高频地震动随机模拟方法研究

基于地震动时程记录、震源破裂过程和场地模型的近断层强地震动模拟方法是目前估计地震动输入的重要方法之一,也是岩土地震工程研究的热点问题之一。由于大部分建筑自振周期在3.0 s以内,因此对地震动的高频成分更为敏感。本文以适用于模拟高频地震动的随机模拟方法为研究对象,系统地归纳和总结了该方法的研究历史和现状,详细介绍了其模拟的原理,并评述了随机点源模型和有限断层模型的特点。在此基础上,针对该方法中存在的一些问题,开展了深入系统的研究,主要研究工作和取得的成果如下:(1)建立了拐角频率和震源破裂速度的关系。推导了震源谱中拐角频率的表达式,明确了推导过程中的假设条件和适用范围,阐明了拐角频率在不同的假设条件下有不同的表达式。结果表明,无论是点源模型还是有限断层模型,拐角频率应和破裂速度有直接的联系。本文给出的拐角频率和破裂速度之间的表达式,可以弥补Boore和Motazedian有限断层模拟程序在理论上的不完善和矛盾之处,在理论上补充和完善了拐角频率的表示方法。(2)统计分析了汶川特大地震主、余震高频衰减参数kappa的分布规律。通过对不同场地、不同震级、不同距离下强震记录的分析,本文认为,高频衰减参数kappa和震级、震中距、场地以及统计的频段有关,同时也存在一定的随机性,且随机性的影响有可能更大。结果表明,水平向强震记录的kappa值大于竖向的,同时发现一定比例的竖向强震记录甚至表现出高频增大的趋势。对于水平向强震记录,在震中距或震级较小的时候,也可能会出现高频增大的情况。按照我国抗震设计规范的场地分类方法,将台站分为三类场地,分别统计了Ⅰ类、Ⅱ类和Ⅲ类场地kappa值随震级和震中距的变化规律,并给出了拟合公式。(3)提出了一种确定输入参数的方法,给出了地震动随机模拟方法中主要输入参数的取值范围,并分析了输入参数取值对地震动模拟结果的影响。本文利用随机模拟方法,分析了应力降、震源处密度、破裂速度、剪切波速、品质因子、高频衰减参数等输入参数对地震动峰值加速度PGA、反应谱Sa和放大系数β的影响。结果表明,上述输入参数取值变化对模拟结果的PGA均有一定的影响,按照敏感程度依次为应力降、高频衰减参数kappa、品质因子Q_0、震源处密度、破裂速度、品质因子指数、剪切波速。其中,kappa对放大系数β的影响最大,会改变放大谱的形状,其他输入参数的变化对放大系数β影响则很小,因此输入参数的取值变化对反应谱的影响主要取决于对PGA的影响程度。针对输入参数对模拟结果的影响程度,本文对输入参数的取值提出了相应的建议。在缺少反演结果的情况下,对于较不敏感的参数,可以在经验值范围内选择;对于敏感的参数,则需要搜索一个最优值使得各台站模拟记录与实测记录之间的误差最小。这一方法可作为随机模拟方法输入参数取值的参考依据。(4)利用随机有限断层模拟方法模拟了鲁甸M_S6.5地震的基岩台记录,提出了一种地震动模拟的工程方法。本文分析并总结了鲁甸地震震源机制的反演结果,结合本文对拐角频率的改进和输入参数的确定方法,利用随机有限断层模拟方法模拟了鲁甸地震基岩台的加速度时程。从结果来看,模拟地震动的峰值加速度PGA和反应谱均与实测结果较为接近,这表明随机有限断层模拟方法可以用于模拟近场地震动,也验证了本文的研究结果的合理性和可行性。对于没有强震记录对比的工程场地,本文提出了一种工程方法,它的原理是将反应谱的模拟分为PGA和放大系数包络线两部分内容分别合成,PGA的取值范围由随机模拟方法和地震动衰减关系联合确定,采用随机模拟方法确定放大系数的包络线。这种方法考虑了不同相位谱对地震动的影响,并结合了地震动衰减关系的研究成果,可以提高模拟地震动的精度,并给出了多条地震动时程曲线,拟合得到的时程反应谱包络线可以有效涵盖实测记录。该方法可用于模拟缺少强震记录工程场地的地震动。     

基于随机有限断层方法的唐山地震强地面运动模拟

基于动力学拐角频率的随机有限断层模型,以1976年唐山大地震的极震区为研究目标,通过梳理前人的研究成果,建立了目标区的计算模型并确定了震源模型参数,依靠目标区的局部场地资料和场地动力学参数,利用四分之一波长法,获取局部场地放大效应参数;利用随机有限断层模型地震动模拟方法,给出了唐山大地震近场强地震动场模拟结果,并与历史地震宏观烈度进行对比,结果表明:在Ⅷ、Ⅸ度影响烈度的范围与宏观资料吻合较好。     

地震动随机合成中与震源谱相关的动力学拐角频率

介绍了基于有限断层震源的地震动随机合成中静力学拐角频率和动力学拐角频率,讨论了两者的缺点;进而提出了一种改进的震源谱模型,它能够表达破裂面上地震波频率辐射不均匀性、大震时拐角频率随破裂面积增加而有所下降的趋势．据此,可以形成与该震源谱模型相关联的动力学拐角频率,应用于地震动的随机合成,避免结果对子源尺寸的依赖．通过对美国北岭Mw6.7地震近场6个基岩台站合成的地震动与实际记录的比较,验证了本文方法的有效性.      

随机有限断层法模拟中强地震近场地震动的研究及应用

核工程是对地震安全性要求极高的工程,在其工程场地地震危险性评价工作中,弥散地震地震动估计往往对厂址设计基准地震动具有关键性影响。然而,弥散地震不是由特定构造引起的,因此,评定其地震影响时会遇到较大困难。常规方法是采用适当的衰减关系来计算工程场地震级5.0和5.5的弥散地震在距离厂址5 km处的地震动参数。本文针对核电厂地震危险性评价需求,探讨弥散地震评价的新方法,即通过随机有限断层法来模拟中强地震近场地震动参数。通过参数敏感性分析技术筛选了对拟合结果有决定性影响的关键模型参数;研究并改善了有限断层模型拟合中强地震模型应力降参数的方法,并基于多个国家和地区中强地震近场加速度记录估算了应力降参数值;此外,通过建立中强地震类属模型来模拟特定震级-距离的地震动,从而对经验统计方法进行补充和验证。(1)详细研究了模拟地震动时程的随机有限断层法以及近年来对该方法的改进,改进后的随机有限断层法适合模拟中强地震。(2)对随机有限断层法模拟中强地震近场强震动的参数影响情况进行了分析。将随机有限断层法应用于中强地震时,由于震源信息的准确性较差从而使模型参数具有较大的不确定性。为此,本文首先比较了不同场地方位角中强地震近场地震动的时程和平均拟加速度反应谱(PSA),并定量分析了模型主要参数对中强地震近场地震动模拟结果的参数敏感性。结果表明:不同场地方位角的中强地震近场PSA在短周期部分差别较大;应力降是模型最重要的参数,它对反应谱短周期部分影响最大;几何扩散系数对PSA的整体影响也较为明显。将随机有限断层方法应用到工程安全性评价工作时,应当重点关注对反应谱短周期部分影响较大的应力降和该区域的几何扩散系数,同时要调查该区域优势场地方位角的分布,从而更合理地控制中强地震近场强震动的模拟。(3)开展了中强地震模型应力降参数值的估算。基于美国小头骨山(Little Skull Mountain)MW5.6地震两个近场台站记录的地震动模拟,详细研究并改善了采用随机有限断层法拟合中强地震地震动拟加速度反应谱(PSA)来确定应力降参数值的方法。结果表明:采用不同频段反应谱残差和计算得到的应力降值差别较大,确定中强地震应力降较为合适的反应谱频段是中高频,采用该频段确定的应力降参数值模拟的反应谱和峰值加速度与实际记录较为符合。基于该方法并根据美国西部、日本、意大利以及汶川等国家和地区的浅源中强地震近场加速度时程记录,估算了相应的模型子断层应力降参数值。结果表明:各个国家和地区计算得到的中强地震随机有限断层模型应力降参数具有地区差异性;模拟的峰值加速度大致上正确反映了实际记录PGA的衰减规律,并且模拟结果在近场随距离的衰减较快,这可能与计算所使用的中强地震高频成分丰富有关。(4)针对中强地震震源及路径参数难以准确确定的情况,提出了通过建立随机有限断层类属模型参数来考虑随机不确定性,从而进行中强地震近场地震动模拟的方法,即在考虑区域特定参数、选择具有代表性的震源参数的同时,考虑关键参数随机不确定性,开展大量模拟计算。完成了对核电厂工程弥散地震地震动参数评价的工程应用分析。对模拟PGA的统计结果表明:考虑核电厂弥散地震时,MS5.0地震震中距5 km处0.15g的峰值加速度是合适的;MS5.5地震震中距5 km处0.2g的峰值加速度是合适的;MS6.0地震震中距5 km处0.3g的峰值加速度是合适的。该结果为现有弥散地震地震动评价提供了验证信息。模拟PSA统计结果与衰减关系PSA的比较表明,模拟的平均PSA大致上是保守的,可以作为随机有限断层法模拟结果的推荐反应谱。     

随机有限断层方法的改进和芦山地震动模拟

随着随机有限断层方法被逐步推广至宽频带地震动的震前预测与震后模拟,该方法存在的2类问题凸显:(1)模拟地震动的频率非平稳特性缺失;(2)高低频地震动的模拟精度不一致。文中探索上述问题的改进措施:(1)引入区域地震波传播群速度模型以生成频率非平稳地震动相位;(2)引入王国新改进震源谱代替Brune震源谱以实现高低频地震动辐射水平的调整。将改进后的随机有限断层方法应用于2014年芦山地震(M_w6.7)的强地震动模拟,模拟结果验证了改进措施的有效性:新引入相位使得模拟记录的频率非平稳特性趋近于真实记录;新引入震源谱模型在一定程度上可实现高低频地震动的一致精度模拟。     

基岩地震动的一个相干函数模型--倾滑断层情形

本文研究了基岩随机地震动的空间变化规律，考虑了震源破裂速度、子源个数、震源深度和介质传播速度等因素的影响。对应于每个样本，用数值模拟方法计算了采用震源位错模型的弹性半空间近场地震动场，最后通过统计方法给出了一个倾滑断层情形下的近场基岩地震动的相干函数模型。这一方法可以补充常用的统计方法因观测资料有限而导致的欠缺。     

随机有限断层法模拟中强地震近场强震动的参数影响研究

介绍了模拟地震动时程的随机有限断层法及近年来对该方法的改进,改进后的随机有限断层法适合模拟中强地震;比较了不同场地方位角的中强地震近场地震动时程与平均伪加速度反应谱(PSA);定量分析了中强地震近场地震动模拟结果的参数敏感性. 结果表明:不同场地方位角的中强地震近场PSA在短周期部分差别较大;应力降是模型中最重要的参数,其对反应谱短周期部分影响最大;几何扩散系数对PSA的整体影响也较为明显. 将随机有限断层法应用到工程安全性评价工作中时,应当重点关注对反应谱短周期部分影响较大的应力降和该区域的几何扩散系数,同时要调查该区域优势场地方位角的分布,更加合理地控制中强地震近场强震动的模拟.      

2010年4月14日玉树Ms7.1地震加速度场预测

基于有限断层震源、且使用动力学拐角频率的地震动随机模拟方法预测玉树地震近断层的加速度场.首先,基于有限断层震源建模方法建立该次地震的震源模型;然后,基于上述地震动模拟方法预测玉树地震近断层191个节点的加速度时程.在此基础上,取每个结点的加速度峰值绘制该次地震的近断层加速度场.结果表明:(1)近断层加速度场主要受震源破裂过程和断层面上滑动分布的影响.断层面上凹凸体投影到地表的区域附近,加速度峰值最大,也是震害最严重的区域;(2)对于走滑地震,断层沿线附近的场地并非均会发生破裂方向性效应;发生破裂方向性效应的场地与凹凸体在断层面上的位置有关.     

随机点源方法和随机有限断层方法模拟地震动的比较

在对用随机点源方法模拟地震动和随机有限断层方法模拟地震动比较的基础上,介绍了2种方法的局限性和优越性.分别用2种方法对卢龙和宁河地震进行了模拟结果表明:用随机点源方法模拟结果仅在某些频段与记录符合得比较好,而在其它频段内与记录符合得不好;用随机有限断层模型方法模拟结果无论在低频还是在高频都与记录符合得很好.因此加强研究中国大陆的地震动经验关系对提高随机点源方法在中国大陆的适用性是有益的,用有限断层方法模拟地震动的结果与记录符合得比较好,说明现在可以用该方法大量地模拟中国大陆地震动.     

应用动力学拐角频率对经验格林函数法的改进

针对大小震拐角频率的差异,假设大震断层上每个子源的拐角频率与已破裂的子源个数平方根成反比,基于ω2震源谱模型,通过理论推导构建了一个函数,将动力学拐角频率引入经验格林函数法。以汶川地震余震记录为格林函数,分别用改进前和引入动力学拐角频率后的经验格林函数法合成5·12汶川大地震强地面运动。对比合成结果与观测记录,结果表明改进前经验格林函数法合成的地震动在低频部分相对实际记录偏低;引入动力学拐角频率之后的经验格林函数法合成的结果在高频基本保持不变,低频部分得到提高,并与实际记录符合。引入动力学拐角频率后,大部分合成结果很好地符合实际记录。说明动力学拐角频率可有效改善经验格林函数法的低频合成结果,同时验证了经验格林函数法对MW7.9特大地震地震动合成的有效性。     

2013年乌鲁木齐MS5.6和MS5.1地震强地震动模拟研究

利用基于动力学拐角频率的随机有限断层法,针对2013年3月29日和8月30日乌鲁木齐发生的M_S5.6和M_S5.1两次地震,选择不同机构的震源参数对23个台站的45条强震记录进行强地震动模拟,对比分析加速度时程和反应谱,并计算模型偏差.通过与实际场点记录进行对比的结果显示:选取的不同机构震源参数模型得到的模拟加速度时程在持时和形状上与实际记录有一定差距,对于近震源的台站,模拟结果的峰值加速度(PGA)比观测结果小,对于稍远的台站,结果基本能够保持一致;而加速度反应谱,模拟结果与观测结果具有较好一致性; 随机有限断层模型的误差在±0.5以内,拟合效果较好,而且高频段的拟合效果要好于低频段;采用不同机构震源参数模型得到的模拟结果与观测结果得到的PGA分布特征较为一致,但模拟结果的峰值加速度要低于观测结果.      

Strong ground motion simulation for the 2013 Lushan M W6.6 earthquake,Sichuan, China,based on the inverted and synthetic slip models

It is well known that quantitative estimation of slip distributions on fault plane is one of the most important issues for earthquake source inversion related to the fault rupture process. The characteristics of slip distribution on the main fault play a fundamental role to control strong ground motion pattern. A large amount of works have also suggested that variable slip models inverted from longer period ground motion recordings are relevant for the prediction of higher frequency ground motions. Zhang et al. (Chin J Geophys 56:1412–1417, 2013) and Wang et al. (Chin J Geophys 56:1408–1411, 2013) published their source inversions for the fault rupturing process soon after the April 20, 2013 Lushan earthquake in Sichuan, China. In this study, first, we synthesize two forward source slip models: the value of maximum slip, fault dimension, size, and dimension of major asperities, and corner wave number obtained from Wang’s model is adopted to constrain the generation of k ^?2 model and crack model. Next, both inverted and synthetic slip models are employed to simulate the ground motions for the Lushan earthquake based on the stochastic finite-fault method. In addition, for a comparison purpose, a stochastic slip model and another k ^?2 model (k ^?2 model II) with 2 times value of corner wave number of the original k ^?2 model (k ^?2 model I) are also employed for simulation for Lushan event. The simulated results characterized by Modified Mercalli Intensity (MMI) show that the source slip models based on the inverted and synthetic slip distributions could capture many basic features associated with the ground motion patterns. Moreover, the simulated MMI distributions reflect the rupture directivity effect and the influence of the shallow velocity structure well. On the other hand, the simulated MMI by stochastic slip model and k ^?2 model II is apparently higher than observed intensity. By contrast, our simulation results show that the higher frequency ground motion is sensitive to the degree of slip roughness; therefore, we suggest that, for realistic ground‐motion simulations due to future earthquake, it is imperative to properly estimate the slip roughness distribution.     

Stochastic finite fault modelling of M w 4.8 earthquake in Kachchh, Gujarat, India

The modified stochastic finite fault modelling technique based on dynamic corner frequency has been used to simulate the strong ground motions of M _w 4.8 earthquake in the Kachchh region of Gujarat, India. The accelerograms have been simulated for 14 strong motion accelerographs sites (11 sites in Kachchh and three sites in Saurashtra) where the earthquake has been recorded. The region-specific source, attenuation and generic site parameters, which are derived from recordings of small to moderate earthquakes, have been used for the simulations. The main characteristics of the simulated accelerograms, comprised of peak ground acceleration (pga), duration, Fourier and response spectra, predominant period, are in general in good agreement with those of observed ones at most of the sites. The rate of decay of simulated pga values with distance is found to be similar with that of observed values. The successful modelling of the empirical accelerograms indicates that the method can be used to prepare wide range of scenarios based on simulation which provide the information useful for evaluating and mitigating the seismic hazard in the region.     

Dynamic corner frequency in source spectral model for stochastic synthesis of ground motion

The static corner frequency and dynamic corner frequency in stochastic synthesis of ground motion from finite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower corner frequency, can be described by the source spectral model developed by the authors. A new dynamic corner frequency can be developed directly from the model. The d...     

利用混合法合成成都断层宽频地震动

首先,依据成都活断层探测的深、浅层地震勘探资料、钻井资料、地形资料,建立成都地区地下三维介质模型,并基于活断层确定的双石-大川断裂发生7.6级潜在地震的地震活动性探测结果,设定断层破裂震源模型,采用随机有限断层方法模拟短周期地震动、谱元法模拟长周期地震动,利用混合法通过频域合成技术获得了研究区域的宽频地震动。最后,讨论了合成结果的PGA、PGV、PGD以及0.3s和1.0s反应谱的分布特征,依据分布结果对成都市区进行了本次设定地震的地震动讨论。     

A simplified method for simulation of strong ground motion using finite rupture model of the earthquake source

We present a simplified method to simulate strong ground motion for a realistic representation of a finite earthquake source burried in a layered earth. This method is based on the stochastic simulation method of Boore (Boore, D. M., 1983, Bull. Seism. Soc. Am. 73, 1865–1894) and the Empirical Greens Function (EFG) method of Irikura (Irikura, K., 1986, Proceedings of the 7th Japan Earthquake symposium, pp. 151–156). The rupture responsible for an earthquake is represented by several subfaults. The geometry of subfaults and their number is decided by the similarity relationships. For simulation of ground motion using the stochastic simulation technique we used the shapping window based on the kinetic source model of the rupture plane. The shaping window deepens on the geometry of the earthquake source and the propagation characteristics of the energy released by various subfaults. The division of large fault into small subfaults and the method for accounting their contribution at the surface is identical to the EGF. The shapping window has been modified to take into account the effect of the transmission of energy released form the finite fault at various boundaries of the layered earth model above the source. In the present method we have applied the correction factor to adjust slip time function of small and large earthquakes. The correction factor is used to simulate strong motion records having basic spectral shape of ² source model in broad frequency range. To test this method we have used the strong motion data of the Geiyo earthquake of 24th March 2001, Japan recorded by KiK network. The source of this earthquake is modelled by a simple rectangular rupture of size 24 × 15 km, burried at a depth of 31 km in a multilayered earth model. This rupture plane is divided into 16 rectangular subfaults of size 6.0 × 3.75 km each. Strong motion records at eight selected near-field stations were simulated and compared with the observed records in terms of the acceleration and velocity records and their response spectrum. The comparison confirms the suitability of proposed rupture model responsible for this earthquake and the efficacy of the approach in predicting the strong motion scenario of earthquakes in the subduction zone. Using the same rupture model of the Geiyo earthquake, we compared the simulated records from our and the EGF techniques at one near-field station. The comparison shows that this technique gives records which matches in a wide frequency range and that too from simple and easily accessible parameters of burried rupture.     

近断层强地震动场预测

以1997年4月11日新疆伽师地震（M_w6.1）为例,详细介绍了近断层强地震动场的预测方法.首先,用有限断层震源建模方法建立了该次地震的震源模型;然后,基于动力学拐角频率的地震动随机模拟方法,模拟了该次地震仅有主震加速度记录、且位于巨厚土层上的三个台站的加速度时程,并用实际地震记录进行了验证.在此基础上,基于预测的近断层77个节点的加速度时程的峰值绘制了该次地震的加速度场.结果表明,上述方法模拟的加速度时程在0.5 Hz以上的高频段是可行的、实用的;预测的近断层加速度场具有非常明显的上盘效应.地表最大加速度的范围与断层面上最大凹凸体位置相对应,说明与断层面上凹凸体相对应的地面上的建（构）筑物将会遭受到较为严重的震害.     

Broadband Ground Motion Reconstruction for the Kanto Basin during the 1923 Kanto Earthquake

Ground motions of the 1923 Kanto Earthquake inside the Kanto Basin are numerically simulated in a wide frequency range (0?C10?Hz) based on new knowledge of the earthquake??s source processes, the sedimentary structure of the basin, and techniques for generating broadband source models of great earthquakes. The Kanto Earthquake remains one of the most important exemplars for ground motion prediction in Japan due to its size, faulting geometry, and location beneath the densely populated Kanto sedimentary basin. We reconstruct a broadband source model of the 1923 Kanto Earthquake from inversion results by introducing small-scale heterogeneities. The corresponding ground motions are simulated using a hybrid technique comprising the following four calculations: (1) low-frequency ground motion of the engineering basement, modeled using a finite difference method; (2) high-frequency ground motion of the engineering basement, modeled using a stochastic Green??s function method; (3) total ground motion of the engineering basement (i.e. 1?+?2); and (4) ground motion at the surface in response to the total basement ground motion. We employ a recently developed three-dimensional (3D) velocity structure model of the Kanto Basin that incorporates prospecting data, microtremor observations and measurements derived from strong ground motion records. Our calculations reveal peak ground velocities (PGV) exceeding 50?cm/s in the area above the fault plane: to the south, where the fault plane is shallowest, PGV reaches 150?C200?cm/s at the engineering basement and 200?C250?cm/s at the surface. Intensity 7, the maximum value in the Japan Meteorological Agency??s intensity scale, is calculated to have occurred widely in Sagami Bay, which corresponds well with observed house-collapse rates due to the 1923 event. The modeling reveals a pronounced forward directivity effect for the area lying above the southern, shallow part of the fault plane. The high PGV and intensity seen above the southeastern corner of the fault plane and further east are largely due to this effect. Waveforms above the fault plane contain both short- and long-period components, but the short-period components are not observed further afield. Away from the fault, long-period waves (>2?s) dominate the ground motion, and in areas where the base of the third layer is relatively deep, the predominant period is >5?s. Levels of long-period ground motion in the southern part of the study area, around Sagami Bay and the southern parts of Boso Peninsula and Tokyo Bay, exceed that recorded at Tomakomai during the 2003 Tokachi-oki earthquake, when large oil storage tanks collapsed in response to sloshing generated by strong long-period motions.     

Improvements of corner frequency and scaling factor for stochastic finite-fault modeling

In this paper, three existing source spectral models for stochastic finite-fault modeling of ground motion were reviewed. These three models were used to calculate the far-field received energy at a site from a vertical fault and the mean spectral ratio over 15 stations of the Northridge earthquake, and then compared. From the comparison, a necessary measure was observed to maintain the far-field received energy independent of subfault size and avoid overestimation of the long-period spectral level. Two improvements were made to one of the three models (i.e., the model based on dynamic corner frequency) as follows: (i) a new method to compute the subfault corner frequency was proposed, where the subfault corner frequency is determined based on a basic value calculated from the total seismic moment of the entire fault and an increment depending on the seismic moment assigned to the subfault; and (ii) the difference of the radiation energy from each subfault was considered into the scaling factor. The improved model was also compared with the unimproved model through the far-field received energy and the mean spectral ratio. The comparison proves that the improved model allows the received energy to be more independent of subfault size than the unimproved model, and decreases the overestimation degree of the long-period spectral amplitude.