Model for H/V acceleration response spectral ratio for non-scenario earthquakes from the subduction interface
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摘要:
基于日本KiK-net和K-NET台网所获取的59次俯冲带板间地震的3 048条强震记录，采用随机效应算法和数理统计方法，分析了地震类型、谱周期、场地条件等因素对水平与竖向加速度（H/V）反应谱比的影响，并建立了俯冲带板间非设定地震（不包含震源项、路径项等参数）的H/V反应谱比模型，用于调整无震源、无路径信息时的工程抗震设计反应谱。研究结果表明：① 地震类型和场地类别对H/V反应谱比均存在显著影响，H/V反应谱比的峰值周期与各类别场地的平均场地周期接近，预测模型的H/V反应谱比峰值周期与场地的卓越周期具有一定的相关性；② 路径效应项和场地效应项的随机误差对H/V反应谱比离散程度的贡献随谱周期的增加而不断增大，场地效应的贡献在各类场地的平均场地周期处最大。为便于工程应用，模型中未加入震源和路径参数，残差分析表明震源特性和传播路径仍会对H/V反应谱比产生影响，当有明确的地震信息时，引入震级、断层距、断层深度等因素可进一步提高模型预测精度。
Abstract:Vertical ground motions acceleration response spectrum is an important part of the structural seismic design, and the domestic and foreign seismic design codes use the H/V response spectrum ratio to calculate the vertical ground motion response spectrum indirectly, which is a simple and feasible method, but the current seismic codes are still too rough for the vertical ground motions response spectrum, which will underestimate the role of vertical component in the engineering application or will result in redundancy in the application. In addition, the geological structure of the subduction zone is complex and earthquakes occur frequently, and the interface earthquakes have the characteristics of high magnitude and high intensity, so it is necessary to study the interface earthquakes in the subduction zone separately.
In this paper, based on the surface observation data obtained from the KiK-net and K-NET in Japan, the data are first preprocessed so as to improve the accuracy of the model and to eliminate the seismic records that affect the fitting effect, which involves filtering the magnitude and the fault distance of the data, checking the acceleration time history, then correcting the instrumental response and filtering the waveforms. Finally, 3 048 seismic records from 59 interface earthquakes in subduction zones are selected for the study, and the acceleration response spectra are calculated for each record with 5% damping ratio. Random-effects algorithms and mathematical statistics were used to analyze the effects of spectral period, earthquake type and site conditions on the H/V response spectral ratio. Based on the site period Ts division of site classes, the H/V response spectrum ratio model for non-scenario earthquakes （without source and path parameters） from the subduction interface is established, the model coefficients are smoothed and adjusted to facilitate engineering applications, and the standard deviation of model residuals is evaluated and analyzed to explore the magnitude and source of random residuals and to improve the accuracy and reliability of the model. The model can be used to adjust the response spectrum of engineering seismic design when there is no earthquake source and no path information.
The study shows that: ① t-test method verifies that the type of earthquake and the site classes have a significant effect on the H/V response spectral ratio, so it is necessary to establish the corresponding response spectral ratio models according to different types of earthquakes and site classes; ② The peak period of the site effect term coefficients is close to the average period for each type of site, indicating that the site term coefficients are reasonably well taken to elicit a resonant site response. In the prediction model, the peak period of the H/V response spectral ratio is 0.2 s for classⅠsites, 0.27 s for class Ⅱ sites, and 0.5 s for class Ⅲ sites. The peak period of the H/V response spectral ratio in the prediction model has a certain correlation with the site predominant period, which can prove that the H/V response spectral ratio model is well fitted by using the random-effects method; ③ The standard deviation analysis shows that the dispersion generated by the source effect is smaller than that generated by the path effect and the site effect, the random residuals of the path effect term and the site effect term contribute more to the model variability, indicating that the random residuals of the horizontal and vertical components of the seismic records have strong correlation. Different site classes produce the largest dispersion in response spectral ratios at their corresponding mean site period. The increasing dispersion of the H/V response spectral ratio due to path effects with increasing spectral period demonstrates that the correlation between the horizontal and vertical component random path residuals decreases with increasing period.
The H/V response spectral ratio model for non-scenario earthquakes established in this study has the characteristics of simplicity and convenience for engineering application, and the source and path parameters are not added into the model. Residual analysis shows that the between-event residuals are correlated with the magnitude and fault depth, and the effects of magnitude and fault depth on the between-event residuals are clearly segmented at magnitude 7.1 and fault depth of 25 km. There is a correlation between the within-site residuals and the fault distance. Moreover, the effects of magnitude, source depth and fault distance on the residuals change with the spectral period, the seismic source characteristics and propagation paths still affect the H/V response spectral ratio. Therefore, when there is clear seismic information, the introduction of magnitude, fault distance, fault depth and other factors can further improve the model prediction accuracy, and will be committed to constructing a more accurate H/V response spectral ratio model in the future research. The results of this paper are of reference value for the seismic fortification of offshore engineering.
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图 3 四种场地类别之间的统计值|Z|随谱周期的变化
（a） Ⅱ类与Ⅰ类之比；（b） Ⅲ类与Ⅰ类之比；（c） Ⅳ类与Ⅰ类之比；（d） Ⅲ类与Ⅱ类之比；（e） Ⅳ类与Ⅱ类之比；（f） Ⅳ类与Ⅲ类之比
Figure 3. The variations of |Z| values versus spectral periods for each pair of four site classes
（a） The ratio of class Ⅱ to class Ⅰ ；（b） The ratio of class Ⅲ to class Ⅰ ；（c） The ratio of class Ⅳ to class Ⅰ ；（d） The ratio of class Ⅲ to class Ⅱ ；（e） The ratio of class Ⅳ to class Ⅱ ；（f） The ratio of class Ⅳ to class Ⅲ
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图 1 地震数据分布图
（a） 矩震级MW与断层距；（b） 矩震级MW与断层深度
Figure 1. The distribution of earthquake records
（a） Magnitude MW and fault distance；（b） Magnitude MW and fault depth
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图 2 不同类型地震间的显著性检验统计值|Z|
（a） 板间地震与浅壳-上地幔地震之比；（b） 板间地震与板内地震之比
Figure 2. The variation of |Z| values versus spectral period for each pair of three types of earthquakes with four site classes
（a） The ratio of subduction interface earthquakes to shallow crustal and upper mantle earthquakes；（b） The ratio of subduction interface earthquakes and slab earthquakes
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图 4 平滑前后模型系数随谱周期的分布图
（a） 平滑前常数项；（b） 平滑前场地效应项；（c） 平滑后常数项；（b） 平滑后场地效应项
Figure 4. Distribution of model coefficients versus spectral period before and after smoothing
（a） Constant term before smoothing；（b） Site effect terms before smoothing；（c） Constant term after smoothing；（d） Site effect terms after smoothing
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图 5 预测H/V反应谱比随谱周期的变化
Figure 5. The variation of the predicted H/V spectral ratios with spectral periods
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图 6 H/V反应谱比模型标准差随谱周期的分布图
Figure 6. Distribution of standard deviations for H/V response spectral ratio model，including between-event τ，within-event σ，and total standard deviations σT with spectral period
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图 7 四类场地的场地间标准差τs （a）和场地内标准差σs （b）随谱周期的分布
Figure 7. The distribution of between-site standard deviations τs （a） and within-site standard deviations σs （b） with spectral period for four-class sites
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图 8 谱周期T为0.15 s （上）和1.0 s （下）时事件间残差随MW （a，c）和震源深度（b，d）的分布图
Figure 8. Distribution of between-event residuals with MW （a，c） and source depth （b，d） for the spectral period T of 0.15 s （upper） and 1.0 s （lower）
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图 9 四个谱周期T下Ⅰ类场地模型的场地内残差随断层距的分布图
Figure 9. Distribution of within-site residuals of Ⅰ -class site model with fault distance for four spectral periods T
（a） T＝0.15 s；（b） T＝0.5 s；（c） T＝1.0 s；（d） T＝5.0 s
表 1 场地分类标准与数据量
Table 1 Site classification criteria and number of records
场地类别 场地周期Ts /s 平均剪切波速vS30/（m·s−1） 记录数量 Ⅰ类（岩石） Ts＜0.2 vS30＞600 1 464 Ⅱ类（硬土） 0.2 ≤Ts＜0.4 300＜vS30≤600 764 Ⅲ类 （中硬土） 0.4 ≤Ts＜0.6 200＜vS30≤300 280 Ⅳ类（软土） Ts ≥0.6 vS30≤200 540 
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表 2 俯冲带板间非设定地震H/V反应谱比模型平滑后的系数取值
Table 2 The smoothed coefficients of the H/V response spectral ratio model for non-scenario earthquakes from the subduction interface
T/s c S2 S3 S4 T/s c S2 S3 S4 PGA 0.813 0.086 −0.068 0.069 0.35 0.796 0.305 0.106 0.181 0.01 0.808 0.088 −0.066 0.069 0.40 0.735 0.298 0.194 0.209 0.02 0.784 0.095 −0.056 0.077 0.45 0.679 0.287 0.267 0.231 0.03 0.709 0.125 −0.024 0.102 0.50 0.637 0.278 0.310 0.249 0.04 0.545 0.156 0.011 0.134 0.60 0.578 0.263 0.352 0.276 0.05 0.524 0.102 −0.055 0.062 0.70 0.539 0.250 0.360 0.293 0.06 0.607 −0.016 −0.142 −0.051 0.80 0.512 0.239 0.355 0.305 0.07 0.697 −0.108 −0.201 −0.132 0.90 0.493 0.229 0.346 0.314 0.08 0.775 −0.170 −0.231 −0.160 1.00 0.479 0.220 0.336 0.319 0.09 0.832 −0.193 −0.246 −0.164 1.30 0.455 0.197 0.303 0.326 0.10 0.871 −0.181 −0.254 −0.145 1.50 0.446 0.183 0.281 0.326 0.12 0.925 −0.097 −0.258 −0.100 2.00 0.433 0.156 0.237 0.321 0.14 0.956 0 −0.249 −0.055 2.50 0.426 0.137 0.208 0.315 0.15 0.964 0.041 −0.241 −0.037 3.00 0.420 0.122 0.188 0.311 0.16 0.969 0.077 −0.230 −0.019 3.50 0.415 0.111 0.173 0.308 0.18 0.969 0.149 −0.204 0.013 4.00 0.411 0.101 0.162 0.308 0.20 0.961 0.201 −0.173 0.041 4.50 0.406 0.094 0.153 0.310 0.25 0.918 0.283 −0.084 0.099 5.00 0.402 0.088 0.144 0.315 0.30 0.859 0.305 0.012 0.145 注：表中参数为文中式（4）$ {{\mathrm{ln}}R}_{{\mathrm{HV}}}＝c ＋ {S}_{ k} ＋ {\xi }_{i\text{，} j} ＋ {\eta }_{i} $中的参数。
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表 3 不同谱周期下各场地类别的模型标准差
Table 3 Standard deviations for models with different site class in different spectral periods
谱周期
/sⅠ类场地 Ⅱ类场地 Ⅲ类场地 Ⅳ类场地 总体标准差 σs τs σST σs τs σST σs τs σST σs τs σST σ τ σT PGA 0.229 0.230 0.324 0.249 0.218 0.331 0.214 0.270 0.345 0.225 0.192 0.296 0.333 0.093 0.345 0.01 0.228 0.231 0.324 0.249 0.218 0.331 0.214 0.271 0.345 0.225 0.191 0.295 0.333 0.094 0.345 0.02 0.227 0.229 0.323 0.249 0.218 0.331 0.214 0.271 0.346 0.226 0.189 0.294 0.331 0.098 0.345 0.03 0.229 0.231 0.325 0.250 0.222 0.334 0.216 0.276 0.351 0.229 0.184 0.294 0.336 0.116 0.355 0.04 0.236 0.247 0.342 0.257 0.262 0.367 0.231 0.301 0.380 0.248 0.201 0.319 0.361 0.146 0.389 0.05 0.247 0.252 0.353 0.268 0.264 0.376 0.240 0.312 0.394 0.272 0.233 0.358 0.374 0.116 0.392 0.06 0.259 0.287 0.387 0.270 0.269 0.381 0.248 0.302 0.391 0.267 0.290 0.394 0.404 0.080 0.412 0.07 0.258 0.306 0.401 0.273 0.250 0.369 0.242 0.344 0.421 0.260 0.333 0.423 0.426 0.074 0.432 0.08 0.264 0.341 0.431 0.269 0.250 0.368 0.248 0.287 0.379 0.267 0.341 0.433 0.438 0.070 0.444 0.09 0.273 0.367 0.457 0.279 0.257 0.379 0.268 0.253 0.368 0.261 0.350 0.436 0.454 0.073 0.460 0.10 0.276 0.368 0.460 0.275 0.284 0.395 0.275 0.263 0.381 0.264 0.316 0.412 0.453 0.073 0.459 0.12 0.283 0.365 0.462 0.251 0.296 0.388 0.289 0.348 0.453 0.267 0.287 0.392 0.453 0.078 0.460 0.14 0.288 0.357 0.458 0.275 0.332 0.431 0.254 0.356 0.437 0.257 0.280 0.380 0.450 0.089 0.459 0.15 0.288 0.359 0.461 0.289 0.362 0.463 0.242 0.348 0.424 0.248 0.282 0.375 0.461 0.092 0.470 0.16 0.283 0.366 0.463 0.286 0.377 0.474 0.247 0.349 0.428 0.256 0.293 0.389 0.469 0.092 0.478 0.18 0.276 0.365 0.457 0.271 0.397 0.481 0.228 0.358 0.425 0.270 0.331 0.427 0.484 0.087 0.492 0.20 0.270 0.372 0.460 0.263 0.401 0.479 0.238 0.360 0.432 0.273 0.349 0.443 0.496 0.080 0.503 0.25 0.277 0.347 0.444 0.272 0.430 0.509 0.268 0.407 0.487 0.272 0.332 0.429 0.483 0.082 0.490 0.30 0.289 0.309 0.423 0.274 0.419 0.500 0.249 0.488 0.548 0.259 0.348 0.434 0.479 0.065 0.483 0.35 0.291 0.313 0.427 0.264 0.409 0.487 0.251 0.534 0.590 0.273 0.358 0.450 0.481 0.075 0.486 0.40 0.301 0.284 0.414 0.278 0.380 0.471 0.256 0.517 0.577 0.255 0.362 0.443 0.469 0.073 0.475 0.45 0.312 0.249 0.399 0.280 0.348 0.447 0.240 0.445 0.506 0.271 0.322 0.420 0.442 0.079 0.449 0.50 0.310 0.236 0.389 0.292 0.335 0.445 0.277 0.421 0.504 0.262 0.309 0.405 0.426 0.078 0.433 0.60 0.313 0.210 0.377 0.289 0.285 0.406 0.279 0.360 0.455 0.269 0.309 0.410 0.400 0.066 0.406 0.70 0.319 0.202 0.378 0.303 0.257 0.398 0.262 0.344 0.433 0.274 0.314 0.416 0.397 0.066 0.403 0.80 0.320 0.187 0.370 0.328 0.226 0.398 0.270 0.291 0.398 0.262 0.332 0.423 0.397 0.081 0.406 0.90 0.324 0.177 0.369 0.314 0.214 0.380 0.298 0.276 0.406 0.244 0.364 0.439 0.398 0.078 0.406 1.00 0.319 0.186 0.369 0.319 0.228 0.393 0.325 0.264 0.419 0.253 0.365 0.444 0.405 0.077 0.412 1.25 0.313 0.177 0.360 0.316 0.221 0.385 0.303 0.270 0.406 0.251 0.360 0.439 0.395 0.097 0.406 1.50 0.317 0.201 0.375 0.322 0.210 0.384 0.327 0.242 0.407 0.251 0.377 0.453 0.406 0.110 0.421 2.00 0.332 0.203 0.389 0.332 0.222 0.399 0.313 0.276 0.417 0.275 0.372 0.463 0.412 0.120 0.429 2.50 0.326 0.211 0.388 0.326 0.215 0.390 0.323 0.315 0.451 0.309 0.352 0.468 0.408 0.132 0.429 3.00 0.343 0.200 0.397 0.334 0.203 0.390 0.359 0.264 0.445 0.334 0.311 0.456 0.410 0.140 0.433 3.50 0.350 0.187 0.396 0.339 0.186 0.387 0.354 0.229 0.422 0.329 0.284 0.434 0.404 0.184 0.444 4.00 0.354 0.176 0.396 0.347 0.190 0.396 0.365 0.215 0.423 0.359 0.265 0.446 0.408 0.201 0.455 4.50 0.375 0.177 0.414 0.351 0.178 0.394 0.350 0.207 0.406 0.353 0.262 0.439 0.414 0.223 0.470 5.00 0.370 0.189 0.415 0.353 0.185 0.399 0.352 0.170 0.391 0.363 0.251 0.441 0.413 0.242 0.479 注：σs为场地内标准差，τs为场地间标准差，σST为总场地标准差，σ为事件内标准差，τ为事件间标准差，σT为总标准差。
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