Estimation of High-Frequency Wave Radiation Areas of Wenchuan Earthquake by the Envelope Inversion of Acceleration Seismograms and Synthesis of Near-Field Accelerograms
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摘要: 合理地估计汶川破坏区域的地震动有助于地震灾害的研究.通过利用芦山地震记录建立的加速度包络衰减关系和汶川地震近场30个台站的加速度包络，基于线源模型，采用差分进化方法反演了汶川地震断层面上高频 (＞1 Hz) 辐射区域分布.结果表明：断层面上高频辐射分布很不均匀，辐射较强的区域主要位于：(1) 产生较大地表破裂的映秀、北川和南坝区域；(2) 映秀和北川等凹凸体的周边区域，包括震中东北侧60~90 km区域、北川和南坝东北侧30 km处；(3) 断层破裂停止的东北端约30 km长的区域.其中，破裂贯穿到地表的映秀、北川和南坝是低频和高频辐射都很强的区域.对于无观测记录场点，选择其临近且场地条件类似的台站加速度提取平稳随机过程，结合高频辐射分布和衰减关系得到的包络，合成了加速度时程，可为汶川地震结构震害分析提供地震动输入.Abstract: It s helpful for studying earthquake disaster by estimating seismic oscillation reasonably in Wenchuan area. Based on the line source model, the high-frequency ( > 1 Hz) wave radiation areas on the Wenchuan earthquake fault plane are inversed by the differential evolution method, using the acceleration envelopes attenuation relationship of Lushan earthquake and envelopes of 30 near-field stations acceleration seismograms in Wenchuan earthquake. The results indicate that the high-frequency wave radiation areas are very nonuniform, with most of the High-frequency waves radiated in: (1) the surface rupture areas, including Yingxiu, Beichuan and Nanba areas; (2) the areas close to the boundaries of the asperities, including that with epicentral distance from 60 to 90 km northeast of epicenter, and areas 30 km northeast of Beichuan and Nanba; (3) the area within 30 km length near the fault northeastern tip. Both high and low frequency wave radiation were much higher in areas with large surface rupture. Utilizing the inversed high-frequency wave radiation areas and the acceleration envelopes attenuation relationship, near-field accelerations are synthesized. The accelerations in areas with no seismic records are synthesized by the synthetic envelopes and a stationary stochastic process extracted from its near station with similar site conditions. The results could be used as the earthquake input for analyzing seismic damage of structures in Wenchuan earthquake.
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图 1 (a) 线源模型示意图；(b)51AXT台的东西向加速度包络
a.红色五角星表示震中，蓝色圆表示子断层，倒三角表示子震；b.右上图为线源模型中每个子断层在51AXT产生的包络，右下图为51AXT台观测包络及合成包络
Fig. 1. (a) Schematic diagram of the line source model. (b) Acceleration envelope of EW component at the station 51AXT
图 3 本文震中距与包络参数t1、ts和C的关系与霍俊荣 (1989)、肖亮 (2011)相应结果的对比
黑色表示霍俊荣的结果，褐色表示肖亮的结果，红色表示本文南北向结果，蓝色表示本文东西向结果
Fig. 3. Comparison about the relation of envelope parameters t1, ts and C to epicentral distance in the article, Huo (1989) and Xiao (2011)
图 4 汶川地震线源模型及所用30个近场台站分布
Fig. 4. Line source model of Wenchuan earthquake and the distribution of 30 near-filed stations
图 5 子断层间隔为10 km, 15 km和20 km时，不加噪声与加10%噪声反演得到的子震个数与输入模型对比
Fig. 5. Comparison about subsource number between input model and the inversion result under the condition of noiseless or 10% noise for the subfault interval 10 km, 15 km and 20 km
图 8 子断层包含子震的分布
3个红色小三角形分别表示映秀、北川和南坝地区
Fig. 8. The distributions of the subsources in the fault plane
图 6 合成包络与观测包络残差对应迭代次数的变化
Fig. 6. The variation of the residue between synthetic and observed envelopes versus iterations
图 7 观测包络与合成包络对比
实线表示观测包络，虚线表示合成包络，每幅图的上侧字母表示台站及分量
Fig. 7. Comparison of the observed and the synthetic envelopes
图 9 51AXT台、映秀和北川合成加速度记录及反应谱
Fig. 9. The synthetic accelerations and their response spectra at 51AXT station, Yingxiu and Bei chuan
表 1 芦山地震43个台站位置及震中距
Table 1. Locations and epicentral distance of the 43 stations of Lushan earthquake
台站代码 经度 (E) 纬度 (N) 震中距 (km) 51BXD 102.81° 30.37° 16.5 51BXZ 102.89° 30.47° 21.8 51BXM 102.71° 30.38° 25.7 51BXY 102.90° 30.53° 27.8 51YAM 103.11° 30.07° 28.1 51LSF 102.90° 30.02° 29.8 51QLY 103.27° 30.41° 32.9 51YAD 103.01° 29.98° 34.2 51HYT 103.37° 29.91° 58.1 51PJW 103.65° 30.30° 67.1 51KDZ 102.18° 30.12° 77.1 51XJW 102.64° 30.96° 81.4 51HYQ 102.62° 29.58° 84.8 51HYY 102.45° 29.65° 86.0 51XJD 102.36° 31.00° 97.6 51LDJ 102.21° 29.69° 98.1 51KDT 101.96° 30.05° 99.1 51DJZ 103.59° 31.02° 102.3 51PXZ 103.76° 30.91° 103.7 51CDZ 104.09° 30.56° 113.4 51HYW 102.90° 29.22° 118.2 51KDG 101.57° 29.96° 137.7 51DFB 101.48° 30.48° 142.9 51KDX 101.50° 30.04° 143.1 51GLQ 102.77° 28.97° 147.8 51SFB 104.00° 31.28° 149.1 51MNW 102.28° 28.81° 177.1 51HSS 103.42° 31.94° 190.0 51MNC 102.24° 28.64° 195.3 51MNA 102.17° 28.61° 201.2 51MNJ 102.18° 28.55° 207.2 51MNT 102.16° 28.55° 208.3 51MNH 102.07° 28.46° 220.7 51LBH 103.79° 28.44° 220.9 51JYH 104.61° 31.77° 228.6 51LBD 103.57° 28.26° 232.8 51MNL 102.19° 28.29° 233.9 51JYT 104.75° 31.78° 238.4 51MNM 102.17° 28.20° 243.8 51MNZ 102.07° 28.20° 246.8 51JYW 104.78° 31.88° 248.8 51XCY 102.16° 27.74° 293.8 51YYJ 101.96° 27.72° 301.9 
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表 2 包络衰减关系的回归系数
Table 2. Regression coefficient of attenuation relationship of envelope
方向 参数 C1 C2 C3 R0(km) ε 东西 t1 -1.836 0.234 0.674 10 0.176 I0 -0.257 0.752 -1.721 10 0.247 ts -2.036 0.295 0.573 10 0.137 C 1.361 -0.221 -0.488 10 0.107 南北 t1 -1.303 0.145 0.730 10 0.101 I0 -0.396 0.716 -1.523 10 0.211 ts -2.073 0.334 0.439 10 0.129 C 1.321 -0.242 -0.405 10 0.104
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表 3 汶川地震30个台站位置及震中距、断层距
Table 3. The locations of 30 stations and their epicenter and fault distance
代码 经度 (E) 纬度 (N) 震中距 (km) 断层距 (km) 上盘 下盘 51WCW 103.18° 31.04° 18.0 16.1 是 51DXY 103.52° 30.59° 46.9 43.9 是 51LXT 103.45° 31.56° 64.0 43.6 是 51LXM 103.34° 31.57° 64.5 51.4 是 51QLY 103.27° 30.41° 65.1 43.4 \ \ 51BXY 102.91° 30.53° 66.4 10.8 \ \ 51SFB 103.99° 31.28° 68.1 14.0 是 51XJD 102.64° 30.97° 68.7 44.0 是 51LXS 102.91° 31.53° 73.7 74.9 是 51MXN 103.73° 31.58° 74.4 27.8 是 51PJW 103.63° 30.29° 82.0 76.2 是 51PJD 103.41° 30.25° 82.4 65.9 \ \ 51MZQ 104.09° 31.52° 91.0 0.2 是 51LSJ 102.93° 30.16° 101.1 49.3 \ \ 51AXT 104.30° 31.54° 108.3 11.2 是 51DYB 104.46° 31.29° 109.9 42.5 是 51HSL 103.26° 32.06° 119.4 98.1 是 51MXD 103.68° 32.04° 120.6 70.2 是 51JYH 104.63° 31.78° 149.2 11.3 是 51JYD 104.74° 31.78° 157.7 18.2 是 51SPA 103.64° 32.51° 171.1 112.6 是 51JYC 104.99° 31.90° 184.8 23.6 是 51SPC 103.62° 32.78° 200.5 136.8 是 51PWM 104.52° 32.62° 211.8 67.1 是 51JZW 104.21° 33.03° 240.6 121.2 是 51JZG 104.32° 33.12° 253.5 122.0 是 51CXQ 105.93° 31.74° 257.9 95.8 是 51GYS 105.84° 32.15° 268.0 55.2 是 62WUD 104.99° 33.35° 304.0 99.7 是 51GYZ 106.11° 32.62° 316.8 31.9 \ \
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表 4 采用4种不同破裂速度和5种不同时间间隔得到的合成包络与观测包络的残差
Table 4. Residue of synthetic and observed envelopes at 4 different rupture velocity and 5 time interva
vr(km/s) Δt(s) 0.6 0.8 1.0 1.2 1.4 2.6 257.7 258.1 258.4 257.2 257.8 2.8 243.5 241.9 240.8 241.1 240.2 3.0 239.9 234.4 232.5 229.2 230.2 3.2 239.8 233.1 229.0 224.5 227.3
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