proposed methodology differs from the conventional mainshock PSHA in that mainshock occurrence rates remain constant for a conventional (homogeneous Poisson) earthquake occurrence model, whereas aftershock occurrence rates decrease with increased elapsed time from the initial occurrence of the mainshock. In addition, the aftershock ground motion hazard at a site depends on the magnitude and location of the causative mainshock, and the location of aftershocks is limited to an aftershock zone, which is also dependent on the location and magnitude of the initial mainshock. APSHA is useful for post‐earthquake safety evaluation where there is a need to quantify the rates of occurrence of ground motions caused by aftershocks following the initial rupture. This knowledge will permit, for example, more informed decisions to be made for building tagging and entry of damaged buildings for rescue, repair or normal occupancy. Copyright © 2008 John Wiley & Sons, Ltd.     

Spatiotemporal seismic hazard and risk assessment of M9.0 megathrust earthquake sequences of wood‐frame houses in Victoria,British Columbia,Canada

Megathrust earthquake sequences, comprising mainshocks and triggered aftershocks along the subduction interface and in the overriding crust, can impact multiple buildings and infrastructure in a city. The time between the mainshocks and aftershocks usually is too short to retrofit the structures; therefore, moderate‐size aftershocks can cause additional damage. To have a better understanding of the impact of aftershocks on city‐wide seismic risk assessment, a new simulation framework of spatiotemporal seismic hazard and risk assessment of future M9.0 sequences in the Cascadia subduction zone is developed. The simulation framework consists of an epidemic‐type aftershock sequence (ETAS) model, ground‐motion model, and state‐dependent seismic fragility model. The spatiotemporal ETAS model is modified to characterise aftershocks of large and anisotropic M9.0 mainshock ruptures. To account for damage accumulation of wood‐frame houses due to aftershocks in Victoria, British Columbia, Canada, state‐dependent fragility curves are implemented. The new simulation framework can be used for quasi‐real‐time aftershock hazard and risk assessments and city‐wide post‐event risk management.     

基于工程特性的主余震型地震动降维模拟

余震是由主震孕育而来,两者之间存在着一定的关联性,如何构造主余震型地震动模型,是工程结构抗震分析的基础。着眼于地震动的工程特性,根据主余震之间的峰值加速度、强震持时、场地卓越频率等要素,分别建立主震和余震自身的演变功率谱模型,基于非平稳随机过程的谱表示,通过引入随机函数降维模拟方法,实现仅用三个基本随机变量即可精确模拟主余震型地震动过程。研究表明,采用该降维模拟方法的效率和精度均满足工程需求,且与实测主余震型地震动记录的反应谱和幅值谱拟合一致,验证该模型与方法的优越性,为工程结构在主余震型随机地震作用下的抗震分析提供有效途径。     

Bayesian estimation of the Modified Omori Law parameters for the Iranian Plateau

The forecasting of large aftershocks is a preliminary and critical step in seismic hazard analysis and seismic risk management. From a statistical point of view, it relies entirely on the estimation of the properties of aftershock sequences using a set of laws with well-defined parameters. Since the frequentist and Bayesian approaches are common tools to assess these parameter values, we compare the two approaches for the Modified Omori Law and a selection of mainshock–aftershock sequences in the Iranian Plateau. There is a general agreement between the two methods, but the Bayesian appears to be more efficient as the number of recorded aftershocks decreases. Taking into account temporal variations of the b-value, the slope of the frequency-size distribution, the probability for the occurrence of strong aftershock, or larger main shock has been calculated in a finite time window using the parameters of the Modified Omori Law observed in the Iranian Plateau.     

Strong motion observations and recordings from the great Wenchuan Earthquake

The National Strong Motion Observation Network System （NSMONS） of China is briefly introduced in this paper. The NSMONS consists of permanent free-field stations, special observation arrays, mobile observatories and a network management system. During the Wenchuan Earthquake, over 1,400 components of acceleration records were obtained from 460 permanent free-field stations and three arrays for topographical effect and structural response observation in the network system from the main shock, and over 20,000 components of acceleration records from strong aftershocks occurred before August 1, 2008 were also obtained by permanent free-field stations of the NSMONS and 59 mobile instruments quickly deployed after the main shock. The strong motion recordings from the main shock and strong aftershocks are summarized in this paper. In the ground motion recordings, there are over 560 components with peak ground acceleration （PGA） over 10 Gal, the largest being 957.7 Gal. The largest PGA recorded during the aftershock exceeds 300 Gal.     

汶川地震强余震统计特性及地震动衰减关系

2008年"5·12"汶川特大地震发生后,固定及流动台站获得了数量可观的余震地震动数据,为地震危险性分析和地震动衰减规律研究提供了丰富的数据。通过Gutenberg-Richter关系分析得到汶川地震余震震级-频度分布（FMD）,结合Båth定律预估得到逼近实际的最大预估余震震级,基于修正的Omori定律拟合得到余震发生率与主震后时间的关系。主余震统计特性显示M_s4.0~6.4范围内的余震记录震中距及震级分布相对均匀,可作为建立地震动衰减规律的依据。故针对土层地表及基岩地表分别进行了EW、NS和UD三个方向的统计回归分析,给出了2种地表情况下三向地震动峰值加速度的定量衰减关系表达式。     

九寨沟MS7.0地震强地震动模拟及漳扎镇地震动强度预测

破坏性地震强度预测可用于工程领域抗震设防以及地震危险性分析评估,是防震减灾中一项很重要的基础工作.为了再现九寨沟地震的地震动强度,评估缺失强震记录的九寨章扎台站的地震动强度,本文用经验格林函数法对九寨沟地震进行了数值模拟.选取了震源周边地震动峰值加速度超过10 Gal的10个强震台站进行模拟.因未得到九寨沟地震的余震,初次尝试将汶川地震和定西地震的余震作为格林函数模拟九寨沟地震.模拟结果整体上可以反映各台站地震动的强度特征,尤其是地震动高频成份拟合较好.模拟值的地震动峰值加速度、时程数据、反应谱等与观测值拟合较好.预测结果显示漳扎镇的地震动峰值加速度值约为180~200 Gal.预测结果也表明在缺少大震的余震记录时,经验格林函数法使用其他大震的余震同样可以再现目标地震的强度特征.本研究也为经验格林函数方法在缺乏小震记录地区的使用积累了经验.最后总结了格林函数的选取标准,为经验格林函数方法来预测未来强震动特征积累了经验.     

基于经验模型和物理模型研究2013 M_S7.0芦山地震余震序列

基于中国地震台网中心2013 MS7.0芦山地震余震数据我们首先确定了余震空间分布范围并根据G-R关系计算了主震后半小时内的完备震级Mc=3.5,并且得到了ML≥3.5和ML≥3.0的地震在2001年至芦山地震前的背景场地震发生率.通过Omori-Ustu经验定律和两种Dieterich模型对芦山地震余震发生率的拟合,我们发现阶梯型Dieterich模型只能模拟p=1的情况,从而造成了模拟曲线与观测数据的差别;前人研究表明震后滑移同样是产生余震的原因,如果假设余震序列由主震静态剪应力Δτ和震后滑移共同作用所产生,我们数值模拟得到的对数型Dieterich模型能够较好地推断余震发生率R随时间t增加而衰减的趋势,能够从物理机制上解释MS7.0芦山地震余震序列衰减指数大于1这一现象.通过对数型Dieterich模型的拟合并结合Andrews的方法,我们还得到MS7.0芦山地震Aσ约为0.155 MPa,ta约为8.4年,这一值与前人研究结果十分接近.     

Comparison of the spatial distribution of ground motion between main shocks and strong aftershocks

Using the ground motion attenuation relation, we calculated and compared the effective peak acceleration (EPA) generated by main shocks and their strong aftershocks of 21 earthquake sequences with MS≥7 occurred in Chinese mainland and offing of China during 1966~2002. The result shows that EPA of strong aftershocks usually exceed that of main shock for 76.2% earthquake sequences and EPA of more than 50% strong aftershocks are greatly lar-ger than that of main shocks in large area, which suggests that it is necessary to take damage produced by strong aftershock into account in the probabilistic seismic hazard analysis and the seismic design.     

Shaking table test on the seismic failure characteristics of a subway station structure on liquefiable ground

In order to investigate the seismic failure characteristics of a structure on the liquefiable ground, a series of shaking table tests were conducted based on a plaster model of a three‐story and three‐span subway station. The dynamic responses of the structure and ground soil under main shock and aftershock ground motions were studied. The sand boils and waterspouts phenomena, ground surface cracks, and earthquake‐induced ground surface settlements were observed in the testing. For the structure, the upward movement, local damage and member cracking were obtained. Under the main shock, there appeared longer liquefaction duration for the ground soil while the pore pressure dissipated slowly. The acceleration amplification effect of the liquefied soil was weakened, and the soil showed a remarkable shock absorption and concentration effect with low frequency component of ground motion. However, under the aftershock, the dissipation of pore pressure in the ground soil became obvious. The peak acceleration of the structure reduced with the buried depth. Dynamic soil pressure on the side wall was smaller in the middle and larger at both ends. The interior column of the model structure was the weakest member. The peak strain and damage degree for both sides of the interior column exhibited an ‘S’ type distribution along the height. Moreover, the seismic response of both ground soil and subway station structure exhibited a remarkable spatial effect. The seismic damage development process and failure mechanism of the structure illustrated in this study can provide references for the engineers and researcher. Copyright © 2013 John Wiley & Sons, Ltd.     

最小能量准则用于1995年河北沙城ML 4.1地震序列破裂性质的探讨

运用变分原理,我们得到了最小地震波辐射能量约束准则并用于研究震源的物理过程.通过研究1995年ML4.1河北沙城地震序列主震和余震的动力学过程,可知主震和余震震源的动态破裂过程明显不同;ML4.1主震的破裂速度与瑞利波速相近,约为剪切波速度的0.89倍;而28个余震的破裂速度远远小于剪切波速度,大约是剪切波速度的0.05到0.55倍.根据裂纹扩展模型,计算得到其余震的地震波辐射效率多在10%以下,这也说明了余震的地震效率较低.我们认为余震震源的动态破裂过程应与断层内部新生裂纹的扩展有关,而非简单的岩体间的相对滑动.余震震源的动态破裂传播与破裂能占主导地位的小地震有关.这些小震所带来的破裂能也导致了断层的进一步扩展.在对该地震序列的研究中,我们发现主震与余震的震源破裂过程在能量分配上有着本质的区别.因此当地震断层尺度相当小时,破裂能的贡献不能忽略,它的大小将显著地影响地震波辐射能的大小.     

最小能量准则用于1995年河北沙城ML 4.1地震序列破裂性质的探讨

运用变分原理,我们得到了最小地震波辐射能量约束准则并用于研究震源的物理过程.通过研究1995年M_L4.1河北沙城地震序列主震和余震的动力学过程,可知主震和余震震源的动态破裂过程明显不同;M_L4.1主震的破裂速度与瑞利波速相近,约为剪切波速度的0.89倍;而28个余震的破裂速度远远小于剪切波速度,大约是剪切波速度的0.05到0.55倍.根据裂纹扩展模型,计算得到其余震的地震波辐射效率多在10％以下,这也说明了余震的地震效率较低.我们认为余震震源的动态破裂过程应与断层内部新生裂纹的扩展有关,而非简单的岩体间的相对滑动.余震震源的动态破裂传播与破裂能占主导地位的小地震有关.这些小震所带来的破裂能也导致了断层的进一步扩展.在对该地震序列的研究中,我们发现主震与余震的震源破裂过程在能量分配上有着本质的区别.因此当地震断层尺度相当小时,破裂能的贡献不能忽略,它的大小将显著地影响地震波辐射能的大小.     

Ms8.0汶川地震断层的应力状态以及对余震危险性的影响

利用中国地震局在汶川地震前后对四川盆地以及龙门山断裂进行的水压致裂绝对应力测量数据、近断层强震记录、以及由美国USGS公布的包括地震矩和地震波能量等在内的远场震源参数解,从简单断层模型出发,应用地震能量分配原理和库仑摩擦准则,初步估算和判断了2008年Ms8.0汶川地震断层破裂过程和震源参数,以及滑移弱化模型下应力变化...     

人工岛余震再液化数值模拟研究

主震结束后,余震引起的再液化会对土工结构物带来进一步的严重灾害。以人工岛为研究对象,基于FE-FD耦合有限元方法,考虑有无余震、不同余震大小和主余震不同时间间隔因素,探讨对人工岛再液化灾害的影响规律。研究结果表明:主震结束后,随着超孔隙水压力的消散,人工岛砂土层液化区域逐渐减小,余震发生时液化区域又开始扩展,甚至可能大于主震结束时的液化区域面积,且其灾害程度比无余震发生时的要大得多;随着主、余震的时间间隔增加,间隔期的土层固结排水很大程度地提高人工岛的抗再液化能力,当超孔隙水压力消散完后,在相同余震等级情况下很难再次达到完全液化;随着余震峰值加速度的增加,人工岛的沉降量和水平侧移量都随之增加,再次液化时间点会向前提前数秒,主震结束后,随着土层的固结排水,人工岛的沉降会继续增加,甚至超过主震引起的沉降量,而水平侧移的产生主要发生在地震液化过程中,在后续的固结排水中几乎不变;余震发生前,如果人工岛的砂土土层仍处于液化状态,则液化层可能会起到隔震作用,减轻余震对岛体造成的灾害。     

Simulation of synthetic ground motions for specified earthquake and site characteristics

A method for generating a suite of synthetic ground motion time‐histories for specified earthquake and site characteristics defining a design scenario is presented. The method employs a parameterized stochastic model that is based on a modulated, filtered white‐noise process. The model parameters characterize the evolving intensity, predominant frequency, and bandwidth of the acceleration time‐history, and can be identified by matching the statistics of the model to the statistics of a target‐recorded accelerogram. Sample ‘observations’ of the parameters are obtained by fitting the model to a subset of the NGA database for far‐field strong ground motion records on firm ground. Using this sample, predictive equations are developed for the model parameters in terms of the faulting mechanism, earthquake magnitude, source‐to‐site distance, and the site shear‐wave velocity. For any specified set of these earthquake and site characteristics, sets of the model parameters are generated, which are in turn used in the stochastic model to generate the ensemble of synthetic ground motions. The resulting synthetic acceleration as well as corresponding velocity and displacement time‐histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. Furthermore, the statistics of their resulting elastic response spectra closely agree with both the median and the variability of response spectra of recorded ground motions, as reflected in the existing prediction equations based on the NGA database. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions. Copyright © 2010 John Wiley & Sons, Ltd.     

兰德斯地震断层面及其附近余震产生的位移场研究

根据兰德斯(Landers)地震断层面及其附近余震目录计算这些余震产生的位移场, 并与根据兰德斯地震破裂面滑动分布计算的主震产生的位移场进行对比. 结果表明, 断层面及其附近余震产生位移场的方向与主震大体一致, 余震破裂总体来看是继承性的. 余震产生的位移场达厘米量级, 足可以被GPS观测所捕获. 在利用地震震后随时间变化位移场研究地球粘性结构、 地震震后滑动分布等地球物理问题时, 扣除余震产生的位移场可以最大限度地减小反演结果的不确定性, 得到符合实际的结果.