Difference Analysis of Site Dominant Frequencies Obtained from Response Spectra and Fourier Spectra of Earthquake Motion
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摘要: 强震动记录的HVSR法常用于评估场地卓越频率，计算强震动记录HVSR时常采用加速度反应谱或加速度傅里叶谱，但两者会给出不同的评估值。为揭示反应谱比和傅里叶谱比评估场地卓越频率的差异，本文选取日本KiK-net台网中场地条件可近似为一维场地模型的16个台站，以其获取的强震动记录开展场地卓越频率研究。首先提出了评估场地卓越频率的数据处理方法，主要包括S波截取、Taper预处理、基于高斯拟合的自动寻峰。探讨并给出了阻尼比、平滑的带宽系数取值对场地卓越频率评估的影响规律；对反应谱阻尼比取10%，对傅里叶谱平滑的带宽系数取20～40之间获取的场地卓越频率较为准确。然后对比分析了利用地震动加速度反应谱比和傅里叶谱比得到的场地卓越频率与场地土层模型计算得到的基于传递函数的自振频率。研究结果表明，对大多数台站而言，采用傅里叶谱比计算场地卓越频率具有明显的优势，对于Ⅱ、Ⅲ、Ⅳ类场地上的台站均有如此结论，只有对少数特定台站，采用反应谱比方法效果更好。Abstract: The Horizontal-to-Vertical Spectral Ratio (HVSR) method for strong motion records is commonly used to evaluate a site’s predominant frequency. Both the acceleration response spectrum and the acceleration Fourier spectrum are frequently employed to calculate the HVSR of strong motion records, but these two approaches often yield different results. To investigate the differences in predominant site frequency between the response spectrum ratio and the Fourier spectrum ratio, this study analyzes 16 stations from Japan’s KiK-net network, where site conditions can be approximated using a one-dimensional site model. First, data processing methods for evaluating site predominant frequency were developed. These include S-wave interception, taper preprocessing, and automatic peak identification based on Gaussian fitting. The effects of damping ratio and smoothed bandwidth ratio on site frequency evaluation were examined. It was found that using a 10% damping ratio for the response spectrum and a smoothing bandwidth ratio of 20~40 for the Fourier spectrum yielded more accurate results. Next, the predominant site frequencies obtained from the ground motion acceleration response spectrum and Fourier spectrum were compared with the natural frequency calculated from the site soil model using the transfer function. The results indicate that the Fourier spectrum ratio provides a more accurate estimate of the predominant site frequency compared to the response spectrum ratio for most stations, particularly those located on Class II, III, and IV sites. However, a few specific stations showed better results when using the response spectrum method.
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图 6 全区域高斯拟合和分段局部高斯拟合对比
Figure 6. Comparison between full-area Gaussian fitting and local Gaussian fitting
图 7 典型台站不同阻尼比取值的谱比图
Figure 7. Spectral ratios of typical stations with different damping ratio values
图 8 典型台站不同平滑的带宽系数取值谱比图
Figure 8. Spectrogram of different values of smooth bandwidth factor for typical stations
图 10 不同台站谱比曲线与传递函数对应状况
Figure 10. Correspondence between spectral ratio curves and transfer functions at different stations
表 1 16个选定台站详细信息
Table 1. Details of the 16 selected stations
台站名称 台站编号 纬度 经度 覆盖土层厚度/m 钻孔深度/m 场地分类 中国场地
分类类别选取强震动
记录数量/个VS30/(m·s−1) 类别 TAKAHAGI IBRH13 66°33'N 140°57'E 24 100 144 E Ⅱ 61 KASUMIGAURA IBRH17 36°08'N 140°31'E 235 510 335 D Ⅱ 38 TAMAYAMA IWTH02 39°82'N 141°38'E 19 102 168 E Ⅱ 55 KUJI-N IWTH08 40°26'N 141°78'E 20 100 301 D Ⅱ 27 KANEGASAKI IWTH24 39°19'N 141°01'E 56 150 390 C Ⅱ 12 RIKUZENTAKATA IWTH27 39°03'N 141°53'E 4 100 375 C Ⅱ 50 TSURUI-E KSRH06 43°22'N 144°42'E 70 237 240 D Ⅱ 21 HAMANAKA KSRH10 43°20'N 145°11'E 36 255 486 C Ⅱ 9 KAWANISHI NIGH11 37°17'N 138°74'E 56 205 237 D Ⅱ 4 UJIIE TCGH12 36°69'N 139°98'E 50 120 670 C Ⅱ 39 TAIKI TKCH08 42°48'N 143°15'E 36 100 326 D Ⅱ 21 YABUKI FKSH11 37°20'N 140°33'E 86 115 204 D Ⅲ 41 TSURUI-S KSRH07 43°13'N 144°32'E 82 222 305 D Ⅲ 22 IWAKI-E FKSH14 37°02'N 140°97'E 52 147 213 D Ⅲ 24 BEKKAI-E NMRH04 43°39'N 145°12'E 186 216 353 D Ⅳ 16 ISHIGE IBRH10 36°11'N 139°98'E 190 900 344 D Ⅳ 19 
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表 2 典型台站不同阻尼比取值峰值频率变化
Table 2. Peak frequency variation of typical stations with different damping ratio values
台站名 阻尼比 峰值频率/Hz 传递函数峰值频率/Hz IWTH02 0.01 5.3413 4.91 0.05 5.1903 0.1 5.0582 KSRH07 0.01 2.4020 2.51 0.05 2.4066 0.1 2.4128 IWTH08 0.01 2.4883 3.37 0.05 2.4916 0.1 2.5366
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表 3 典型台站不同平滑的带宽系数取值峰值频率变化
Table 3. Peak frequency variation of typical stations with different values of smooth bandwidth factor
台站名 平滑的带宽系数 峰值频率/Hz 传递函数峰值频率/Hz IWTH02 20 5.9310 4.91 30 6.0793 40 6.0942 50 6.1148 60 6.1354 70 6.1580 KSRH07 20 2.5778 2.51 30 2.5740 40 2.5759 50 2.5791 60 2.5745 70 2.5781 IWTH08 20 2.7308 3.37 30 2.7280 40 2.7157 50 2.7268 60 2.6971 70 2.7232
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表 4 台站峰值数量统计
Table 4. Peak number statistics of 16 one-dimensional stations
台站名（场地类别） 显著峰数量/个 峰的数量变化 阻尼比 平滑的带宽系数 0.01 0.05 0.1 20 30 40 50 60 70 IWTH02（Ⅱ） 1 1 1 1 1 1 1 1 2 2 IBRH13（Ⅱ） 1 2 1 1 1 1 2 3 3 3 IWTH27（Ⅱ） 1 1 1 1 1 1 1 1 1 1 KSRH06（Ⅱ） 1 1 1 1 1 2 2 2 3 3 KSRH10（Ⅱ） 2 4 3 2 2 2 3 3 4 4 TCGH12（Ⅱ） 2 2 1 1 2 3 3 4 4 4 IWTH08（Ⅱ） 3 3 3 3 3 3 4 4 4 5 TKCH08（Ⅱ） 3 5 5 3 3 4 4 6 6 7 KSRH07（Ⅲ） 2 2 2 2 2 2 2 2 2 2 FKSH11 （Ⅲ） 3 4 3 2 3 3 5 5 5 5 FKSH14（Ⅲ） 5 5 4 4 4 5 6 6 7 8 IBRH10（Ⅳ） 4 4 3 2 4 4 5 5 5 5 FKSH14（Ⅲ） 5 5 4 4 4 5 6 6 7 8 NMRH04（Ⅳ） 5 7 4 2 5 5 6 7 7 8 IBRH17（Ⅱ） 6 9 2 2 6 8 9 9 9 9 NIGH11（Ⅱ） 6 4 4 3 5 6 6 7 8 11
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表 5 16个一维观测台站峰值数据统计
Table 5. Peak number statistics of 16 one-dimensional stations
场地类别 显著峰数量/个 反应谱最优参数对应的峰值频率 傅里叶谱最优参数对应的峰值频率 理论传递函数对应的
峰值频率/Hz阻尼比 峰值频率/Hz 带宽系数 峰值频率/Hz IBRH13（Ⅱ） 1 0.1 2.5910 20 3.0665 3.11 IWTH02（Ⅱ） 1 0.1 5.0582 20 5.9310 4.91 IWTH08（Ⅱ） 1 0.01 2.5883 20 2.7308 3.37 2 0.1 6.4100 40 8.0736 9.23 3 0.1 10.9237 40 15.3087 15.01 IWTH27（Ⅱ） 1 0.01 6.1773 20 7.7455 9.4 KSRH10（Ⅱ） 1 0.1 1.8353 20 1.9810 1.99 IBRH17（Ⅱ） 1 0.01 0.3534 20 0.3504 0.39 2 0.01 0.9096 20 0.9047 1.06 3 0.01 1.3833 20 1.4935 1.5 IWTH24（Ⅱ） 1 0.1 2.5140 20 2.7376 3.37 2 0.1 6.3388 40 8.1129 9.23 3 0.1 10.8505 20 15.3724 15.01 KSEH06（Ⅱ） 1 0.1 5.7812 20 6.3617 6.65 NIGH11（Ⅱ） 2 0.1 4.5118 20 4.6040 3.9 3 0.1 6.8949 20 8.4756 6.09 4 0.1 10.01 20 14.5878 9.36 TCGH12（Ⅱ） 1 0.1 5.2806 20 6.6765 7.22 2 0.05 7.2384 20 9.3454 9.25 TKCH08（Ⅱ） 3 0.1 6.7590 20 8.1318 8.35 FKSH11 （Ⅲ） 1 0.1 1.5472 60 1.6730 2.12 2 0.1 4.5552 70 5.2341 5.86 3 0.01 6.8218 50 8.0801 9.61 KSRH07（Ⅲ） 1 0.01 2.4128 60 2.5635 2.51 2 0.01 6.9196 20 8.8538 7.02 FKSH14（Ⅲ） 1 0.1 1.1760 40 1.1875 1.35 2 0.1 3.6658 20 3.9909 4.01 3 0.1 5.2186 40 5.9271 6.4 4 0.1 6.3233 40 7.7832 8.83 NMRH04（Ⅳ） 3 0.1 0.4053 20 0.4089 0.61 4 0.1 1.7428 30 1.9726 1.61 5 0.1 2.3917 20 4.3434 2.04 IBRH10（Ⅳ） 1 0.01 0.7869 40 0.7931 0.78 2 0.01 1.1389 20 1.1897 1.27
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表 6 场地卓越频率或其范围统计
Table 6. Frequency of excellence or its range statistics
场地类别 显著峰数量/个 卓越频率值/Hz 卓越频率值范围/Hz 选取方法 IWTH02（Ⅱ） 1 5.05 — SA KSRH10（Ⅱ） 1 1.98 — FAS IWTH27（Ⅱ） 1 7.74 — FAS IBRH13（Ⅱ） 1 3.06 — FAS KSRH06（Ⅱ） 1 6.36 — FAS KSRH07（Ⅲ） 2 — 2.560～8.850 FAS FKSH14（Ⅲ） 2 — 1.180～7.780 FAS IBRH10（Ⅳ） 2 — 0.790～1.180 FAS TCGH12（Ⅱ） 2 — 0.107～0.381 FAS IWTH08（Ⅱ） 3 — 2.730～8.070 FAS TKCH08（Ⅱ） 3 — 0.123～0.551 FAS IWTH24（Ⅱ） 3 — 0.084～0.593 FAS FKSH11 （Ⅲ） 3 — 1.670～8.00 FAS NMRH04（Ⅳ） 5 — 0.263～2.467 SA NIGH11（Ⅱ） 6 — 0.097～0.355 SA IBRH17（Ⅱ） 6 — 0.163～0.297 FAS
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