Repeating earthquakes and temporal changes of the Earth's inner core
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摘要: 地球内核是地球最中心的圈层，它的一个很重要的特性是在几年至十年的尺度上存在着明显的时变性. 利用重复地震经过内核的波随时间的变化给内核的时变性提供了最有力的且毫无争议的证据. 然而时变信号的来源仍有待商榷. 一般解释认为与内核的差速旋转有关；另一个解释为内核边界的快速变化. 最新的研究表明，内核的时变信号主要来源于内核的内部而非边界. 这一新发现排除了内核边界作为时变唯一信号来源的可能性. 最简单而合理的解释依然是内核的差速旋转：内核以每年0.05°～0.1°的速率相对于地幔超速旋转，并有变速旋转的可能性，使得内核浅部不均一的横向结构发生位移，重复地震的体波沿着固定路径传播时会采样到不同的内核结构而产生时变信号. 这一模型可以解释此前研究观测到的所有时变信号. 内核时变现象和其成因的探究对于我们认识地球深部的运行方式，尤其是磁场的运行机制，有着重要的启发意义.Abstract: One of the most intriguing features of the Earth's inner core is its temporal variability over decadal time scale. Time-varying sesismic waves traversing the inner core, from high-quality repeating earthquakes, provide unequivocal evidence for the feature. However, the mechanism of the temporal change remains in debate. There have been two competing models, differential rotation of the inner core shifting its lateral heterogeneities and the rapid localized changes of the inner core boundary (ICB). Recent studies suggest that the time-varying seismic waves originate from the interior of the inner core, rather than the ICB. Consequently, the model of differential rotation provides so far the simplest and most reasonable explanation. Inner core is inferred to rotate at the rate of 0.05～0.1 degree per year, with the possibility of decadal fluctuation. The model can reconcile all the time-varying signals observed in previous studies. The investigations on the temporal change of the inner core and its mechanism shed lights on understanding the inner workings of our planet, especially the operation of the geodynamo.
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Key words:
- repeating earthquakes /
- inner core /
- temporal changes /
- differential rotation
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图 1 穿透地核的地震波的射线路径和走时曲线. （a）震源（红色五角星）产生的信号分别被距离135°和150°的两个台站（蓝色三角形）接收（修改自Yang and Song, 2020b）. 内核的PKP波穿透内核（标注为IC）的路径称为DF，在内核边界反射的称为CD，从外核（标注为OC）底部通过的路径称为BC，外核中部通过的路径称为AB. SKP是在震源产生的横波（S）经过核幔边界转化为纵波（外核K；回到地幔P）的震相. （b）PKP波的走时曲线（震源深度在50 km）
Figure 1. Raypaths and travel time curves of core phases. (a) Raypaths from an example event (red star) at 0° to two stations (blue triangles) at 135° and 150° (modified from Yang and Song, 2020b). PKP waves include DF branch sampling the inner core (labeled as IC), BC branch sampling the bottom of the outer core (labeled as OC), AB branch sampling the middle of the outer core, and CD branch reflected from the inner core boundary. SKP wave takes off as shear wave (S) and converted to compressional wave at the core-mantle boundary (K in the outer core and P back to the mantle). (b) PKP travel time curves (source depth at 50 km)
图 2 重复地震的相似波形和其内核透射波DF时变现象的例子（修改自Yang and Song, 2020a）. （a）显示1995年和2011年的一对重复地震的P波及后续波和尾波在LPAZ台站（震中距18°）的记录几乎一致，利用互相关对齐并振幅归一化之后近乎重叠. （b）类似于图（a），显示了PKP波在CHKZ台站的记录，可见外核的BC和AB震相几乎一样；而对于内核的DF震相，2011年的信号比1995年的早到了约0.13 s，并且波形也出现了变化
Figure 2. Example of highly similar waveforms and temporal changes of DF from repeating earthquakes (modified from Yang and Song, 2020a). (a) Nearly identical wavefroms from a pair of repeating earthquakes in 1995 and 2011 to station LPAZ (distance 18°). They are aligned with cross-correlation and normalized by their peak amplitudes. (b) Similar to (a), but time-varying DF waveforms recorded by station CHKZ. The outer-core phases BC and AB remain similar, but the inner-core phase DF in 2011 arrives 0.13 s earlier and shows different waveforms compared to that in 1995
图 3 中高强度重复地震分布和内核时变路径汇总图. 图中的曲线代表从重复地震（红色五角星）到地震台站、局域台网、或者区域台阵（蓝色三角形）并检测出内核时变信号的路径（Zhang et al., 2005; Wen, 2006; Cao et al., 2007; Song and Dai, 2008; Zhang et al., 2008; Yao et al., 2015, 2019; Yang and Song, 2020a, 2020b）. 曲线中的黑色加粗段代表DF波在内核中的传播路径. 为了让此图更清晰易读，同一个地区的只选取了一个代表性的台站，包括阿拉斯加，哈萨克斯坦KZ台网，吉尔吉斯坦KN台网等. 灰色三角形代表Yang和Song（2020a）系统性地搜索出的全球的中高强度（震级5～6）的重复地震
Figure 3. Compilation of paths with temporal changes of the inner core from strong repeating earthuakes. The dark lines represent surface projections of raypaths from repeating earthquakes (red stars) to receivers (stations, arrays, and regional networks) reported by previous studies (Zhang et al., 2005; Wen，2006；Cao et al., 2007; Song and Dai, 2008; Zhang et al., 2008; Yao et al., 2015, 2019; Yang and Song, 2020a, 2020b). The black bold parts of the lines indicate the wave legs traversing the inner core. In the same region (e.g., Alaska, KZ network in Kazakhstan, KN network in Kyrgyzstan), only one representative station is plotted out to avoid overcrowding. Gray stars denote all strong repeating earthquakes (magnitude 5~6) searched out by Yang and Song (2020a)
图 4 内核时变信号来源的分析（修改自Yang and Song, 2020b）. 图中数据来源于15组重复地震（12组全球分布的高质量重复地震和3组SSI地区的质量略差的重复地震）. 图中ddt代表一对重复地震的两个震相的双差到时（Song and Dai, 2008），定义为ddt(A−B)=dt(A)−dt(B)=[t(A2)−t(A1)]−[(t(B2)−t(B1)]，其中下标1和2分别用来代指早发生和晚发生的重复地震. 横轴ddt(CD−DF)代表利用CD和DF互为参考来判断它们是否有时变信号（非零）；纵轴ddt(SKP−DF or CD)代表利用SKP做参考震相，分别显示CD和DF的时变大小；图上的红线和蓝线分别代表它们与ddt(CD−DF)的线性拟合，斜率分别为0.796±0.081和−0.204±0.081. 倘若只使用12组高质量重复地震的数据，则斜率分别为0.861±0.114和−0.139±0.114
Figure 4. Analyses of the origin of time-varying inner-core waves (modified from Yang and Song, 2020b). The data points are from 15 pairs of repeating earthquakes (12 high-quality global pairs and 3 slightly inferior SSI pairs). The ddt represents the double differential time between two phases (A and B) from a pair of repeating earthquakes (Song and Dai, 2008), and is formulated as ddt(A−B)=dt(A)−dt(B)=[t(A2)−t(A1)]− [t(B2)−t(B1)], where the subscirpts 1 and 2 denote the earlier and later event, respectively. The horizontal axis, ddt(CD-DF), represent the inner-core temporal changes, using CD and DF phases. The vertical axis, ddt(SKP-DF or CD) indicates the changes of DF or CD, using SKP phase as reference, and the red and blue lines are their linear regressions with ddt(CD-DF), with slopes of 0.796±0.081 and −0.204±0.081, respectively. If using 12 high-quality pairs only, the corresponding slopes would be 0.861±0.114 and −0.139±0.114, respectively
图 5 内核时变信号来源的示意图. 外核液态铁镍合金的对流受到地球自转影响产生螺旋状环形流动（金色螺旋线），产生地磁场（灰色细线和箭头的磁力线）. 磁场与内核的地磁力矩驱动内核的差速旋转（旋转箭头）. 由于内核介质的不均一性，台站（褐色三角形）接收到的重复地震（红色五角星）发出的穿透内核的体波（DF，蓝线）会显示出可观测到的时变性；相较而言，在内核边界反射的体波（CD，绿线）的时变性并不显著（Yang and Song, 2020b）
Figure 5. Cartoon illustration of the origin of time-varying inner-core waves. The circulations of the outer core currents are twisted by the earth’s rotation to form helical flows (golden bands), which generate magnetic field (gray lines). Electromagenetic torque drives the differential rotation of the inner core, and hence shifts the position of the heteregenieties inside of the inner core. Temporal changes of seismic waves traversing the inner core (DF, blue line) are clearly observed from repeating earthquakes (red star) to seismic station (brown triangle). In contrast, temporal changes of seismic waves reflecting off the ICB (CD, green line) are not significant (Yang and Song, 2020b).
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