Stochastic procedure for the simulation of synthetic main shock‐aftershock ground motion sequences

According to the current seismic codes, structures are designed to resist the first damaging earthquake during their service life. However, after a strong main shock, a structure may still face damaging aftershocks. The main shock‐aftershock sequence may result in major damage and eventually the collapse of a structure. Current studies on seismic hazard mainly focus on the modeling and simulation of main shocks. This paper proposes a 3‐step procedure to generate main shock‐aftershock sequences of pairs of horizontal components of a ground motion at a site of interest. The first step generates ground motions for the main shock using either a source‐based or site‐based model. The second step generates sequences of aftershocks' magnitudes, locations, and times of occurrence using either a fault‐based or seismicity‐based model. The third step simulates pairs of ground motion components using a new empirical model proposed in this paper. We develop prediction equations for the controlling parameters of a ground motion model, where the predictors are the site condition and the aftershock characteristics from the second step. The coefficients in the prediction equations and the correlation between the model parameters (of the 2 horizontal components of 1 record and of several records in 1 sequence) are estimated using a database of aftershock accelerograms. A backward stepwise deletion method is used to simplify the initial candidate prediction equations and avoid overfitting the data. The procedure, based on easily identifiable engineering parameters, is a useful tool to incorporate effects of aftershocks into seismic analysis and design.     

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.     

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.     

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.     

MS8.1昆仑山口西地震和MS8.0汶川地震余震序列的时空分布特征和持续时间的对比

2001年M_S8.1昆仑山口西地震和2008年M_S8.0汶川地震发生在同一构造单元,但其余震序列无论在个数、空间分布,还是持续时间上都表现了显著的差别.余震通常由主震区域内背景场地震活动性受到的扰动所引起,这样的扰动则来自于主震造成的应力场状态的变化.本文从滑移速率和状态相依赖的摩擦定律(Rate- and State-Dependent Friction Law)出发,结合区域主震前后的地震活动性资料,定量地估算了这两个大地震后余震序列可能的持续时间,并对不同模型所得的结果进行了比较和对比.结果表明,汶川地震余震持续时间约为昆仑山口西地震余震持续时间的20倍,这是由于昆仑山口西地震和汶川地震余震序列的个数和持续时间不仅与地震成核过程的状态变化有关,还与作用在断层面上的正应力 σ_N 和剪应力加载速率 τ· 的大小有关.主震前后剪应力速率 τ· 的差别导致了在相同大小应力扰动ΔCFS之后的余震的活动性变化率的明显不同,导致了所触发的余震的个数和余震序列的持续时间的巨大差别.通过对昆仑山口西地震和汶川地震余震序列的时空分布特征和持续时间的定量化认识,可以为地震灾害定量评估提供合理和有益的物理参数.     

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.     

Rapid estimation of the hazard posed by strong aftershocks for Kamchatka and the Kuril Islands

This paper deals with the rapid estimation of the hazard posed by strong aftershocks for Kamchatka and the Kuril Islands based on the 12-hour aftershocks, namely, their rate, time of expectation, and maximum magnitude. The data set consists of main shocks and aftershocks as reported in the Catalog of the Kamchatka Branch of the Geophysical Survey, Russian Academy of Sciences (GS RAS) for 1968–2016. We used both the Gutenberg–Richter relation and the Omori–Utsu law to find that the aftershock rates in two time intervals are connected by a relationship of proportionality, with the constant of proportionality being independent of the lowest magnitude of these earthquakes. With this property in mind, we calculated the constants of proportionality for estimating the rate of aftershocks with a magnitude above threshold values based on the data for the first 12 hours after the main shock. We have derived easily remembered rules for estimating the aftershock rates that can be expected for 5 days and for 1 month with magnitudes above a fixed value based on the 12-hour aftershock observations. We also derived empirical regression relations to estimate the magnitude of the largest aftershock that can be expected to occur during 1 year after the main shock and the time of the last aftershock to occur whose magnitude is 5.2 or greater.     

Accurate Location of the Yao＇an Earthquake Sequence and the Yongsheng Earthquake Sequence

The Yao＇an Ms6.5 earthquake occurred on Jan. 15, 2000 and the Yongsheng Ms6.0 earthquake occurred on Oct. 27, 2001 in Yunnan Province, China. They are both located in the middle of the Dian block. Their epicenters are close to each other, the tectonic and strain characters of the earthquakes were similar, and there were many aftershocks after the two main shocks. In order to further study the spatial-temporal distributions and fault rupture characters of the main shocks and aftershocks, the latter are located using the Geiger earthquake location algorithm （Geiger） and the double difference earthquake location algorithm （DD） based on the seismic phase data of the two earthquake sequences. They were recorded by two Near Source Digital Seismic Networks （YNSSN and YSNSSN） deployed by the Yunnan Seismological Bureau （YNSB）. Then, two main shock parameters were relocated using DD based on the data of larger magnitude aftershocks and the two main shocks that were recorded by the Kunming Regional Digital Seismic Network （KMSN）. Combining the spatial- temporal distributions of the two earthquake sequences, the tectonic and strain characters of earthquakes, the rupture processes of the two aftershock sequences along faults are analyzed and discussed contrastively.     

Accurate Location of the Yao''''an Earthquake Sequence and the Yongsheng Earthquake Sequence

INTRODUCTIONEarthquake sequence is a series of centralized earthquake events in space-time after a largerearthquake.Since these earthquake events occur in a small space and are sequential in one specialtime,their seismogenic structure,mediumcharacteristics and earthquake mechanisms must be similar.By studying one earthquake sequence,the seismic activitytrend after a large earthquake can beconjectured.Some characteristics of the earthquake source development process and physic states canal…     

On the possible effect of round-the-world surface seismic waves in the dynamics of repeated shocks after strong earthquakes

Based on the observation data for hundreds of the main shocks and thousands of aftershocks, the existence of effect of round-the-world surface seismic waves is demonstrated (let us conditionally refer to them as a round-the-world seismic echo) and the manifestations of this effect in the dynamics of the repeated shocks of strong earthquakes are analyzed. At the same time, we by no means believe this effect has been fully proven. We only present a version of our own understanding of the physical causes of the observed phenomenon and analyze the regularities in its manifestation. The effect is that the surface waves excited in the Earth by the main shock make a full revolution around the Earth and excite a strong aftershock in the epicentral zone of the main shock. In our opinion, the physical nature of this phenomenon consists in the fact that the superposition leads to a concentration of wave energy when the convergent surface waves reach the epicentral zone (cumulative effect). The effect of the first seismic echo is most manifest. Thus, the present work supports our hypothesis of the activation of rock failure under the cumulative impact of an round-the-world seismic echo on the source area which is releasing (“cooling”) after the main shock. The spatial regularities in the manifestations of this effect are established, and the independence of the probability of its occurrence on the main shock magnitude is revealed. The effect of a round-the-world seismic echo can be used to improve the reliability of the forecasts of strong aftershocks in determining the scenario for the seismic process developing in the epicentral zone of a strong earthquake that has taken place.     

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。     

Forecasting Aftershock Activity: 3. Båth’s Dynamic Law

In seismology according to Båth’s well-known law, the magnitude of the strongest aftershock is on average by unity lower than the magnitude of the main shock. At the same time, most of the strongest aftershocks typically occur within a few hours after the main shock. From the practical standpoint, this activity is quite naturally perceived as a direct continuation of the main earthquake. The subsequent strong aftershocks occur against the rarer background shocks, are less expected, and therefore constitute a separate hazard. The average difference in magnitudes between the main shock and the strongest aftershock that occurs a certain time after the main shock gradually increases. In this work, we consider the problem of estimating the magnitudes of the strongest future aftershock at the successive instants of time after the main shock without taking into account the information about the aftershocks that have already occurred before a given time. For these estimates, we construct the theoretical distributions whose shape proves to be independent of time, whereas the time dependence of the shift in the magnitude proves to be known a priori. The predetermination of these dependences at the moment of the strong earthquake gives us grounds to characterize the constructed theoretical model as Båth’s dynamic law.     

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.     

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.     

主余震序列型地震动作用下RC框架结构损伤耗能研究

强震发生后通常伴随着余震,余震的发生会加重结构损伤甚至引发倒塌。为了量化研究主余震序列型地震动对结构损伤的影响,以一栋3层钢筋混凝土框架结构为研究对象,选取了10条实际的主余震记录作为地震动输入,采用ABAQUS非线性有限元软件对该框架结构进行非线性动力时程分析,并依据结构局部和整体损伤耗能指标来评价主余震序列型地震动对框架结构累积损伤的影响。研究结果表明:序列地震会加剧结构底层柱的局部损伤耗能,特别是对底层中柱的影响更加明显;序列地震作用下的结构整体损伤耗能平均值相对于单主震作用下增加约30%;当余震与主震的第一周期谱加速度指标的比值Sa （T₁）_余震/Sa （T₁）_主震较大时,序列地震对结构损伤需求的影响更为显著。     

由宽频带辐射能量目录和地震矩目录给出的视应力及其地震学意义

对NEIC宽频带地震辐射能量目录和哈佛矩心矩张量（CMT）目录的比较，给出了关于视应力的一些可能是有意义的结果，尽管目前的结果误差仍很大，可靠性也是有限的，但这种比较所提供的线索却颇值得注意，视应力的计算给出关于地震断层面上非线性动摩擦函数的线索，能量／地震矩之比随地震大小的变化表明，在BK模型框架下，对于走滑型地城,依赖于滑动速度的摩擦似乎占主要地位，而对于非走滑型地震，依赖于位移的摩擦似乎占主要地位，主震和余震的能量／地震矩之比的比较表明，对于走滑型地震，余震的视应力平均地说来低于主震的视应力，而对于非直滑型地震，余震的视应力即有高于主震的也有低于主震的，这对于障碍体和凹凸模式的讨论及模型中地震破裂停止条件的设置可能具有一定的参考意义。     

强余震持续时间的早期估计

本研究旨在解决地震序列中强余震持续时间的早期估计问题。文中首先给出了强余震的震级定义，指出：主震型与强震群型序列的强作震持续时间存在差异。使用模式识别方法对主震型序列中强余震持续时间大于１天，小于１天及无强余震等３种情况进行划分之后，给出了两类序列的强余震持续时间与序列和第一震震级的粗略相关关系。     

Study on displacement field generated by aftershocks in Landers earthquake fault zone and its adjacent areas

Introduction The displacement field produced by earthquake can be measured on the Earth surface. The displacement field variation with time can be used to study lots of geodynamics parameters such as the Earth′s viscosity structure (Nur and Mavko, 1974; Sun et al, 1994; Deng et al, 1998), after-slip distribution (Shen et al, 1994; Reilinger et al, 2000), etc. Furthermore, earthquake also pro-duces lots of aftershocks, which have nearly the same focal mechanism as the main shock (e.g. Hard…     

Early Estimation of Strong Aftershock Duration Time

In order to solve the problem of early estimation of moderately strong aftershock duration time in an earthquake sequence,this study has been conducted.First,the definition of the strong aftershock has been given.It is pointed out that there is a difference in the strong aftershock duration time between the main shock type sequence and the strong earthquake swarm sequence.After dividing the three cases,i.e.,a strong aftershock duration time larger than 1 day,smaller than 1 day,and no strong aftershock occurred in a main shock type sequence by using the pattern recognition method,we gave the rough correlation relation between strong aftershock duration time and first large shock magnitude for two types of sequences.Finally,the judgment index and method of estimating strong aftershock duration times for different sequence types have been given.     

余震序列的持续时间ht

研究了近年来我国39个较大地震的余震序列的持续时间的一般特征及其与主震应力降、主震后波速比负异常的关系。提出了以震后波速比由下降变为上升的转折点将余震活动分为早期和晚期两个阶段的看法,并阐述了不同阶段余震的不同活动规律。