Probabilistic Fault Displacement Hazard Analysis Based on Monte Carlo Simulation
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摘要:
同震位错对川藏铁路等跨断层工程的安全造成严重威胁，合理评价活断层的位错参数具有重要的应用价值.由于传统的确定性评价方法存在无法区分工程场点的重要程度和其在断层上的相对位置等缺陷，越来越多的学者推荐采用概率断层位错危险性分析（PFDHA）.然而基于经典的概率性方法开展PFDHA原理复杂且实现困难，不利于吸收断层地震活动性研究的最新成果，也有碍于PFDHA的普及和推广.相比经典的概率性方法，蒙特卡洛模拟具备逻辑清晰易懂、程序易于实现且兼容性和扩展性好的优点.本研究基于蒙特卡洛模拟实现了概率断层位错危险性分析的一般性算法，并将该方法应用于鲜水河断裂带的炉霍段.结果显示，PFDHA的结果随着超越概率水准或工程场点在断层上的相对位置的不同而显著变化.适当考虑最大同震位错和地表破裂长度的不确定性得到的位错参数更加合理.超越概率大于等于100年2%时，PFDHA的结果显著小于确定性方法的结果.然而随着断层活动性的提高，100年超越概率1%的结果可能会大于确定性方法的结果.按照不同类型工程的抗震设防水准选择相应的PFDHA评价结果，既有利于工程的安全，也有助于大多数工程节约成本.PFDHA相比确定性方法具备多种优势，有望为川藏铁路等重大工程的抗断参数评估提供技术支撑.
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关键词:
- 活动断层 /
- 概率断层位错危险性分析 /
- 蒙特卡洛模拟 /
- 炉霍断裂 /
- 地震学
Abstract:Coseismic displacement poses a serious threat to the safety of cross-fault projects such as the Sichuan-Tibet Railway, and a reasonable evaluation of the displacement parameters of active faults has important application value. Because traditional deterministic evaluation methods cannot distinguish the importance of engineering sites and their relative positions on the fault, more and more scholars recommend the use of probabilistic fault displacement hazard analysis (PFDHA). However, the principle of PFDHA based on classic probabilistic method is complicated and difficult to implement, which is not conducive to application of the latest results of fault seismic activity research, and it also hinders the popularization and promotion of PFDHA. Compared with the classic probabilistic method, Monte Carlo simulation has the advantages of clear and easy-to-understand logic, easy implementation, and good compatibility and scalability. In this study, a general algorithm for probabilistic fault displacement hazard analysis is realized based on Monte Carlo simulation, and the method is applied to the Luhuo section of the Xianshuihe fault zone. The results show that the results of PFDHA vary significantly with the level of exceeding probability or the relative position of engineering site points on the fault. The displacement parameters obtained by properly considering the uncertainty of the maximum displacement and surface rupture length are more reasonable. When the probability of exceedance is greater than or equal to 2% in 100 years, the results of PFDHA are significantly smaller than that of the deterministic method. However, as the fault activity increases, the result of 1% probability of exceeding in 100 years may be larger than that of the deterministic method. Selecting the corresponding PFDHA evaluation results according to the seismic fortification standards of different types of projects is not only beneficial to the safety of the project, but also helps to reduce the costs of most projects. Compared with the deterministic method, PFDHA has many advantages, and is expected to provide reasonable fault displacement parameters for major projects such as the Sichuan-Tibet Railway.
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图 1 基于蒙特卡洛模拟的概率断层位错危险性分析流程
Fig. 1. Flow chart of probabilistic fault displacement hazard analysis based on Monte Carlo simulation
图 2 破裂长度与震中到断层近端点距离的关系
图中O点为震中位置，S为根据式（9）算得的地表破裂长度
Fig. 2. Diagram of the relationship between the rupture length and the distance from the epicenter to its nearest end of the fault
图 3 不同模型的位错分布示意
图中O点为震中位置，S为根据式（9）算得的地表破裂长度
Fig. 3. Schematic diagram of displacement distribution of different models
图 4 鲜水河断裂的几何展布及其强震分布图（底图改自梁明剑等, 2020）
Fig. 4. The geometry and strong earthquakes distribution of the Xianshuihe fault (revised from Liang et al., 2020)
图 6 炉霍断裂中点处的位错均值超越概率曲线
Fig. 6. Exceeding probability curve of average displacement at the midpoint of Luhuo fault
表 1 炉霍潜在震源区的空间分布函数
Table 1. The spatial distribution function of the potential source area of Luhuo
震级档 M4.0~4.9 M5.0~5.4 M5.5~5.9 M6.0~6.4 M6.5~6.9 M7.0~7.4 M7.5以上 空间分布函数 0.006 64 0.004 86 0.007 55 0.005 10 0.008 34 0.025 81 0.064 07 
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表 2 炉霍断裂的概率断层位错危险性分析结果
Table 2. The results of probabilistic fault displacement hazard analysis of Luhuo fault
超越概率 目标点
位置（1）考虑不确定性时的位错值（m） （2）不考虑不确定性时的位错值（m） 三角形 正弦 椭圆 均值 三角形 正弦 椭圆 均值 50年2% A 3.522 3 4.485 2 5.191 6 4.399 7 3.763 8 4.726 1 5.434 7 4.641 5 B 2.899 4 3.806 7 4.635 0 3.780 4 3.047 6 4.085 2 4.927 1 4.020 0 C Nan Nan 0.014 0 Nan Nan Nan 0.015 0 Nan 100年2% A 5.378 9 6.750 4 7.562 5 6.563 9 5.612 7 7.227 5 7.568 4 6.802 9 B 4.660 7 5.908 1 6.966 6 5.845 1 4.531 7 5.708 7 7.289 0 5.843 1 C Nan 0.000 1 0.022 6 Nan Nan 0.000 1 0.021 3 Nan 100年1% A 7.091 9 8.779 4 9.643 1 8.504 8 6.915 6 8.436 0 9.639 6 8.330 4 B 6.361 4 7.844 7 8.904 5 7.703 5 6.252 8 7.600 7 8.108 5 7.320 7 C 0.000 1 0.000 2 0.032 4 0.010 9 0.000 1 0.000 1 0.029 8 0.010 0 注：目标点位置A、B和C分别代表断层中点处、断层长度¼处和近断层端点处.Nan表示无有效计算结果，此时3个模型的均值也记为Nan.
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