Estimation of time error for a single station based on Green’s function by ambient noise cross-correlation
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摘要: 从江苏省数字地震台网2011年的宽频带记录数据中， 选取了不同背景噪声区域下的两组不同台间距的台站(A, B每组4个台站)， 两组台站的平均台间距分别为44.6和30.5 km. 首先， 运用滑动窗互相关技术， 测量出各台站对间背景噪声互相关格林函数随时间的偏移量ΔDSi-Sj， 然后通过奇异值分解来求解由ΔDSi-Sj与系数矩阵构成的超定方程， 从而计算出单个台站的时钟误差ΔSi；并引入协方差矩阵来估计不同置信水平下计算结果的误差范围. 计算结果表明, 除去明显的钟差误差(>3 s)外， 8个台站的时间误差平均均方根为0.4215 s， A与B两组台站在置信水平为95%时的时间误差范围分别为±0.4544 s和±0.4283 s; 而采用HYPOSAT定位方法对2010—2011年江苏地区的地震进行定位, 得到的平均走时残差约为0.386 s. 两者的计算精度基本相当， 表明基于背景噪声互相关格林函数计算出的单台时间误差是可信的.Abstract: From the broadband data recorded by the digital seismic network of Jiangsu Province in 2011, this paper selected two station groups A and B (each has four stations). The two groups were under different ambient noise area and the average station distances were 44.6 km and 30.5 km, respectively. Firstly, by the sliding window cross-correlation technique, the offsets of the Green’s function were measured by ambient noise cross correlation between station-pairs in the year 2011. Then, the singular value decomposition was applied to solve the over-determined equation of ΔDSi-Sj and the coefficient matrices, so as to calculate clock error ΔSi for a single station. And the covariance matrix was introduced to estimate the error range of calculation results under different confidence level. The results showed that ignoring the obvious clock error ( >3 s), the average RMS of time errors for eight stations was about 0.4215 s, and on the 95% confidence level, the errors ranges for the two groups of stations were ±0.454 4s and ±0.4283, respectively. The average travel time residual was about 0.386 s by adopting HYPOSAT to locate actual earthquakes in Jiangsu region during the period of 2010—2011. Therefore, both residuals are consistent in accuracy, suggesting it is reliable to estimate the time error for a single station based on Green’s function by noise cross-correlation.
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图 1 选用的台站分布示意图(a)和2011年江苏省台站背景噪声的功率谱概率密度(b)
Figure 1. The distribution of seismic stations in this study (a) and the probability density function of power spectrum density of ambient noise in Jiangsu Province in 2011(b)
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图 2 2011-03-10台站对PX-DHS和MCH-WX的背景噪声互相关格林函数(a)和2011-01-10 XW台人为加入30 s钟差前(上图)后(下图)的背景噪声互相关格林函数(b)
Figure 2. The cross-correlation Green’s function of the ambient noise for station pairs PX-DHS and MCH-WX on March 10, 2011 (a) and that for station pair LYG-XW before (upper) and after (lower) artificially adding the 30 s clock error on original data of the station XW on January 10, 2011 (b)
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图 3 2011年台站对MAS-JN背景噪声互相关格林函数的信噪比(a)和各台站对 采用不同窗长(分别为10， 20， 30， 60天)叠加得到的信噪比结果(b)
Figure 3. The signal-to-noise ratio of the cross-correlation Green’s function of ambient noise for station pair MAS-JN in 2011 (a) and the superimposed signal-to-noise ratio results of all station pairs with different window length (10， 20， 30， 60 days) (b)
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图 4 2011年A组(a)、 B组(b)台站对互相关格林函数随时间的走时差
Figure 4. The travel time lag of cross-correlation Green’s function with time for the station pairs of groups A (a) and B (b), respectively, in 2011
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图 5 2011年A组(a)与B组(b)各台站置信水平为95%时的时间偏差和误差范围
Figure 5. The time deviation and time error of all stations for groups A (a) and B (b) under 95% confidence level in 2011
表 1 不同置信水平下计算结果的均方根和误差范围
Table 1 The RMS results and error ranges of calculation results under different confidence level
系数矩阵 G 中的随机误差 置信水平 标度因子 均方根时差/s 误差范围/s A组 B组 A组 B组 0.00 90.00% 1.644 9 0.750 1 0.450 4 ±0.381 3 ±0.359 4 95.00% 1.960 0 0.750 1 0.450 2 ±0.454 4 ±0.428 3 99.00% 2.575 8 0.750 1 0.450 4 ±0.597 1 ±0.562 8 0.10 90.00% 1.644 9 0.710 5 0.474 6 ±0.374 2 ±0.367 5 95.00% 1.960 0 0.783 0 0.473 7 ±0.492 6 ±0.420 2 99.00% 2.575 8 0.760 3 0.430 5 ±0.618 0 ±0.610 2 0.15 90.00% 1.644 9 0.842 0 0.474 0 ±0.394 6 ±0.378 6 95.00% 1.960 0 0.762 9 0.446 9 ±0.412 3 ±0.443 1 99.00% 2.575 8 0.721 0 0.428 2 ±0.531 5 ±0.510 7 0.20 90.00% 1.644 9 0.666 6 0.469 6 ±0.339 8 ±0.307 4 95.00% 1.960 0 0.672 6 0.434 1 ±0.388 8 ±0.381 6 99.00% 2.575 8 0.802 3 0.424 2 ±0.624 6 ±0.481 7 0.25 90.00% 1.644 9 0.857 8 0.506 3 ±0.526 5 ±0.509 5 95.00% 1.960 0 0.786 2 0.565 6 ±0.509 3 ±0.689 9 99.00% 2.575 8 0.708 3 0.501 6 ±0.527 7 ±0.665 1 0.30 90.00% 1.644 9 0.786 9 0.383 7 ±0.345 6 ±0.376 5 95.00% 1.960 0 0.837 4 0.495 2 ±0.573 3 ±0.588 2 99.00% 2.575 8 0.732 2 0.521 4 ±0.558 5 ±0.688 2 
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