Composition and amplitude-frequency characteristics of ground motion acceleration based on fast Fourier transform analysis
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摘要: 根据2008年汶川MS8.0地震广元曾家台(GYZJ)的强震记录，运用Matlab软件对东西向55—75 s的加速度时程进行快速傅里叶变换，得到有限复傅里叶系数，从而将离散的加速度记录转化为加速度随时间变化的函数表达式. 该表达式中包含了50组不同频率的正弦波和余弦波，由此确定了地震波加速度的主要构成. 经回归分析可知, 函数计算值与原始记录的相关系数R为0.9，拟合程度良好； 利用SeismoSignal软件对地震波加速度时程进行谱分析，结果表明在原来的波中频率约为2.8 Hz的谐振分量振幅最大且0—10 Hz这一频段的波最为丰富. 这一结果与函数表达式中频率与振幅的分布基本吻合, 为深入研究汶川地震的动力特性及其对山体动力效应的分析提供了重要的理论依据，具有广阔的应用前景.Abstract: This paper analyzed the strong ground motion records of the 2008 Wenchuan MS8.0 earthquake at the station GYZJ, and used Matlab software to carry on the fast Fourier transform on the acceleration records of E--W component in 55—75 s, and then obtained a function expression of the acceleration variation with time. The expression contains 50 groups of sine and cosine waves with different frequencies, which are the main composition of the seismic wave. A correlation coefficient of 0.9 deduced from regression analysis shows well fitting between the calculated values and observed records. In addition, we used the SeismoSignal software to analyze the spectrum of the ground motion acceleration. Our results show that the harmonic component with frequency of 2.8 Hz in the original wave has the maximum amplitude and a dominant range of seismic waves has a frequency band of 0—10 Hz. These results generally agree well with the frequency and amplitude distribution of the functional expression. This paper provides an important theoretical basis for the research of wave characteristics and the analysis on the dynamic effect of slope in Wenchuan earthquake.
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图 1 地震台站分布与2008年汶川MS8.0地震地质灾害区划的对应关系(据王秀英等 (2010)修改)
Figure 1. Distribution of ground motion observation stations and their relationship with zonation map of geologic disasters induced by the 2008 Wenchuan MS8.0 earthquake (revised after Wang et al,2010)
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图 2 广元曾家台(GYZJ)记录到的汶川地震未校正加速度时程(东西向)
Figure 2. Uncorrected acceleration time history of Wenchuan earthquake at GYZJ station (EW component)
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图 3 广元曾家台接收到的汶川地震加速度能量在时域上的分布图
Figure 3. Distribution characteristics of acceleration energy of Wenchuan earthquake at GYZJ station in the time domain
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图 4 广元曾家台记录的55—75 s时段汶川地震东西向加速度时程
Figure 4. A section of acceleration time history of Wenchuan earthquake at GYZJ station (EW component) in the time period of 55-75 s
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图 5 广元曾家台在截取时段上的原始加速度时程与拟合函数曲线的对比图
Figure 5. Comparison of uncorrected acceleration observation curve (bule) and fitted function curve (red) recorded at GYZJ station in the time period 55-75 s
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图 6 广元曾家台记录的原始加速度值与拟合函数值的残差分布图
Figure 6. Distribution of residuals between original acceleration values recorded at GYZJ station and its fitted function values
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图 7 广元曾家台加速度记录的傅里叶幅值谱
Figure 7. Fourier amplitude spectrum of acceleration records at GYZJ station
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图 8 广元曾家台加速度记录的傅里叶功率谱
Figure 8. Fourier power spectrum of acceleration records at GYZJ station
表 1 广元曾家台加速度记录的有限复傅里叶系数
Table 1 The finite complex Fourier coefficients of acceleration records at GYZJ station
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