Modification of fitting parameters in coherency model for spatial variation of seismic ground motion
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摘要: 采用SMART-1台阵第5次和第45次地震的水平向分量加速度记录，首先计算了不同间距台站对的地震动空间相干函数；然后讨论了台站距离对相干函数拟合结果的影响，即某一特定距离的相干函数与所有不同距离的相干函数的拟合结果存在明显差异。为减小这一差异，提出了一种对各个不同距离的相干函数拟合参数进行二次回归的方法，并选用Loh相干函数模型进行了验证，最后给出了基于Loh相干函数模型的拟合参数的修正结果。结果表明本文提出的修正方法将大大提高相干函数模型中参数的拟合精度。
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关键词:
- SMART-1 台阵 /
- 地震动空间相关性 /
- 相干函数 /
- 台站间距 /
- 参数拟合
Abstract: In this study, the horizontal component of the 5th and the 45th seismic records of the SMART-1 array were selected. Firstly the lagged coherencies of seismic ground motion of station pairs with different separation distances were calculated. Then the influence of station distance on the fitting of parameters of the coherency function model was discussed, that is, there were obvious differences between the fitting results of the coherency function of a certain distance and the coherency functions of all different distances. In order to reduce this deviation, a method of quadratic regression on the fitting parameters of the coherency of different distances was proposed, and the Loh coherency function model was selected for verifying the method. Finally, the correction results of the fitting parameters based on the Loh coherency function model were given. The results show that the correction method proposed in this paper will greatly improve the fitting accuracy of the parameters in the coherence function model. -
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图 2 两次地震震中位置示意图
Figure 2. Schematic diagram of the epicenter location of two earthquakes
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图 3 不同间距的相干系数γ与根据所有不同间距的相干系数γ12的拟合曲线对比（以第5次地震为例）
Figure 3. Comparison between fitting curves with lagged coherency γ of different distances and fitting curves with lagged coherency γ12 of all distance （taking the 5th earthquake as an example）
（a） d＝200 m；（b） d＝282 m；（c） d＝400 m；（d） d＝800 m；（e） d＝980 m；（f） d=1 000 m；（g） d＝1 200 m； （h） d＝1 732 m；（i） d＝1 800 m；（j） d＝2 000 m；（k） d＝2 200 m；（l） d＝3 000 m
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图 4 不同间距的相干系数γ与根据所有不同间距的相干系数γ12的拟合曲线对比 （以第45次地震为例）
Figure 4. Comparison between fitting curve with lagged coherency γ of different distances and fitting curve with lagged coherency γ12 of all distance（taking the 45th earthquake as an example）
（a） d＝200 m；（b） d＝282 m；（c） d＝400 m；（d） d＝800 m；（e） d＝980 m；（f） d＝1 000 m；（g） d＝1 200 m； （h） d＝1 732 m；（i） d＝1 800 m；（j） d＝2 000 m；（k） d＝2 200 m；（l） d＝3 000 m
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图 5 第5次（蓝色）和第45次（红色）地震的参数a （a），b （b）值随距离的变化及修正结果
Figure 5. Changes of parameters a （a） and b （b） with distance and modified results of the 5th （blue） and the 45th （red） earthquakes
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图 6 基于Loh相干函数模型，不同间距的相干系数γ、由所有不同间距的相干系数γ12和修正后的相干系数γs拟合曲线对比（以第5次地震为例）
Figure 6. Based on Loh coherency function model，comparison of fitting curve with lagged coherency γ of different distances，fitting curve with lagged coherency γ12 of all distance and fitting curve with lagged coherency γs of modified parameter （taking the 5th earthquake as an example）
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图 7 基于LOH相干函数模型，不同间距的相干系数γ、根据所有不同间距的相干系数γ12和修正后的相干系数γs拟合曲线对比（以第45次地震为例）
Figure 7. Based on Loh coherency function model，comparison of fitting curve of lagged coherency γ of different distances，fitting curve of lagged coherency of all distance γ12 and fitting curve with lagged coherency of modified parameter γs （taking the 45th earthquake as an example）
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图 8 不同间距的相干系数经修正前γ、后γs的拟合曲线与根据所有不同间距的相干系数γ12拟合曲线的比较（以两次地震为例）
Figure 8. Comparison of fitting curve of lagged coherency γ of different distances，fitting curve of lagged coherency γ12 of all distance and fitting curve with lagged coherency γs of modified parameter （take two earthquakes as examples）
表 1 台站间距和对应的台站对及数量
Table 1 Distance between stations and the corresponding number of station pairs
台站距离d/m 台站对 台站对个数 台站距离d/m 台站对 台站对个数 200 C00−I03 4 1 200 I06−M12 2 282 I03−I06 2 1 732 M06−O09 2 400 I03−I09 2 1 800 I03−O03 2 800 I03−M03 2 2 000 C00−O03 4 980 I03−M06 2 2 200 I03−O09 2 1 000 C00−M03 4 3 000 M03−O09 2 
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表 2 基于Loh相干函数模型的拟合系数结果
Table 2 Fitting coefficient results based on Loh coherency function model
台站距离d/m 第5次地震 第45次地震 a b a b 200 0.476 49 0.000 72 0.299 25 0.001 60 282 0.328 58 0.000 38 0.359 96 0.001 10 400 0.300 20 0.000 29 0.461 33 0.000 88 800 0.305 26 0.000 21 0.408 63 0.000 46 980 0.325 09 0.000 11 0.449 52 0.000 23 1 000 0.260 01 0.000 13 0.496 97 0.000 38 1 200 0.208 47 0.000 08 0.471 04 0.000 16 1 732 0.193 98 0.000 04 0.475 44 0.000 06 1 800 0.180 25 0.000 04 0.425 02 0.000 05 2 000 0.169 69 0.000 06 0.449 15 0.000 07 2 200 0.161 71 0.000 04 0.374 76 0.000 05 3 000 0.164 18 0.000 00 0.321 45 0.000 01 12d 0.189 77 0.000 08 0.357 08 0.000 36
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表 3 a和b二次拟合系数的修正结果
Table 3 Modified results of a and b
地震 a1 a2 a3 b1 b2 b3 第5次 0.733 53 −0.133 37 −0.482 98 0.000 10 −0.114 25 −0.805 45 第45次 −0.000 57 −3.410 92 0.432 46 0.000 82 0.573 00 −2.470 90
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表 4 a和 b的统一修正结果
Table 4 Unified modified results of a and b
a1 a2 a3 b1 b2 b3 −0.022 1.759 9 0.416 3 0.011 9 1.531 3 −4.367
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