An improved algorithm for simulating waveforms of SS and its precursors based on propagation matrix method
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摘要:
410 km和660 km地幔间断面在地球内部动力学研究中具有重要意义. 在研究地幔间断面的方法中, SS前驱波由于具有全球采样优势得以广泛应用. SS及其前驱波模拟可利用有限差分和谱元法等数值模拟方法, 它们在模拟全球尺度地震波传播时具有高精度的特点, 但往往计算量很大. 因此, 该类方法难以应用于反射点广泛分布的情形. 而基于传播矩阵发展的SS及其前驱波模拟方法在保持高精度计算的同时, 可大幅提高计算效率. 本文针对SS及其前驱波的传播特征, 改进了基于传播矩阵方法的波形合成算法FASHSHWF. 通过简单层状模型对该算法进行了测试, 验证了算法及相应程序的正确性. 计算效率测试表明改进算法相较常规传播矩阵算法可节约50%以上的计算时间. 通过与AxiSEM计算的波形对比, 验证了FASHSHWF用于SS及其前驱波模拟的有效性. 在上述工作的基础上, 本文进一步探讨了新算法在研究全球近地表结构对地幔间断面复杂性探测影响中的应用.
Abstract:The 410 km and 660 km mantle discontinuities are vital for studying the dynamics of the earth's interior. Among numerous research methods of mantle discontinuity, SS precursors have been widely used due to its advantage of global sampling. SS and its precursors can be simulated by numerical methods such as the finite-difference and spectral-element methods featuring high precision in simulating worldwide seismic wave propagation. However, massive computations are necessary for these simulating methods when bounce points are widely distributed. The simulation method for SS and its precursors based on propagation matrix can significantly improve the calculation efficiency while maintaining high accuracy. According to propagation characteristics of SS and its precursors, this work improves the waveform synthesis algorithm FASHSHWF based on the propagation matrix method. The algorithm is verified through a simple layered model. The calculation efficiency saves more than 50% of time compared with conventional algorithm. Furthermore, the effectiveness of FASHSHWF in SS and its precursors' simulation is verified comparing with the waveforms calculated by AxiSEM. Based on the above work, application of the new algorithm in detection of mantle discontinuities affected by the near-surface complex structure is discussed.
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Key words:
- SS precursor /
- Mantle discontinuity /
- Propagation matrix /
- Waveform simulation
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图 1
SS及其前驱波(S410S和S660S)射线路径示意图
Figure 1.
Schematic diagram of the ray paths of SS and its precursors (S410S and S660S)
图 4
基于FASHSHWF程序合成不同位置的SS及其前驱波波形
Figure 4.
Synthetic SS and its precursors simulated by FASHSHWF
图 5
地震事件波形(实线)与FASHSHWF合成波形(虚线)对比图
Figure 5.
Comparison diagram of seismic event waveform (solid line) and FASHSHWF synthetic waveform (dashed line)
图 6
使用CRUST1.0与PREM合成地球模型的示意图
Figure 6.
Schematic diagram of synthetic earth model using CRUST1.0 and PREM
图 7
基于CRUST1.0与PREM合成地球模型计算得到的全球走时差TSS-SdS和振幅比SdS/SS分布
Figure 7.
Global distribution of the differential traveltimes TSS-SdS and the amplitude ratios SdS/SS calculated from synthetic earth model using CRUST1.0 and PREM
图 8
FASHSHWF(红线)和AxiSEM(黑线)计算的合成地震图对比
Figure 8.
Comparison of synthetic seismograms computed from FASHSHWF (red line) and AxiSEM(black line)
图 9
本文改进算法(虚线)和常规算法(实线) 计算耗时随模型层数的变化
Figure 9.
Comparison of the computational time between the improved algorithm (dashed line) and the regular algorithm (solid line)
图 10
410 km间断面过渡区宽度的影响
Figure 10.
Effects of the transition zone width of 410 km discontinuity
图 11
410 km间断面顶部低速带的影响
Figure 11.
Effects of the low-velocity layer atop of 410 km discontinuity
表 1
简单层状模型参数
Table 1.
Parameters of a simple layered model
厚度/km VP/(km·s-1) VS/(km·s-1) ρ/(g·cm-3) 海水 3.00 1.45 0.00 1.02 上地壳 12.00 5.80 3.20 2.60 下地壳 9.40 6.80 3.90 2.90 
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表 2
合成波形到时和振幅的测量值与理论计算值的比较
Table 2.
Comparison of measured arrival times and amplitudes from synthetic waveform and corresponding theoretical values
波峰(谷)编号 测量到时/s 理论到时/s 绝对误差/s 测量振幅 理论振幅 相对误差/% 1 0.00 0.00 0.00 0.15232 0.15232 0.000 2 7.48 7.50 0.02 0.97504 0.97680 0.180 3 15.00 15.00 0.00 -0.14878 -0.14878 0.000 4 22.48 22.50 0.02 0.02262 0.02266 0.177
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