Study on the rupture directivity of the 2021 Yangbi earthquake sequence
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摘要:
基于2021年云南漾濞MS6.4地震序列的强震动记录，建立了地震动参数预测方程，采用破裂方向性效应拟合方法估计了强震动记录丰富且空间分布均匀的九次地震的震源破裂方向性特征。结果表明：其中的四次地震（1号、4号、8号、9号）表现出破裂方向性效应，且均为不均匀双侧破裂，但优势破裂方向不同（4号和8号为东南向，1号西北向，9号西南向），说明2021年漾濞地震序列的地震破裂较为复杂；由于主震（4号地震）的破裂速度较慢（约为2.2 km/s），其破裂方向性效应较弱且主要对峰值速度有影响，其它三次地震破裂方向性效应十分显著，破裂速度大于主震；此外，四次地震的破裂方向性效应还存在一定的周期相关性。
Abstract:This study used the strong-motion recordings of the MS6.4 Yangbi earthquake sequence in Yunnan Province to establish the prediction equations of ground motion parameters, and then estimated the focus rupture directivities characteristics for nine Yangbi earthquakes with abundant recordings in a good spatial station coverage based on the rupture directivity effect fitting method. The results indicated that the rupture directivity effects are observed in four of these earthquakes （i.e., the 1st, 4th, 8th, and 9th earthquakes）. The four earthquakes are all characterized by the bilateral ruptures with various predominant rupture directions （i.e., southeast for the 4th and 8th events, northwest for the 1st event, and southwest for the 9th event）, which illustrates the rupture complexities of the Yangbi earthquake sequence. Since the estimated rupture velocity （about 2.2 km） of the mainshock （the 4th event） is very slow, its rupture directivity effects are not strong and mainly affect the peak ground velocity. However, the rupture directivity effects for the other three earthquakes are very strong and the rupture velocities are faster than that of the mainshock. The dependency of the rupture directivity effects on the period was also observed in the four earthquakes.
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图 1 （a） 用来建立地震动预测方程的记录所对应的震级-距离分布图；（b）可用记录数随周期的变化
Figure 1. （a） Magnitude-distance distribution of the recordings for developing ground motion prediction equations； （b） The number of the usable recording varied with the period
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图 2 PGA和PGV观测值随距离衰减及其预测中位值
Figure 2. The distance attenuation of the observed PGA and PGV values with distance and the predicted medians
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图 3 本文选用的9次地震及其记录的台站空间分布
Figure 3. The nine earthquakes analyzed in this study and the spatial distribution of stations for each event
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图 4 PGA距离校正事件内残差随方位角的变化以及Cd最佳拟合结果
Figure 4. The path-corrected intra-event residuals varied with azimuth for PGA in each event and the azimuthal dependence of the best-fitted Cd
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图 5 PGV距离校正事件内残差随方位角的变化以及Cd最佳拟合结果
Figure 5. The path-corrected intra-event residuals varied with azimuth for PGV in each event and the azimuthal dependence of the best-fitted Cd
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图 6 基于不同地震动强度指标给出的$\max C_{\rm{d}}^{0.5}/\min C_{\rm{d}}^{0.5} $，纵坐标数值表示不同周期的PSA
Figure 6. The $\max C_{\rm{d}}^{0.5}/\min C_{\rm{d}}^{0.5} $ values based onvarious ground motion intensity measures，numbers on the ordinate indicate the period of PSA
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图 7 基于不同周期PSA估计的破裂方向及其标准差范围
Figure 7. Rupture directions and standard deviations based on PSAs at various periods
表 1 地震动参数预测方程回归系数及标准差
Table 1 Regression coefficients and standard deviations of the parameter prediction equations of ground motion
地震动强度指标 回归系数 a1 a2 a3 a4 a5 a6 a7 φ τ σ PGA 2.907 4 −0.089 5 0.028 5 −1.719 0 0.142 1 −0.009 6 −0.085 5 0.340 8 0.192 4 0.391 4 PGV 2.226 0 −0.106 2 0.046 6 −1.481 1 0.099 0 −0.008 6 −0.521 2 0.358 9 0.244 6 0.434 3 PSA T＝0.10 s 2.581 5 0.066 6 0.026 1 −1.456 6 0.043 9 −0.005 4 −0.023 1 0.357 2 0.171 4 0.396 2 T＝0.15 s 2.650 7 0.082 0 0.025 9 −1.081 5 0.041 3 −0.008 2 −0.241 3 0.368 8 0.205 0 0.421 9 T＝0.20 s 2.818 1 0.090 8 0.029 2 −1.117 1 0.027 4 −0.006 6 −0.333 8 0.419 9 0.230 2 0.478 9 T＝0.26 s 2.902 3 0.030 4 0.042 1 −0.963 7 −0.000 5 −0.006 7 −0.405 1 0.456 1 0.237 0 0.514 0 T＝0.30 s 2.764 9 0.046 3 0.044 1 −0.900 2 −0.013 7 −0.006 5 −0.426 5 0.448 0 0.230 3 0.503 7 T＝0.36 s 3.021 2 0.068 7 0.043 0 −1.003 7 −0.008 1 −0.005 4 −0.556 9 0.424 4 0.224 9 0.480 3 T＝0.40 s 3.165 0 0.103 1 0.039 3 −1.1328 0.005 1 −0.005 3 −0.624 6 0.420 0 0.223 8 0.475 9 T＝0.46 s 2.810 6 0.198 6 0.037 9 −0.977 2 −0.050 5 −0.003 7 −0.637 0 0.404 7 0.230 9 0.465 9 T＝0.50 s 2.657 4 0.251 2 0.034 4 −0.949 4 −0.059 6 −0.004 0 −0.646 8 0.403 3 0.232 5 0.465 5 T＝0.60 s 2.190 3 0.343 8 0.036 4 −0.735 3 −0.130 6 −0.001 5 −0.654 1 0.402 5 0.244 5 0.470 9 T＝0.70 s 2.026 6 0.344 0 0.035 3 −0.619 7 −0.124 0 −0.003 1 −0.677 0.400 3 0.241 0 0.467 2 T＝0.90 s 1.713 3 0.364 3 0.034 4 −0.429 3 −0.142 6 −0.002 0 −0.721 1 0.403 5 0.246 0 0.472 6 T＝1.00 s 1.416 7 0.430 2 0.028 6 −0.294 7 −0.147 7 −0.003 0 −0.749 4 0.411 8 0.232 4 0.472 9 T＝1.50 s 1.015 6 0.548 5 0.018 0 −0.079 2 −0.155 4 −0.001 9 −0.919 5 0.457 7 0.260 7 0.526 7 
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表 2 震级相关的h值
Table 2 Magnitude-dependent h values
M h M h M h M h 2.8—3.5 1.00 3.6—3.7 1.05 4.0—4.5 1.10 4.6—4.7 1.20 5.0 1.50 5.2 1.50 5.6 2.00 6.4 3.90
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表 3 选用的9次地震的基本信息及记录数
Table 3 Basic information and the number of recordings for the nine events considered
地震编号 发震时刻（北京时间） MS 北纬/° 东经/° 震源深度/km 记录数 年-月-日 时:分:秒 1 2021-05-19 20:05:56 4.6 25.65 99.91 10 50 2 2021-05-21 21:21:25 5.6 25.65 99.92 10 96 3 2021-05-21 21:21:57 4.2（ML） 25.63 99.96 10 50 4 2021-05-21 21:48:34 6.4 25.70 99.88 10 100 5 2021-05-21 21:55:28 5.0 25.67 99.89 9 62 6 2021-05-21 22:31:10 5.2 25.61 99.97 8 97 7 2021-05-21 23:23:34 4.5 25.59 99.98 9 72 8 2021-05-22 02:28:43 4.2（ML） 25.63 99.92 19 37 9 2021-05-22 20:14:36 4.7 25.60 99.92 10 63
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表 4 基于PGA，PGV分别估计的地震破裂方向性参数
Table 4 Rupture directivity parameters estimated based on PGA and PGV，respectively
地震编号 峰值参数 φ/° vr/β k $ {\max C_{\rm{d}}^{0.5} }$ ${\min C_{\rm{d}}^{0.5} } $ ${{\max C_{\rm{d} }^{0.5} }/{\min C_{\rm{d} }^{0.5} } }$ 1 PGA 316.0±11.4 0.93±0.04 0.96±0.03 3.73 0.75 4.95 PGV 309.0±33.6 0.70±0.16 0.86±0.10 1.70 0.80 2.14 2 PGA 296.1±51.4 0.61±0.16 0.68±0.10 1.32 0.83 1.59 PGV 220.6±38.4 0.64±0.10 0.88±0.14 1.56 0.79 1.97 3 PGA 119.0±69.9 0.58±0.17 0.27±0.16 1.31 0.83 1.59 PGV 130.3±104.2 0.64±0.19 0.27±0.15 1.44 0.82 1.75 4 PGA 233.1±58.6 0.63±0.14 0.78±0.14 1.45 0.82 1.78 PGV 167.1±6.8 0.62±0.04 0.82±0.04 1.42 0.81 1.82 5 PGA 247.1±108.1 0.51±0.14 0.71±0.15 1.21 0.82 1.47 PGV 197.4±82.4 0.68±0.18 0.72±0.18 1.50 0.83 1.81 6 PGA 99.4±55.6 0.66±0.17 0.19±0.17 1.55 0.81 1.92 PGV 130.2±64.9 0.70±0.17 0.24±0.17 1.59 0.82 1.94 7 PGA 114.6±41.9 0.63±0.13 0.34±0.14 1.34 0.83 1.61 PGV 97.1±51.4 0.64±0.15 0.22±0.14 1.47 0.82 1.80 8 PGA 149.8±21.9 0.76±0.10 0.87±0.11 1.90 0.80 2.39 PGV 155.6±19.9 0.84±0.12 0.93±0.09 2.43 0.77 3.16 9 PGA 244.4±11.2 0.65±0.08 0.87±0.06 1.57 0.80 1.98 PGV 242.5±18.7 0.70±0.13 0.87±0.08 1.73 0.79 2.18
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