融合三维断层源和二维潜在震源区的随机抽样概率地震危险性分析算法研发

doi:10.3969/j.issn.0253-4967.2023.02.008

摘要/Abstract

摘要：

文中采用蒙特卡罗随机抽样方法, 研发了一套融合传统二维潜在震源区(下文简称“潜源”)和三维断层源的概率地震危险性算法。该算法不仅适用于传统的区域面源, 同时还能考虑地震的破裂尺度并兼容三维断层源的概率地震危险性计算。文中研发的算法可高效实现断层源地震事件集的三维模拟, 并将地震破裂尺度引入到概率地震危险性计算中, 显著提高了近断层地区地震危险性计算的合理性。为了提高程序的执行效率, 算法采用预先在平面潜源中充填网格点的方式随机模拟地震事件在潜源内的均匀分布。对于椭圆衰减的地震危险性计算, 算法采用了预先构建不同震级、距离及不同场点与潜源长轴方向夹角下的短轴距的三维矩阵, 通过查表和插值方式直接获得相应场点的短轴距, 避免了循环迭代逼近短轴距计算效率低下的问题。分别利用五代图的概率地震危险性程序和文中研发的算法, 计算了湖南长-株-潭(长沙-株洲-湘潭)城市群所处的中强地震活动环境的区域地震危险性以及近断层源的常德、株洲2个场点在不同概率水平下(重现期分别为50a、475a和2 475a)的地震危险性。比较研究表明, 五代图的程序低估了三维断层源附近的地震危险性, 且随着概率水平的降低, 低估的程度越来越高。最后, 利用太平洋地震工程中心(Pacific Earthquake Engineering Research Center, PEER)验证概率地震危险性程序的算例(数据集1案例10)验证了文中算法的可靠性。

关键词: 概率地震危险性分析, 潜在震源区, 三维断层源, 蒙特卡罗

Abstract:

Using the Monte Carlo random sampling method, a set of probabilistic seismic hazard analysis calculation programs that integrates our country’s traditional planar potential seismic source zone and three-dimensional fault sources is developed. The program is not only suitable for our country’s traditional regional area sources, but also considers the rupture scale of earthquakes and is compatible with the probabilistic seismic hazard calculation of three-dimensional fault sources. The algorithm developed in this paper efficiently realizes the three-dimensional simulation of the seismic event set of the fault source and introduces the earthquake rupture scale into the probabilistic seismic hazard analysis calculation in China, which significantly improves the rationality of the seismic hazard calculation in the near-fault area. In order to improve the execution efficiency of the program, the algorithm adopts the method of filling grid points in the planar potential seismic source zone in advance and randomly simulating the uniform distribution of seismic events in the planar potential seismic source zone. For the seismic hazard calculation of elliptical attenuation relationship, the algorithm uses pre-constructed three-dimensional matrices of the distance of the ellipse minor axis under different magnitudes, distances, and different angles between sites and the ellipse long axis direction of potential seismic source zone, and directly obtains the corresponding distance of ellipse minor axis through table look-up and interpolation. The algorithm developed in this paper avoids the problem of low computational efficiency in the iterative approximation of the distance of the ellipse minor axis. The mathematical expression of the three-dimensional fault source is based on the Frankel fault plane form of the 2002 edition of the National Seismic Hazard Map of the United States. The surface track and average dip Angle of the fault are used to create the rectangular fault plane, in which the dip direction of each rectangle is always perpendicular to the strike of its local fault segment. To maintain the coordination between the rupture area and the magnitude, the rupture of the earthquake occurring on the fault plane should not exceed the fault plane or the combination of fault planes. If the boundary of the rupture plane is outside the fault boundary, the entire rupture plane will move so that the boundary of the entire rupture plane matches the boundary of the fault plane. Using the probabilistic seismic hazard program of the Seismic ground motion parameters zonation map of China(2015)and the algorithm developed in this paper, the regional seismic hazard of the study area including Changsha-Zhuzhou-Xiangtan of the urban agglomeration in Hunan Province with moderate to strong seismic activity are calculated. Seismic hazard at different probability levels(return periods of 50.8, 475 and 2 475 years, respectively)for the Changde near-fault sources and Zhuzhou sites are also computed. The comparative study shows that the procedure of the Seismic ground motion parameters zonation map of China(2015)underestimates the seismic hazard near the three-dimensional fault source, and the degree of underestimation becomes more significant as the probability level decreases. Considering the influence of the earthquake rupture scale at the low exceedance probability level, the decomposition results of the seismic hazard for sites near fault show that the contribution of the seismic hazard is different from that of the traditional method of the Seismic ground motion parameters zonation map of China(2015), which mainly focuses on the earthquake of high magnitude. However, earthquakes of all magnitudes on the fault source can contribute to the seismic hazard, but the proportion of high magnitudes is the largest. Finally, an example verifying the probabilistic seismic hazard program(data set 1 case 10)from the Pacific Earthquake Engineering Research Center(PEER)is used to verify the reliability of the algorithm developed in this paper.

Key words: Probabilistic Seismic Hazard Analysis, potential seismic source zone, three-dimensional fault sources, Monte Carlo

中图分类号:

P315.9

陈鲲, 高孟潭, 俞言祥, 徐伟进, 杜义, 李雪靖, 陆东华. 融合三维断层源和二维潜在震源区的随机抽样概率地震危险性分析算法研发[J]. 地震地质, 2023, 45(2): 435-454.

CHEN Kun, GAO Meng-tan, YU Yan-xiang, XU Wei-jin, DU Yi, LI Xue-jin, LU Dong-hua. PROBABILISTIC SEISMIC HAZARD ANALYSIS ALGORITHM INTEGRATING THREE-DIMENSIONAL FAULT SOURCES AND POTENTIAL SEISMIC SOURCE ZONE USING RANDOM SAMPLING[J]. SEISMOLOGY AND GEOLOGY, 2023, 45(2): 435-454.

图/表 12

图1 模拟地震目录的流程示意图

Fig. 1 Flowchart of simulating earthquake catalog.

图2 工作区内模拟2 475a的地震分布图

Fig. 2 Distribution map of simulated earthquakes in the work area for 2 475 years.

图3 用长江中下游地震带模拟地震目录的震级-频度(G-R)统计(模拟时长247 500a)

Fig. 3 Statistics of the magnitude frequency for simulated earthquakes in the middle and lower reaches of the Changjian River seismic belt(simulation duration 247 500 years).

图4 地震危险性计算的流程示意图

Fig. 4 Schematic diagram of the seismic hazard calculation process.

图5 用本文研发的算法计算得到的长沙的超越概率曲线图

Fig. 5 Plot of mean-hazard curves for Changsha constructed by the algorithm developed in this study.

表1 太阳山断裂的三维断层源参数

Table1 3D fault source parameters of the Taiyangshan fault

地表形迹坐标	宽度/km	倾角/(°)	顶面埋深/km
29.47°N, 112.00°E; 29.33°N, 111.91°E; 29.25°N, 111.83°E	60	60	0
29.15°N, 111.76°E; 29.04°N, 111.73°E; 28.99°N, 111.70°E

图6 用本文研发算法模拟的三维断层源的地震目录空间分布图

Fig. 6 Spatial distribution map of earthquake catalogs of 3D fault sources simulated by the algorithm developed in this paper.

图7 研究区不同方案、不同概率水平下的地震动峰值加速度分布 a 50a超越概率63%(方案1); b 50a超越概率63%(方案2); c 50a超越概率63%(方案3); d 50a超越概率10%(方案1); e 50a超越概率10%(方案2); f 50a超越概率10%(方案3); g 50a超越概率2%(方案1); h 50a超越概率2%(方案2); i 50a超越概率2%(方案3).

Fig. 7 Distribution of ground motion peak acceleration with different probability levels for different schemes in the study area.

图8 株洲、常德不同方案、不同震级-距离档的地震对不同概率水平下峰值加速度危险性的贡献 a 超越概率63%(株洲, 方案2); b 超越概率10%(株洲, 方案2); c 超越概率2%(株洲, 方案2); d 超越概率63%(常德, 方案2); e 超越概率10%(常德, 方案2); f 超越概率2%(常德, 方案2); g 超越概率63%(常德, 方案3); h 超越概率10%(常德, 方案3); i 超越概率2%(常德, 方案3)

Fig. 8 Contribution of different magnitude-distance bins to PGA hazard with different probability levels in Zhuzhou and Changde.

图9 常德、株洲不同方案的地震动峰值加速度超越概率曲线的对比

Fig. 9 Comparison of mean-hazard curves of ground motion peak acceleration in Changde and Zhuzhou for different schemes.

图10 太平洋工程地震中心验证概率地震危险性算例的示意图(数据集1、案例10)

Fig. 10 Schematic diagram of Validation Example of Probabilistic Seismic Hazard analysis in PEER(Set 1, Case 10).

图11 太平洋地震工程中心概率地震危险性算例验证(数据集1, 案例10)

Fig. 11 Verification of Probabilistic seismic hazard calculation example in Pacific Earthquake Engineering Center(Set 1, Case 10).

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