Simulation of Broadband Ground Motion in Yangbi Earthquake by Integrating Spectral Element Method and Artificial Neural Network
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摘要: 宽频带地震动模拟是工程地震中的关键科学问题，针对现有方法在低频物理建模与高频随机成分的结合中存在频谱不匹配和能量相位冲突的问题，提出一种基于谱元法（SEM）的模拟与基于人工神经网络（ANN）的宽频带地震动模拟方法.首先建立中国强震动记录Flatfile训练短周期反应谱的非线性映射关系，其次采用谱元法模拟低频地震动，并通过调幅因子缩放高频随机成分，最终根据能量校准获得宽频带地震动时程.以漾濞MS6.4地震为例，利用反演得到的有限断层模型和精细三维速度结构模型，模拟得到起伏地表观测点的低频地震动时程，使用以上方法合成对应的宽频带模拟时程.宽频带模拟加速度时程、峰值地震动与观测记录均具有较好的一致性，可应用于区域地震危险性评估.Abstract: Broadband ground motion simulation is a critical issue in engineering seismology. As traditional methods often face issues of spectral mismatch and energy phase conflicts when combining low-frequency physics-based modeling with high-frequency stochastic components, this paper introduces a hybrid method that integrates artificial neural network (ANN) with spectral element method (SEM). The ANN is trained on the Strong Motion Flatfile of China to capture the nonlinear mapping of short-period response spectra, while the SEM is employed to simulate low-frequency ground motions. High-frequency stochastic components are optimized using scaling factors, and energy alignment is applied to synchronize low- and high-frequency time histories, ensuring stable broadband simulation results. Taking the Yangbi MS6.4 earthquake as a case study, a finite fault model derived from inversion and a refined 3D velocity structure model are used to generate low-frequency time histories for monitors. The broadband method is then applied to produce corresponding broadband simulation time histories. The results demonstrate that the simulated broadband acceleration time histories exhibit strong consistency with observed records, providing reliable and realistic inputs for seismic hazard analysis.
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图 1 选取的CNF记录震中分布以及震级‒距离分布
Fig. 1. Epicenter locations of the selected strong motion flatfile of China and distribution between magnitude vs. rupture distance
图 3 东西向分量两个版本的ANN模型在归一化周期下的性能检验
SAANN代表ANN模型预测得到的反应谱幅值，SAObs表示训练前数据库内的观测值.训练集、验证集和测试集使用不同灰度的颜色表示
Fig. 3. Two of ANN performance in predicting the EW component of the CNF, in which SAANN denotes the response spectral ordinates predicted by the ANN and SAObs is the observed ones
图 4 宽频带、低频数值模拟和高频随机方法得到的加速度反应谱(a)和傅里叶幅值谱对比(b)
Fig. 4. Comparison of spectral (a) and Fourier amplitude of acceleration (b) from broad-band, low frequency simulation, and high-frequency stochastic methods
图 5 宽频带、低频数值模拟和高频随机方法加速度、速度和位移时程的对比
Fig. 5. Comparison of time histories of acceleration, velocity, and displacement from broad-band, low-frequency simulation, and high-frequency stochastic methods
图 6 漾濞地震模拟区域震中及区域内台站的位置分布和计算模型示意图
IDP.印度板块；SYRB.四川‒云南菱形块体；SCB.四川盆地；YA.扬子块体；F1.澜沧江断层；F2.维西‒乔后‒巍山断层；F3.红河断层
Fig. 6. Epicenters and stations of the Yangbi earthquake series and the computational region
图 7 有限断层的(a)滑动量、(c)τ和(e)Trup分布，以及断层的(b)矩函数MF，(d)矩率函数MRF和(f)MRF的FAS
虚线对应的值为τ的倒数
Fig. 7. Distribution of (a) slip, (c) randomized rise time (τ) and (e) rupture time (Trup) on the fault plane, and (b) the total Moment Function (MF) on the fault plane, (d) the corresponding Moment Rate Function (MRF) and (f) the Fourier amplitude spectrum of the MRF
图 8 六个台站模拟的位移、速度、加速度时程和速度时程的FAS与观测记录的对比
Fig. 8. Comparison of simulated displacement, velocity, acceleration and Fourier amplitude spectra (FAS) of velocity and recordings at six stations
图 9 模拟记录PGA、PGV、PGD和SA3s随断层投影距的衰减
Fig. 9. Comparison of simulated and observed PGA, PGV, PGD and spectral acceleration SA at 3 s in natural log units plotted as a function of RJB for the GMH component and the UD component
图 10 低频模拟地震烈度和宽频带地震烈度分布
Fig. 10. Distribution of intensity for low-frequency simulation and broadband simulation
表 1 速度结构模型
Table 1. Velocity structure model
层数 密度
(t/m3)VP (m/s) QP VS(m/s) QS 厚度H (m) 谱自由度 1 1.74×VP0.25 1 330+42×Z0.5 $ \frac{{V}_{\mathrm{P}}}{10} $ 700+42×Z0.5 $ \frac{{V}_{\mathrm{S}}}{10} $ 2 500 4 2 2.67 4 850 485 2 800 280 1 500 4 3* 2.74 6 100 610 3 550 355 21 000 4 注：Z代表土层的深度，星号表示震源所在层. 
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表 2 运动学震源模型参数
Table 2. Parameters of the kinematic seismic source model
震源参数 矩震级MW 6.1 地震矩M0(N·m) 1.43×1018 震中
(纬度, 经度)(25.66°, 99.87°) 震源深度(km) 11.2 断层长度L(km) 36 断层宽度W(km) 18 走向角(°) 136 倾角(°) 83 上升时间τ(s) 0.38 子断层尺寸(m) 125 滑动角平均值(°) -192 破裂速度VR (km/s) 2.2 断层滑动分布(m) 朱音杰等(2022), 见图 7 震源时间函数 指数函数，见图 7
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