Progress and prospect of studies on elastic normal modes of Earth's free oscillation
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摘要: 在构建现代地球模型时，地球内部分层结构主要是根据地震波资料确定的；而地球内部密度及弹性参数，特别是地幔以下大尺度结构的密度分布，则主要是根据地球自由振荡的弹性简正模观测资料确定的. 本文概述了地球自由振荡简正模本征值的求解理论和方法，介绍了球型和环型模态位移场表达式，讨论了地球自由振荡模态的衰减、分裂与耦合效应；总结了多线态分裂谱线探测和分裂参数估计的方法，综述了利用弹性简正模开展地震矩张量、地球三维非均匀性结构和内核超速旋转约束与反演研究的主要进展和存在的问题. 最后作为展望，本文还讨论了地球自由振荡简正模的未来研究趋势.
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关键词:
- 弹性简正模 /
- 地球模型 /
- 模态分裂 /
- 反演问题 /
- 地球三维非均匀性结构
Abstract: In constructing modern Earth model, Earth's interior layered structure is mainly determined according to seismic data; while the density and elastic parameters of the interior Earth, especially the large-scale structure of the density distribution below the mantle, are mainly determined according to the Earth's free oscillation observations. This paper summarizes the theories and methods of solving the eigenvalues of normal modes of Earth's free oscillation, introduces the expressions of the displacement fields in spheroidal and toroidal modes, and discusses attenuation, splitting and coupling effects of the free oscillation modes. In addition, this paper summarizes the methods of detecting the splitting spectral lines of multiplets and estimating the corresponding splitting parameters, and reviews the main progress and existing problems in researching the constraints and inversion of the seismic moment tensor, three-dimensional (3D) heterogeneous structure of the Earth and inner core's super rotation by using elastic normal modes. Finally, we discuss the future development trend in studying normal modes of Earth's free oscillation. -
图 1 环型模态0T2、0T3、1T1和1T2的位移示意图. 图中箭头表示质点运动方向，纵横直线表示球面节点线，内部圆圈表示球型节点面（修改自Stein and Wysession, 2003）
Figure 1. Examples of the displacements for several torsional modes 0T2, 0T3, 1T1 and 1T2. The arrows show the particle movement direction, the vertical and horizontal straight lines indicate the nodal lines on the surface, and the internal circles represent the spherical nodal surfaces within the Earth (modified from Stein and Wysession, 2003)
图 2 球型模态0S2、0S3、0S0、1S0和1S1的位移示意图（修改自Stein and Wysession, 2003）
Figure 2. Examples of the displacements for several spheroidal modes 0S2, 0S3, 0S0, 1S0 and 1S1 (modified from Stein and Wysession, 2003)
图 3 2011年3月11日东日本MW9.1大地震后德国BFO台站记录的地震波时间序列垂直分量振幅谱
Figure 3. Amplitude spectrum of the radial component of a seismogram following the great March 11, 2011, eastern Japan earthquake, recorded at BFO, Germany
图 4 （a）～（c） 2004年苏门答腊MW9.0地震、2010年智利马乌莱MW8.8地震和2011年东日本MW9.1大地震后所得到的0S2的功率谱；（d）～（f）为对应地震后所得到的0S3的功率谱. 黑色和灰色阴影分别表示未经过EEMD处理和经过EEMD处理后的功率谱图，竖直虚线表示相应谱峰的PREM模型预测频率（修改自Shen and Ding, 2014）
Figure 4. (a)～(c) Product spectra of 0S2 obtained from the 2004 Sumatra MW9.0 earthquake, the 2010 Maule MW8.8 earthquake and the 2011 Tohoku MW9.1 earthquake, respectively; (d)～(f) product spectra of 0S3 obtained from the corresponding earthquakes in (a)～(c). Black and grey area respectively show the results obtained without using EEMD and using EEMD. Dashed vertical lines denote the corresponding spectral peak frequencies of PREM-re predictions (modified from Shen and Ding, 2014)
图 5 斯通利模态的分裂函数观测图与预测图. （a, f）2S16和3S26模态的密度（红色曲线）、剪切波速（黑色实线）和压缩波速（黑色虚线）敏感核函数；（b）2S16模态的分裂函数观测图，对应最大结构系数s=6；（c）SP12RTS地幔模型的分裂函数预测图；（d）高密度LLSVPs的分裂函数预测图；（e）低密度LLSVPs的分裂函数预测图；（g～j）与（b～e）类似，但针对3S26模态，对应最大结构系数s = 4（修改自Koelemeijer et al., 2017）
Figure 5. Observed and predicted Stoneley mode splitting function maps. (a, f) Sensitivity kernels for density (red), shear-wave velocity (solid) and compressional-wave velocity (dashed) structure for modes 2S16 and 3S26, respectively. (b) Observed splitting for 2S16 plotted up to maximum structural degree s = 6. (c) Predicted splitting for mantle model SP12RTS. (d) Predicted splitting for dense LLSVPs. (e) Predicted splitting for light LLSVPs. (g～j) Similar as (b～e) but for mode 3S26 up to s = 4 (modified from Koelemeijer et al., 2017)
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