Broadband ground motion simulations applied to the Luding MS6.8 earthquake on September 5，2022 based on spectral element method
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摘要: 2022年9月5日12时52分四川甘孜州泸定县发生MS6.8地震，此次地震造成泸定县及其周边地域的严重破坏和人员的重大伤亡，为重现此次地震的地震动影响场，分析近场强地面运动的空间分布特征，将确定性的凹凸体震源模型与随机震源模型结合得到有限断层运动学混合震源模型，进而将上述混合震源模型开发到SPECFEM 3D谱元法开源代码中，实现了基于谱元法和运动学混合震源模型的泸定MS6.8地震的全过程宽频带（0.1—5 Hz）地震动模拟。首先，将模拟结果与6个台站的时程记录、对应的反应谱以及NGA-West2地震动衰减曲线进行比较，检验了方法的精度和适用性；进而给出了此次地震的三分量速度波场快照图，再现了地震波传播时近场地震动的方向性效应和局部场地效应；最后给出了泸定地区100 km范围内的地震动峰值加速度（PGA）和峰值速度（PGV）云图，分析了泸定地震下近场强地面运动的空间分布特征，并基于模拟结果给出了基于模拟结果的地震烈度分布图。结果显示，震中PGA接近600 cm/s2，PGV接近50 cm/s，烈度达到Ⅸ度，且由于泸定地区内高山峡谷地形对地震动的影响，地震动峰值在山顶和峡谷处明显放大，山顶处PGA和PGV分别放大1.9倍和1.5倍，峡谷谷底处PGA和PGV分别放大1.7倍和1.4倍，这里出现的地震放大现象以及可能造成的次生地质灾害亟需引起注意。Abstract: At 12:52 on September 5, 2022, a MS6.8 earthquake occurred in Luding County, Garze Prefecture, Sichuan Province. The earthquake caused severe damage and heavy casualties in Luding County and its surrounding areas. In order to reproduce the ground motion influence field of the earthquake and analyze the spatial distribution characteristics of near-field ground motion, the deterministic asperity source model is combined with the random source model to obtain the kinematic hybrid source model. Then, the hybrid source model is developed into the SPECFEM 3D, and the whole-process broadband （0.1−5 Hz） ground motion simulation based on the spectral element method and kinematic hybrid source model is realized. Firstly, the simulation results are compared with the time history records of six stations, the corresponding response spectra and the NGA-West2 ground motion attenuation curves to test the applicability of the method. Secondly, the three-component velocity wave field snapshots of the earthquake is given to reproduce the directional effect and local site effect of the near field when the seismic wave propagates. Finally, the peak acceleration （PGA） and peak velocity （PGV） maps of the ground motion in the range of 100 km centered on the Luding area are given, and the spatial distribution characteristics of the ground motion in the near field intensity under the Luding earthquake are analyzed. Based on the simulation results, the seismic intensity distribution map is given. The results show that the epicenter PGA and PGV is close to 600 cm/s2 and 50 cm/s, respectively, and the seismic intensity reaches Ⅸ degree. Due to the influence of mountain-canyon topography in Luding area on the ground motion, the peak of ground motion is significantly amplified at the top of the mountain and the bottom of the canyon, and the amplification of PGA and PGV at the top of the mountain is 1.9 times and 1.5 times, respectively. The amplification of PGA and PGV at the bottom of the canyon is 1.7 times and 1.4 times. Attention should be paid to the phenomenon of earthquake amplification and possible secondary geological disasters in mountain-canyon region.
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图 1 2022年泸定地震震中和震源机制解（中国地震台网中心，2022）及周边地区断裂带分布（Ma et al，2022）
Figure 1. The epicentral location and mechanism solution of the 2022 Luding earthquake （China Earthquake Networks Center，2022） and the distribution of the fault zones around Luding （Ma et al，2022）
图 2 2022年泸定MS6.8地震的运动学混合震源模型
（a） 凹凸体分布；（b） 混合滑动分布；（c） 破裂时间分布；（d） 上升时间分布
Figure 2. Hybrid kinematic source model of Luding MS6.8 earthquake in 2022
（a） Asperity distribution；（b） Hybrid slip distribution；（c） Rupture time distribution；（d） Rise time distribution
图 4 泸定地区包含起伏地形的三维波速结构模型
（a） 三维网格划分模型；（b） 地壳速度结构模型
Figure 4. 3D wave velocity structure model of Luding area including undulating surface
（a） Three-dimensional grid division model；（b） Crustal velocity structure model
图 5 台站加速度观测记录（红线）与模拟的加速度时程（黑线）对比
Figure 5. Comparison of acceleration time histories from simulation （black lines） with from recordings （red lines）
图 6 观测记录（红线）与模拟的伪加速度反应谱（黑线）结果对比
Figure 6. Comparison of pseudo spectral accelerations （PSAs） from simulation （black lines）with those recordings （red lines）
图 7 不同周期下模拟的加速度反应谱RotD50 （阻尼比为5%）和GMPEs对比结果
Figure 7. Comparison between the simulated acceleration response spectrum RotD50 results （damping ratio is 5%） and GMPEs under different periods
图 9 无地形PGA（a）与有地形PGV （b）的对比
Figure 9. Comparison of PGAs without terrain （a） with those with terrain （b）
图 10 无地形PGV（a）与有地形（b）的峰值速度PGV对比
Figure 10. Comparison of PGVs without terrain （a） with those with terrain （b）
图 11 沿地面高程的PGA和PGV放大倍数
Figure 11. PGA and PGV magnification along the ground elevation
图 12 地震烈度的模拟结果 （a）与实地调查结果 （b） 的对比
Figure 12. Comparison of seismic intensity results from simulation （b） with that from field investigation （b）
表 1 确定性大尺度宽频带地震动模拟实例
Table 1. Large-scale broadband ground motion simulation methods based on deterministic method
模拟方法 自由度数
或单元数网格尺寸
/m模型尺寸/km 模拟频率 模拟区域 参考文献 长 宽 高 间断伽辽金法 960亿 10 兰德斯，丹麦 Heinecke et al （2014） 有限差分法 23.4 万亿 8 147.84 140.4 58 18 唐山，中国 Fu et al （2017） 有限差分法 259亿 12.5 120 80 35 5 加利福尼亚，美国 Rodgers et al （2019） 有限差分法 2030亿 6.25 120 80 30 10 北加利福尼亚，美国 Rodgers et al （2020） 有限差分法 25 102 88 31 10 加利福尼亚，美国 Pitarka et al （2021） 有限差分法 单元数量
（150，486，336，000）8 147.84 140.4 58 5 加利福尼亚，美国 Hu et al （2022） 谱元法 135亿 35—130 44 44 63 10 阿尔戈斯托利，希腊 Touhami et al （2022） 
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表 2 2022年泸定MS6.8地震断层全局震源参数（中国地震台网中心，2022）
Table 2. Global parameters of Luding MS6.8 earthquake fault （China Earthquake Networks Center，2022）
走向/° 倾角/° 滑动角/° 破裂面长度/km 破裂面宽度/km 破裂起始深度/km 343 79 9 28 13 15.5
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表 3 泸定地震断层局部震源参数
Table 3. Local parameters of Luding earthquake fault
局部参数 单位 定标律* 参数值 最大
凹凸体面积Sm km2 lgSm＝lgS－0.80 57 平均错动量${\overline D_m}$ cm ${\lg {\overline D_m}＝\lg{\overline D}＋0.38}$ 206.5 长度Lm km lgLm＝lgL－0.48 9.5 宽度Wm km Wm＝Sm/Lm 6 沿走向中心Xm km lgXm＝lgL－0.32 13.5 沿倾向中心Ym km lgYm＝lgW－0.35 6 其它
凹凸体面积Sm0 km2 lgSm＝lgS－1.15 24.75 平均错动量${\overline D_{m0}}$ cm ${\lg {\overline D_m}＝\lg{\overline D}＋0.31} $ 175.8 长度Lm0 km lgLm＝lgL－0.69 5.5 宽度Wm0 km Wm＝Sm/Lm 4.5 沿走向中心X0 km X0＝0.44（L－Xm－0.5Lm）＋Xm＋0.5Lm 22.5 沿倾向中心Y0 km lgYm＝lgW－0.43 5
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