Power-law variation of seismic spatial correlation length in Pg wave velocity transitional zone of Hetao seismic belt
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摘要: 基于Pg波速度反演和地震重新定位， 运用单键群算法对Pg波速度过渡带的地震空间相关长度进行了幂律拟合分析． Pg波速度反演结果表明， 其速度的横向变化表现出构造相依的特征， 速度高低与地壳厚度呈正相关， 并在包头—西山嘴凸起和岱海凹陷两个区域形成Pg波速度过渡带． 利用重新定位的地震数据计算了这两个速度过渡区的地震空间相关长度， 结果显示其幂律拟合曲线均呈一定的增长趋势， 表明2008年以来两个Pg波速度过渡区域的应力作用不断集聚、 增强， 断层有逐步进入协同化阶段的可能， 加之速度过渡带通常是地壳运动强烈区域， 未来将成为孕育中强地震的有利场所． 在有效控制定位误差的条件下， 重新定位可以明显减小地震空间相关长度的离散形态， 提高计算精度．Abstract: Based on Pg wave velocity inversion and earthquake relocation, this paper analyzes the seismic spatial correlation length of Pg wave velocity in the transition zone of Hetao seismic belt by using the single link cluster (SLC) algorithm and power-law fitting. The inversion results of Pg velocity show that the lateral variation of Pg wave velocity images is dependent on the structure, the velocity of Pg wave is positively correlated to the thickness of the crust, and two transitional zones of Pg wave velocity are formed in Baotou-Xishanzui bulge and Daihai sag. Furthermore, the seismic spatial correlation lengths of the two velocity transition zones are calculated based on the relocation data. The results show that the power-law fitting curve exhibits a trend growth to a certain degree, suggesting that the stress level of the above two Pg wave velocity transitional zones have been enhanced since 2008, and regional faults are likely to be entered into the stage of coordination. In addition, the Pg wave velocity transitional zone is usually a strong area of crustal movement， therefore it is deduced that the two zones will become the favorable place for occurrence of moderate earthquakes in future. On the condition of effective control of the positioning error, seismic relocation can reduce the discrete form and improve the calculation accuracy of seismic spatial correlation length.
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甘肃省地震局荣代潞研究员提供了地震空间相关长度计算程序，中国科学院青藏高原研究所裴顺平研究员提供了Pg波反演程序，最小完整性震级由Zmap程序包①计算完成，审稿专家对本文提出的修改建议，作者在此一并表示感谢. ① http://www.earthquake.ethz.ch/
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图 1 研究区构造背景及1970年以来MSS≥4.7地震的震源机制
F1： 狼山山前断裂； F2： 磴口—本井断裂； F3： 鄂尔多斯北缘断裂； F4： 色尔腾山山前断裂； F5： 大青山山前断裂； F6：和林格尔断裂. 断裂名称下同
Figure 1. Tectonic settings of the studied area and focal mechanisms of MSS≥4.7 earthquakes since 1970
F1： Langshan piedmont fault； F2： Dengkou--Benjing fault； F3： Northern Ordos marginal fault； F4: Serteng mountain piedmont fault; F5: Daqingshan piedmont fault; F6: Horinger fault，the same below
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图 2 地震台站数目的时序变化(a)和最小完整性震级MSc(b) a和b为古登堡-里克特公式中的常数
Figure 2. Temporal variation of seismic station number(a)and minimum completeness magnitude Mc (b) a and b are constants in the Gutenberg-Richter recurrence law. In Fig.(a)，the triangle represents station. In Fig.(b)，the square represents cumulative frequency versus magnitude，the solid triangle represents noncumulative frequency versus magnitude，the line represents Gutenberg-Richter power-law
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图 3 射线路径(a)、 检测板理论速度模型(b)和Pg波速度(平均值为6.0 km/s)的横向变化(c)
Figure 3. Ray path(a)，theoretical velocity model of checkerboard(b) and lateral variation of Pg wave velocity，while their average value is 6.0 km/s(c)
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图 4 数据方差与模型方差的关系曲线
Figure 4. The relationship between data variance and model variance. The solid dot indicates the optimum damping coefficient
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图 5 Pg波反演得到的走时残差分布直方图(a)及其随震中距Δ的变化(b)
Figure 5. Histogram distribution(a)of travel-time residual obtained by Pg wave inversion and its variation with epicentral distance Δ(b)
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图 7 3种速度结构模型的重定位结果及震源深度分布
(a)基于3种速度结构模型得到的重定位结果，大圆圈和方框分别为Pg波速度横向变化异常区域A和B; (b)--(d)分别为组合模型、 魏文博等(2007)模型和Crust1.0模型给出的重定位后的震源深度统计图
Figure 7. Relocation results and focal depth distribution calculated based on three crustal velocity models
(a)The relocation results of earthquakes calculated based on three crustal velocity models，and the large circle and frame show the anomaly regions A and B of lateral variation of Pg velocity； (b)--(d)are statistics on focal depth after relocation based on combined model， Wei et al’s(2007)model and Crust1.0 model，respectively
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图 8 由组合模型(a)、 Crust1.0模型(b)和魏文博等(2007)模型(c)得到的定位误差统计结果
第1—3列分别为EW向、 NS向和UD向定位误差分布，第4列为走时残差分布
Figure 8. Statistical results of location errors calculated by combined model(a)， Crust1.0 model(b)and Wei et al’s(2007)model(c)
The first column to the third column represent distribution of location errors in EW，NS and UD directions， respectively. The fourth column represents distribution of travel-time residuals
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图 9 由滑动时间窗法计算地震空间相关长度示意图
Figure 9. Schematic diagram for calculating seismic spatial correlation length by sliding time window method t0 and tf represent the starting time and ending time，respectively. Δt is sliding step，N is window length， ξ(ti)is seismic spatial correlation length in each calculation window length
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图 10 重新定位前后A区(a)和B区(b)地震空间相关长度的幂律拟合曲线及其时序变化
k为幂律指数，反映了地震空间相关长度的增长程度
Figure 10. Power-low fitting curves and temporal variation of seismic spatial correlation length in the regions A(a)and B(b)before and after relocation
Grey dot，red square，green star and blue triangle indicate the location results based on original records from seismic network，Wei et al’s(2007)model，Crust1.0 model and combined model，respectively. Grey，red，green and blue lines indicate corresponding fitting curves of location results. k is the power index，reflecting the growth degree of seismic spatial correlation length
表 1 P波速度模型
Table 1 Velocity model of P wave
组合模型 魏文博等(2007)模型 Crust1.0模型 界面深度/km vP/(km·s-1) 界面深度/km vP/(km·s-1) 界面深度/km vP/(km·s-1) 0 2.2 1 4.6 1 4.5 6 5.0 10 6.15 16 6.1 9 5.6 20 6.3 30 6.3 20 6.34 30 6.55 37 7.0 30 6.55 35 6.6 35 6.6 
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