The Characteristics of Co-seismic and Post-seismic Surface Deformation of Destructive Earthquakes and Its Significance in Engineering Seismic Resistance
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摘要: 地震地表变形会对基础设施造成巨大破坏，如何减轻其造成的破坏，成为设计人员关注的重点。本文在自行整理我国自1900年以来有同震地表破裂的地震案例基础上，将数据分为逆断层型、正断层型与走滑断层型3类，分别进行最小二乘法分析，得到不同断裂类型的震级与地震破裂参数及其位移量之间的关系式，同时针对我国西部地区震级与地震破裂参数的回归关系式进行了讨论；并对搜集到的我国21例震后地表形变监测数据进行讨论。结果显示，同震阶段的拟合公式相关系数较大，标准偏差较小，所得经验关系更接近中国地质实际情况；震后2年内近场形变量大多位于5～7cm、震后10 年内近场地表形变量大多位于8～10cm；说明可以定量及半定量的分析同震、震后破裂参数，为地震易发区穿越潜在活动断层的基础设施设计以及安全性评价提供参考依据。Abstract: Surface deformation caused by earthquakes can cause tremendous damage to infrastructure, and how to mitigate such damage has become a major concern for designers. Based on self-compiled cases of earthquakes with coseismic surface ruptures in China since 1900, this paper classifies the data into three types: reverse fault, normal fault, and strike-slip fault. Least squares analysis is performed separately for each type to derive the relationship between the magnitude of earthquakes, seismic rupture parameters, and their displacement. Meanwhile, the regression relationship between the magnitude of earthquakes and seismic rupture parameters in western China is discussed. Furthermore, 21 cases of post-earthquake surface deformation monitoring data collected in China are analyzed. The results show that the fitting formulas for the coseismic stage have high correlation coefficients and low standard deviations, indicating that the empirical relationships obtained are closer to the actual geological conditions in China. Within two years after the earthquake, the near-field deformation is mostly within 5～7 cm, and within 10 years after the earthquake, the near-field surface deformation is mostly within 8～10 cm. This indicates that coseismic and post-seismic rupture parameters can be analyzed quantitatively and semi-quantitatively, providing a reference for the design and safety evaluation of infrastructure crossing potential active faults in earthquake-prone areas.
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图 1 震级与各破裂参数拟合曲线图
Figure 1. The fitting curve graph of earthquake magnitude and various rupture parameters
图 2 西部地区震级与各破裂参数拟合曲线图
Figure 2. The fitting curve graph of earthquake magnitude and various rupture parameters in the western region
图 3 震级与震后2年内、震后10年内近场地表最大形变量关系图
Figure 3. Relationship between earthquake magnitude and maximum surface deformation in the near field within 2 years and 10 years Post-Earthquake
表 1 同震破裂参数经验关系回归数据表
Table 1. Regression Data Table for Empirical Relationships of Co-seismic Fracture Parameters
回归方程形式 滑动类型 地震数目 系数和标准误差 标准偏差 相关系数 a （sa） b （sb） $ \log L=a+b\times {M}_{\text{s}} $ 逆断层 16 −2.67（0.53） 0.60（0.07） 0.23 0.82 正断层 11 −2.98（0.79） 0.60（0.11） 0.16 0.76 走滑断层 42 −3.14（0.51） 0.65（0.07） 0.28 0.67 所有样本 69 −3.04（0.36） 0.64（0.05） 0.26 0.69 $ \log W=a+b\times {M}_{s} $ 逆断层 10 −5.72（1.38） 0.97（0.18） 0.46 0.77 正断层 11 −1.67（0.52） 0.41（0.07） 0.11 0.77 走滑断层 21 0.85（2.19） 0.07（0.29） 0.69 0.002 所有样本 42 −2.49（1.09） 0.53（0.15） 0.58 0.23 $ \log D=a+b\times {M}_{\text{s}} $ 逆断层 12 −2.60（0.49） 0.44（0.06） 0.19 0.80 正断层 10 −0.24（0.18） 0.11（0.02） 0.03 0.72 走滑断层 22 −2.10（0.41） 0.36（0.05） 0.14 0.68 所有样本 44 11.06（5.20） 1.91（0.71） 3.0 0.14 $ \log (DL)=a+b\times {M}_{\text{s}} $ 逆断层 12 −4.71（0.69） 0.98（0.05） 0.26 0.91 正断层 10 −3.41（0.83） 0.75（0.11） 0.17 0.83 走滑断层 22 −4.68（0.78） 0.96（0.10） 0.28 0.80 所有样本 44 −4.77（0.46） 0.97（0.06） 0.27 0.84 $ \log (L{D}^{2})=a+b\times {M}_{\text{s}} $ 逆断层 12 −7.32（1.02） 1.41（0.14） 0.39 0.91 正断层 10 −6.59（1.61） 1.39（0.23） 0.33 0.81 走滑断层 22 −6.78（1.02） 1.32（0.13） 0.37 0.81 所有样本 44 −6.33（0.75） 1.29（0.10） 0.44 0.78 
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表 2 西部地区同震破裂参数经验关系回归数据
Table 2. Regression data table for empirical relationships of co-seismic fracture parameters in western regions
回归方程形式 地震数目 系数和标准误差 标准偏差 相关系数 a （sa） b （sb） $ \log L=a+b\times {M}_{s} $ 61 −3.07（0.37） 0.65（0.05） 0.27 0.72 $ \log D=a+b\times {M}_{s} $ 42 −2.07（0.45） 0.36（0.03） 0.26 0.45 $ \log (DL)=a+b\times {M}_{s} $ 42 −5.08（0.72） 1.01（0.09） 0.41 0.72 $ \log (L{D}^{2})=a+b{\times M}_{s} $ 42 −7.16（1.11） 1.38（0.15） 0.65 0.66
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