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Article(id=1322506192740532881, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506166672937516, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.09.431, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1726070400000, receivedDateStr=2024-09-12, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239647326, onlineDateStr=2026-10-29, pubDate=1755187200000, pubDateStr=2025-08-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239647326, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239647326, creator=13701087609, updateTime=1793239647326, updator=13701087609, issue=Issue{id=1322506166672937516, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='8', pageStart='771', pageEnd='880', issueExtLink='null', onlineDate='null', pubDate='1755187200000', pubDateStr='2025-08-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239641110, creator='13701087609', updateTime=1793239641110, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=818, endPage=822, ext={EN=ArticleExt(id=1322506193214489234, articleId=1322506192740532881, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Ground Motion Simulation of Wulong MS5.0 Earthquake Based on Stochastic Finite-Fault Method, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In this paper, the stochastic finite-fault method is used to simulate the ground motion of the Wulong MS5.0 earthquake. The simulation results for four stations within 100 km of the epicenter showed that the simulated acceleration time histories, peak ground acceleration, and response spectra are generally consistent with the actual records. Some discrepancies were observed at individual stations due to the influence of model parameters and environmental noise. Simulations were performed for 323 grid points within 100 km of the epicenter, and the spatial distribution characteristics of the ground motion obtained were consistent with the intensity field survey data. This study provides data support for seismic fortification and risk assessment in the Chongqing region and has both theoretical and practical significance for mitigating earthquake disasters.

, authors=Kai CHEN1, 2, Di DONG1, Jiang YI1, Tongjun WANG1, Bo GENG1, authorsList=Kai CHEN, Di DONG, Jiang YI, Tongjun WANG, Bo GENG, authorCompany=null, correspAuthors=null, authorNote=

CHEN Kai, senior engineer, majors in ground motion simulation, E-mail:

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利用随机有限断层法对武隆MS5.0地震进行地震动模拟。震中100 km内4个台站的模拟结果表明, 模拟得到的加速度时程、峰值加速度、反应谱均与实际记录较为一致; 个别台站受模型参数、环境噪声和局部场地效应影响, 与实际记录存在一定差异。对震中100 km内的323个网格点进行模拟, 得到的地震动空间分布特征与现场烈度调查数据较为一致。本研究可以为重庆地区抗震设防和风险评估等工作提供数据支撑, 对于减轻地震灾害具有理论和实践意义。

, authors=陈凯1, 2, 董娣1, 易江1, 王同军1, 耿波1, authorsList=陈凯, 董娣, 易江, 王同军, 耿波, authorCompany=null, correspAuthors=null, authorNote=

陈凯, 高级工程师, 主要从事地震动模拟研究, E-mail:

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2 Institute of Geophysics, CEA, 5 South-Minzudaxue Road, Beijing 100081, China, bio={"content":"

CHEN Kai, senior engineer, majors in ground motion simulation, E-mail:

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CHEN Kai, senior engineer, majors in ground motion simulation, E-mail:

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陈凯, 高级工程师, 主要从事地震动模拟研究, E-mail:

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Focal mechanism of Wulong MS5.0 earthquake

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震级MW 深度/km节面1 节面2来源
走向/(°) 倾角/(°) 滑动角/(°) 走向/(°) 倾角/(°) 滑动角/(°)
4.9 12 55 24 -79 223 66 -95 CENC
4.9 12 57 32 -69 213 60 -103 GCMT
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武隆MS5.0地震震源机制

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震级MW 深度/km节面1 节面2来源
走向/(°) 倾角/(°) 滑动角/(°) 走向/(°) 倾角/(°) 滑动角/(°)
4.9 12 55 24 -79 223 66 -95 CENC
4.9 12 57 32 -69 213 60 -103 GCMT
), ArticleFig(id=1322506205285696218, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506192740532881, language=EN, label=Tab. 2, caption=

Simulation input parameters of Wulong MS5.0 earthquake

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参数 设定值
矩震级MW 4.9
断层上界面埋深/km 12
震中 107.94°E、29.40°N
断层走向/倾角/类型 57°/32°/正断
断层尺寸/km 3.5×2.5
子断层尺寸/km 0.5×0.5
剪切波速度/km·s-1 3.5
破裂传播速度/km·s-1 0.8×3.5
地壳平均密度/g·cm-3 2.8
应力降/MPa 1.4
品质因子Q(f) 157.6f0.73
高频衰减因子κ/s 0.035
脉冲百分比/% 50
几何扩散模型 $ \left\{\begin{array}{l}\frac{1}{R}, R \leqslant 70 \mathrm{~km} \\\frac{1}{70}, 70 \mathrm{~km}<R \leqslant 130 \mathrm{~km} \\\frac{1}{70}\left(\frac{130}{R}\right)^{0.5}, 130 \mathrm{~km}<R\end{array}\right.$
路径持时模型 $ \left\{\begin{array}{l}0, R \leqslant 10 \mathrm{~km} \\0.16(R-10), 10 \mathrm{~km}<R \leqslant 70 \mathrm{~km} \\9.6-0.03(R-70) \\\quad 70 \mathrm{~km}<R \leqslant 130 \mathrm{~km} \\7.8+0.04 R(R-130), R>130 \mathrm{~km}\end{array}\right.$
), ArticleFig(id=1322506205369582299, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506192740532881, language=CN, label=表2, caption=

武隆MS5.0地震模拟输入参数

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参数 设定值
矩震级MW 4.9
断层上界面埋深/km 12
震中 107.94°E、29.40°N
断层走向/倾角/类型 57°/32°/正断
断层尺寸/km 3.5×2.5
子断层尺寸/km 0.5×0.5
剪切波速度/km·s-1 3.5
破裂传播速度/km·s-1 0.8×3.5
地壳平均密度/g·cm-3 2.8
应力降/MPa 1.4
品质因子Q(f) 157.6f0.73
高频衰减因子κ/s 0.035
脉冲百分比/% 50
几何扩散模型 $ \left\{\begin{array}{l}\frac{1}{R}, R \leqslant 70 \mathrm{~km} \\\frac{1}{70}, 70 \mathrm{~km}<R \leqslant 130 \mathrm{~km} \\\frac{1}{70}\left(\frac{130}{R}\right)^{0.5}, 130 \mathrm{~km}<R\end{array}\right.$
路径持时模型 $ \left\{\begin{array}{l}0, R \leqslant 10 \mathrm{~km} \\0.16(R-10), 10 \mathrm{~km}<R \leqslant 70 \mathrm{~km} \\9.6-0.03(R-70) \\\quad 70 \mathrm{~km}<R \leqslant 130 \mathrm{~km} \\7.8+0.04 R(R-130), R>130 \mathrm{~km}\end{array}\right.$
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基于随机有限断层法的武隆MS5.0地震地震动模拟
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陈凯 1, 2 , 董娣 1 , 易江 1 , 王同军 1 , 耿波 1
大地测量与地球动力学 | 地震地质 2025,45(8): 818-822
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大地测量与地球动力学 |地震地质 2025 , 45 (8) : 818 -822
基于随机有限断层法的武隆MS5.0地震地震动模拟
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陈凯1, 2 , 董娣1, 易江1, 王同军1, 耿波1
作者信息
  • 1 重庆市地震局, 重庆市金石大道300号, 401120
  • 2 中国地震局地球物理研究所, 北京市民族大学南路5号, 100081
作者简介:

陈凯, 高级工程师, 主要从事地震动模拟研究, E-mail:

Ground Motion Simulation of Wulong MS5.0 Earthquake Based on Stochastic Finite-Fault Method
Kai CHEN1, 2 , Di DONG1, Jiang YI1, Tongjun WANG1, Bo GENG1
Affiliations
  • 1 Chongqing Earthquake Agency, 300 Jinshi Road, Chongqing 401120, China
  • 2 Institute of Geophysics, CEA, 5 South-Minzudaxue Road, Beijing 100081, China

    • CHEN Kai, senior engineer, majors in ground motion simulation, E-mail:

出版时间: 2025-08-15 doi: 10.14075/j.jgg.2024.09.431
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摘要
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利用随机有限断层法对武隆MS5.0地震进行地震动模拟。震中100 km内4个台站的模拟结果表明, 模拟得到的加速度时程、峰值加速度、反应谱均与实际记录较为一致; 个别台站受模型参数、环境噪声和局部场地效应影响, 与实际记录存在一定差异。对震中100 km内的323个网格点进行模拟, 得到的地震动空间分布特征与现场烈度调查数据较为一致。本研究可以为重庆地区抗震设防和风险评估等工作提供数据支撑, 对于减轻地震灾害具有理论和实践意义。

随机有限断层  /  地震动模拟  /  武隆MS5.0地震  /  PGA

In this paper, the stochastic finite-fault method is used to simulate the ground motion of the Wulong MS5.0 earthquake. The simulation results for four stations within 100 km of the epicenter showed that the simulated acceleration time histories, peak ground acceleration, and response spectra are generally consistent with the actual records. Some discrepancies were observed at individual stations due to the influence of model parameters and environmental noise. Simulations were performed for 323 grid points within 100 km of the epicenter, and the spatial distribution characteristics of the ground motion obtained were consistent with the intensity field survey data. This study provides data support for seismic fortification and risk assessment in the Chongqing region and has both theoretical and practical significance for mitigating earthquake disasters.

stochastic finite-fault  /  ground motion simulation  /  Wulong MS5.0 earthquake  /  PGA
陈凯, 董娣, 易江, 王同军, 耿波. 基于随机有限断层法的武隆MS5.0地震地震动模拟. 大地测量与地球动力学, 2025 , 45 (8) : 818 -822 . DOI: 10.14075/j.jgg.2024.09.431
Kai CHEN, Di DONG, Jiang YI, Tongjun WANG, Bo GENG. Ground Motion Simulation of Wulong MS5.0 Earthquake Based on Stochastic Finite-Fault Method[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (8) : 818 -822 . DOI: 10.14075/j.jgg.2024.09.431
正文
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地震引发的强地面运动往往会导致山体滑坡、泥石流等次生灾害，造成的破坏和损失经常会超过地震本身直接引起的破坏。研究强地面运动形成的物理过程对于减轻地震可能引发的破坏意义重大。地震动的特性受多种因素影响，其中起主要作用的是震源参数、传播路径和场地效应[1]。常用的地震动模拟方法包括随机有限断层法、经验格林函数法、有限差分法、谱元法等。由于中强地震断层破裂滑移的不均匀性和地震波传播过程中的随机性，地震动受破裂面上离场地较近部分的影响较为明显，所以在地震工程领域进行近场中强震模拟时，往往采用较为成熟的随机有限断层法[2-6]。
本文利用随机有限断层法对2017年武隆MS5.0地震进行模拟，并与区域内台站的实际观测记录进行对比；同时，对震中100 km内的场地进行模拟，得到地震动空间分布特征。研究成果可以为重庆地区强震动的快速模拟提供参考，为区域的抗震设防工作提供数据支撑。
1 数据和方法
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2017-11-23重庆武隆发生MS5.0地震，震中位于29.39°N、107.99°E，震源深度为10 km[7]。本次地震发生在七曜山-金佛山和彭水2条基底断裂所夹持的武隆凹陷束中，震中及台站分布如图 1所示。此次地震共造成数十人受伤，为近年来重庆地区发生的最大地震。由于该区域地震活动性不强，且大震复发周期较长，因此中强地震的影响成为近些年来工程项目较为关注的目标。
随机有限断层法的基本原理是将整个发震断层划分成若干个矩阵子断层，将每个子断层视为一个点源[8]，原理如图 2所示。当断层发生破裂时，破裂会从其起始点向外以辐射状形式扩散，其中每个子断层都可以表征为加速度谱为ω2谱形状的点源。对于基于动力学拐角频率的模型，子断层在观测点的加速度傅里叶振幅谱可表示为震源谱、传播路径以及场地效应之间的乘积[9]。
在地震波从震源向外传播的过程中，起始破裂点附近的子断层具有最高的拐角频率。随着破裂的不断传播，子断层的拐角频率逐渐降低。为了补偿动态拐角频率降低导致的高频辐射能量减少，引入标度因子Hij以确保辐射能守恒。当地震波传播到一个子断层，该子断层就被认为是激发状态。将所有激发的子断层的地震动在观测点以适当的时间延迟叠加，从而模拟出地震动传播到观测点时的加速度：
$a(t)=\sum\limits_{i=1}^{n_l} \sum\limits_{j=1}^{n_w} a_{i j}\left(t+\Delta t_{i j}\right)$
式中，nl、nw分别为沿断层走向和倾向的子断层个数；aij为第i行j列的子断层所产生的地震动；Δtij为对应的时间延迟。
2 模拟过程
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在利用随机有限断层法进行地震动模拟时，需要确定地震的震源参数、传播路径和场地效应等参数作为模型的输入参数[4]。其中，场地效应主要由地壳放大和场地放大2个部分组成[9]。本次模拟中采用的地壳放大系数和场地放大函数参考文献[10]的研究成果。因地震发生时，重庆地区的强震动观测台网还未建成，故选择震中100 km内的4个测震台站XNS、LAX、GOT、QIJ进行地震动模拟。为了便于结果对比，对4个测震台站的速度记录进行微分，得到加速度记录，再对加速度进行基线校正和Butterworth滤波。
根据CENC和GCMT发布的武隆地震震源机制结果(表 1)，此次地震的震源机制解为NE走向的正断型地震。将此次地震的矩震级取为MW4.9，破裂面上界面埋深取为12 km，断层走向和倾角分别取为57°和32°。利用断层破裂面积、应力降和地震矩之间的经验关系式[11]，并参考陈丽娟等[12]对武隆地区应力降的研究结果，计算得到的应力降均为1.4 MPa。此次地震震源区位于基岩山区，没有形成地表破裂带，因此根据Wells等[13]统计得到的震级与断层几何尺寸的经验关系，计算发震断层沿走向和倾向的长度和宽度，结果分别为3.5 km、2.5 km。由于无法确定地震初始破裂点的位置，且地震发震断层面积不大，故使用随机的子断层的滑动权重。
传播路径效应主要包括在非均匀介质中传播引起的几何扩散和滞弹性衰减。本文采用北美东部的三段式几何扩散模型和根据经验关系得到的路径持时模型[14]。滞弹性衰减模型一般使用表示地下介质的非均匀性和非弹性性质的品质因子Q(f)来描述，本文采用汪健等[15]在重庆地区的研究结果Q(f)=157.6f0.73。高频衰减参数采用傅磊等[16]在中国西南地区的研究成果。
3 模拟结果
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考虑到随机有限断层的模拟结果具有一定的随机性，对每个台站进行20次模拟，选择与模拟结果的平均反应谱偏差最小的结果作为最终的模拟结果，模拟得到的加速度时程和反应谱与实际记录的对比如图 3、4所示。此次模拟的4个台站加速度时程与实际记录结果较为一致，能够反映出不同站点受此次地震影响的强震动特征。
XNS台为距离地震震中最近的台站，震中距为22.4 km，模拟得到的峰值加速度(PGA)与真实记录相近。QIJ台震中距为85 km，模拟加速度时程能够较好地再现此次地震的PGA及空间传播特点。从加速度时程的形态上来看，GOT台模拟结果与实际记录存在一定差异，可能是因为在本次模拟时，路径持时选择了简化的模型来计算，且时程的包络是通过高斯白噪声窗进行约束的，与实际情况存在一定的差距。真实记录可能包含环境噪声或其他高频成分，影响时程的波形形态，而模拟记录往往会通过滤波等处理减少噪声影响，导致时程在形态上有一定差异，从而导致模拟结果未能准确还原出实际地震波的传播特点[17]。
如图 4所示，模拟时程反应谱与实际记录在高频和低频处都较为一致，部分台站在大于1 Hz的高频处出现一定的差异，可能是因为高频部分的实际记录包含一定的环境噪声，模拟记录对这部分影响在高频段的放大不足[4]。地震动在传播过程中还会受到场地条件的非线性响应影响，使记录的地震动表现出一些非线性特征，QIJ台在高频段的非线性效应就较为明显。相关研究表明，该台场地响应曲线在高频段内出现明显的放大现象[15]，场地放大效应明显，从而导致与真实记录存在一定的差异[3]。总体来看，本次模拟在上述站点得到的时程和反应谱能够还原实际记录到的波形特点，模拟结果准确可靠。
本次地震发生在山区，震中100 km范围内平均海拔700 m。参考邻近台站的场地放大效应，采用随机有限断层法模拟100 km×100 km范围内323个观测点的加速度时程，每个测点进行10次模拟并取平均，提取各测点的PGA，并根据经验关系[18]计算峰值速度(PGV)，采用克里金插值法得到等值线(图 5)。结果表明，PGA、PGV的空间分布基本一致，PGA的空间分布与断层走向相近，在近场区域PGA等值线分布呈椭圆形，在远场区域呈圆形。PGA和PGV最大值位于震中附近，分别为41.37 Gal和5.24 cm/s。
利用PGA、PGV，根据式(2)[18]计算各观测点的烈度。
$\begin{gathered}I=2.2595+1.3449 \operatorname{lgPGA}+ \\1.8008 \operatorname{lgPGV}\end{gathered}$
根据GB/T 17742—2020《中国地震烈度表》确定仪器地震烈度值的取值范围并插值得到空间分布(图 6)。与重庆市地震局根据现场震害调查发布的地震烈度图进行对比发现，二者的Ⅵ度区形状基本相近，表明本文利用已知震源参数建立的随机有限断层模型是可信的，模拟的武隆MS5.0强地面运动场适用于预估Ⅵ度的地震烈度区，对判断灾情和组织开展震后救援具有参考价值。
4 结语
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以武隆MS5.0地震为例，利用随机有限断层法对4个台站进行地震动模拟，得到的加速度时程和PGA与实际结果较为一致，能够反映此次地震的主要特征。受模型选择及背景噪声等复杂因素的影响，GOT台加速度时程曲线与实际记录存在一定差异。同时对震中周围100 km范围内323个网格点进行模拟，得到地震动Ⅵ度影响场范围大致为29.30°~29.46°N、107.86°~108.02°E，与重庆市地震局根据现场震害调查发布的地震烈度图基本一致。对武隆地震的模拟结果表明，随机有限断层法可以获得与真实地震记录较为一致的时程和峰值加速度，通过模拟可以为地区抗震设防和灾情研判等工作提供数据支撑。
本文模拟过程中部分参数由经验公式计算得到，不够准确。目前重庆地区强震动观测台网已开始试运行，通过观测数据的积累，并结合物探等其他观测手段获得的场地条件，可为该区域未来进行更加精准的场地效应研究及快速准确的近场强震动模拟提供数据支持。
基金
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  • 中国地震局"三结合"课题(3JH-202401084)
  • 重庆市地震局科技创新团队
文献
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doi: 10.14075/j.jgg.2024.09.431
  • 接收时间：2024-09-12
  • 首发时间：2026-10-29
  • 出版时间：2025-08-15
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  • 收稿日期：2024-09-12
基金
Combination Project with Monitoring, Prediction and Scientific Research of Earthquake Technology, CEA(3JH-202401084)
中国地震局"三结合"课题(3JH-202401084)
Seismic Science and Technology Innovation Team of Chongqing Earthquake Agency
重庆市地震局科技创新团队
作者信息
    1 重庆市地震局, 重庆市金石大道300号, 401120
    2 中国地震局地球物理研究所, 北京市民族大学南路5号, 100081
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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2024.09.431
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
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