Joint inversion of teleseismic and co-seismic InSAR data for the rupture process of the 2016 Kumamoto earthquake in Japan
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摘要: 为了深入认识2016年4月15日日本熊本地震破裂的复杂性，利用远场体波资料和同震InSAR资料联合反演了此次地震的震源破裂时空过程. 联合反演结果表明：熊本地震的震源破裂持续时间约为25 s，整个破裂过程释放的总标量矩为6.03×1019 N·m，对应于矩震级MW7.1；同震滑动主要集中分布于浅部，破裂以右旋走滑为主，但在沿倾向0—5 km范围内，破裂呈较强的正断特征；此次地震破裂的最大同震滑动量约为4.9 m，且最大同震位错区位于背离断层走向上、距离起始破裂点约5—10 km的区域；破裂前期（0—7 s），在倾向上向浅表发生破裂，在走向上向东北和西南两侧扩展；大约7 s后，破裂背离断层走向主要向东北方向扩展. 根据有限断层联合反演结果推测，此次熊本地震破裂可能出露至地表.Abstract: On April 15, 2016, a disastrous earthquake struck Kumamoto county in Japan. Aiming to further understand the complexity of the earthquake rupture in detail, we conduct a joint inversion of teleseismic waveforms and co-seismic InSAR data for the spatio-temporal rupture process of this earthquake. The results show that, the whole process lasted for about 25 s and released scalar moment up to 6.03×1019 N·m, corresponding to moment magnitude MW7.1. The major co-seismic slip distribution was centered in shallow region, and it was dominated by dextral strike. But the rupture had strong normal characteristics in the range of 0−5 km along the dip direction. The maximum co-seismic slip is about 4.9 m, and the major rupture patch was about 5−10 km away from the initial rupture point opposite to the strike direction. In the early stage （0−7 s）, it ruptured toward to the shallow region along the dip direction, and ruptured bilaterally along strike direction; about 7 s later, it ruptured toward to the northeast opposite to the strike direction. The joint inversion results suggest that the Kumamoto earthquake may rupture to the earth surface.
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图 1 熊本MW7.0地震区域构造及其破裂特征
Figure 1. Regional tectonic settings and rupture characteristics of the 2016 Kumamoto MW7.0 earthquake
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图 2 用于熊本地震破裂过程联合反演的远场体波台站分布（a）以及同震InSAR资料覆盖区域（b）
红色星形表示主震震中位置。图（a）中蓝色三角形表示台站；图（b）中红色方框表示InSAR覆盖区域，黑色框表示图1中的展示区域，黑色圆圈表示主震发生后一个月内MW≥4.0余震的震中分布（USGS，2016）
Figure 2. Distribution of used teleseismic stations （a） and co-seismic InSAR coverage （b） for joint inversion of rupture process of Kumamoto earthquake
The red star represents the mainshock epicenter. The blue triangles in Fig.（a） represent the stations. The red rectangular in Fig. （b） is the co-seismic coverage，the black rectangular delineates the region shown in Fig. 1，and black circles are the MW≥4.0 aftershocks within one month after the main shock （USGS，2016）
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图 3 有限断层联合反演中不同资料相对权重值搜索结果
Figure 3. Search result of relative weights between co-seismic InSAR data and teleseismic P waveforms for joint inversion
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图 4 基于远场体波资料和同震InSAR资料所得的熊本地震破裂过程联合反演结果
（a） 地震矩率函数；（b） 同震滑动分布，红色圆点表示起始破裂点
Figure 4. Joint inversion result of rupture process of the 2016 Kumamoto earthquake from teleseismic P waveforms and co-seismic InSAR data
（a） Seismic moment rate function; （b） Distribution of co-seismic slip，where the red dot indicates the initial rupture point
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图 5 熊本地震破裂过程滑动速率快照结果。红色圆圈表示起始破裂点位置
Figure 5. Snapshots of slip rate for the rupture process of the 2016 Kumamoto earthquake
The red circles are initial rupture points
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图 6 基于联合反演结果的观测波形（黑色）与合成波形（红色）比较
每幅子图波形的左侧从上至下依次为台站名、震中距（单位：°）和方位角（单位：°），右侧为合成波形与观测波形的相关系数
Figure 6. Comparison of the observed waveforms （black） with synthetic ones （red） based on joint inversion results
On the left side of the waveforms in each subplot are station code，epicentral distance （unit in °） and azimuth （unit in °），and on the right side is correlation coefficient between synthetic waveforms and observed ones
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图 7 同震InSAR观测资料与基于联合反演模型的InSAR合成资料对比
（a） 观测资料；（b） 合成资料；（c） 残差
Figure 7. Comparison of observed and modeled LOS displacements from interferogram
（a） Observations；（b） Model predictions；（c） Residuals
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图 8 熊本地震破裂过程远场体波单独反演结果及同震InSAR资料单独反演结果
（a） 远场体波反演得到的破裂过程地震矩率函数；（b） 远场体波反演得到的同震滑动分布；（c） 同震InSAR资料反演得到的同震滑动分布。图（b）中红色虚线方框尺度与图（c）相同
Figure 8. Inversion results of teleseismic waveforms and co-seismic InSAR data for the rupture process of the 2016 Kumamoto earthquake
（a） Seismic moment rate function from inversion result of teleseismic waveforms；（b） Distribution of co-seismic slip from inversion result of teleseismic waveforms；（c） Distribution of co-seismic slip from inversion result of co-seismic InSAR data. The geometric dimensions of the red dotted rectangular in Fig. （b） are the same as in Fig. （c）
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图 9 基于远场体波单独反演结果的观测波形（黑色）与合成波形（红色）比较
每幅子图波形的左侧从上至下依次为台站名、震中距（单位：°）和方位角（单位：°），右侧为合成波形与观测波形的相关系数
Figure 9. Comparison of the observed waveforms （black） and synthetic ones （red） based on the teleseismic body waveform inversion results
On the left side of the waveforms in each subplot are station code，epicentral distance （unit in °） and azimuth （unit in °），and on the right side is correlation coefficient between synthetic waveforms and observed ones
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图 10 基于同震InSAR数据单独反演结果的LOS合成资料与观测资料对比
（a） 观测资料；（b） 合成资料；（c） 残差
Figure 10. Comparison of observed and modeled LOS displacements from interferogram based on the coseismic InSAR data inversion results
（a） Observations；（b） Model predictions；（c） Residuals
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图 11 基于有限断层联合反演模型的熊本地震震源区东西向（左）、南北向（中）和垂直向（右）的地表同震位移变化估计
Figure 11. Estimation of the earth surface co-seismic displacements in E-W （left），N-S （middle） and vertical （right） directions in source region based on the joint inversion result of the rupture process of the 2016 Kumamoto earthquake
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