﻿ 用随机有限断层方法模拟2016-11-13新西兰M<sub>W</sub>7.8地震
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 大地测量与地球动力学  2019, Vol. 39 Issue (12): 1237-1242  DOI: 10.14075/j.jgg.2019.12.005

### 引用本文

LI Qicheng, HE Shugeng, MIN Ye, et al. Simulation of Amberley New Zealand November 13, 2016 MW7.8 Earthquake Using Stochastic Finite Fault Method[J]. Journal of Geodesy and Geodynamics, 2019, 39(12): 1237-1242.

### Foundation support

Liaoning Provincial Department of Education Project, No.LJYL040(551610001219);Guidance Plan for Key Research and Development Plans of Liaoning Province, No.2019000901.

### 第一作者简介

LI Qicheng, PhD, associate professor, majors in geophysics, E-mail:731732866@qq.com.

### 文章历史

1. 辽宁工程技术大学矿业学院，辽宁省阜新市中华路47号，123000;
2. 朝阳工程技术学校，辽宁省朝阳市凌河街四段483号，122000

1 随机有限断层理论

 $a(t) = \sum\limits_{i = 1}^l {\sum\limits_{j = 1}^n {{a_{ij}}} } \left( {t + \Delta {t_{ij}}} \right)$ (1)

 $\begin{array}{l} {A_{ij}}(f) = \left[ {\frac{{C{M_{0ij}}{{(2\pi f)}^2}}}{{1 + {{\left( {{f_{0ij}}} \right)}^2}}}} \right] \cdot \\ \left[ {\exp ( - \pi f\kappa )\exp \left( { - \frac{{\pi f{R_{ij}}}}{{Q\beta }}} \right)/{R_{ij}}} \right] \end{array}$ (2)

 $C = \frac{{{R_{{\theta _p}}} \cdot {\rm{FS}} \cdot {\rm{PRTITN}}}}{{4\pi {\rho \beta ^3}}}$ (3)

 $f_{0 i}(t)=N_{R}(t)^{-1 / 3} 4.9 E+6 \beta\left(\Delta \sigma / M_{0 i j}\right)^{1 / 3}$ (4)

 $D = 0.02{{\rm{e}}^{0.74M}} + 0.3R$ (5)

2 数据

 图 1 地震记录台站位置 Fig. 1 Locations of seismic station

 图 2 断层面的子断层和滑动位错分布 Fig. 2 The subfault and disloction distribution of each subfault

3 模拟结果

 图 3 12个地震台地震动记录和模拟时程 Fig. 3 Record and simulated time histories at 12 seismic station

 图 4 12个地震台站记录和模拟反应谱 Fig. 4 Record and simulated response spectra at 12 seismic station

 图 5 模拟误差随频率的变化(按图 2中的滑动分布) Fig. 5 The variation of the simulation error with the frequency(sliding distribution as shown in figure 2)

 图 6 准随机形成的子断层滑动位错分布 Fig. 6 The dislocation distribution of subfaults caused by quasi random method

 图 7 准随机形成的滑动分布模拟地震动结果误差随周期的变化 Fig. 7 The earthquake error simulated by quasi random slip distribution changes with period
4 结语

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Simulation of Amberley New Zealand November 13, 2016 MW7.8 Earthquake Using Stochastic Finite Fault Method
LI Qicheng1     HE Shugeng1     MIN Ye1     ZHENG Xinjuan2
1. School of Mining, Liaoning Technical University, 47 Zhonghua Road, Fuxin 123000, China;
2. Chaoyang Engineering Technical School, 483 Linghe Street, Forth Section, Chaoyang 122000, China
Abstract: Drawing on the known seismogenic structures of future large earthquakes, we propose to use empirical formulas to determine the parameters of length, width, seismic moment and sliding distribution of the large earthquake faults, and use the random finite fault method to predict future large earthquakes. Considering the MW7.8 earthquake that occurred in New Zealand on November 13, 2016, the ground motion time history and response spectrum of 12 bedrock stations, are simulated by stochastic finite fault method. The simulation error is determined by the average ratio of the simulated spectrum amplitude to the recorded spectrum amplitude. The results show that the period is in the range of 0-10 s and the simulation error is between 0.92-1.08. The standard deviation of the simulated error of different frequencies is not more than 1, and the width of 95% confidence interval has not changed significantly with the frequency. The simulation results reflect the average effect of ground motion records. Although a specific simulation may differ greatly from records, for engineering purposes we are interested in whether the simulation results are equivalent to the average results of seismic records. The quasi-random method is used to retrieve the initial rupture point and dislocation slip distribution of the New Zealand earthquake fault, simulate the ground motion, calculate the variation of simulation error with frequency, and obtain conclusions similar to those of the original model. This further confirms our proposed method of obtaining the seismic source parameters and the use of stochastic finite fault methods for the prediction of future large earthquakes is reliable, especially for the far-field simulation of large earthquakes.
Key words: earthquake; finite fault; stochastic method; simulation