Constraint on low-velocity layer using higher mode Rayleigh waves in the shallow structure research
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摘要: 在实际中常遇到一类含有低速层的介质，其频散曲线在感兴趣的频率范围并无视觉上的交叉现象，也无明显的低速层指示。针对此类介质，基于地震反射资料中的面波信息，综合实例和数值模拟进行分析，结果显示：如果观测的基阶模式频散曲线不包含对低速层深度敏感的频段，单独基于基阶模式的频散曲线可能无法恢复模型的低速特征；但如果同时利用相同频段的多阶模式信息，即使观测的频散曲线没有明显的低速特征指示，也可以通过多模式频散信息反演重建模型的低速特征。Abstract: Due to high sensitivity to S-wave velocity, Rayleigh-wave dispersion curves of the fundamental and higher modes are usually used to invert near-surface S-wave velocities in engineering geophysical exploration. For the model containing a low-velocity layer, the dispersion curves of the fundamental and higher modes show two typical characteristics. One typical characteristic is that the crossover would be observed between different modes, and the fundamental mode shows obvious indication of low-velocity characteristics in interested frequency ranges. For the other kind of model with low-velocity layers, the dispersion curves have no visual crossing phenomenon in the frequency range of interest, and the low-velocity characteristics may not be observed in the measured dispersion curves. For the latter model containing a low-velocity layer, which is often encountered in practice, investigations on the inversion of multi-mode Rayleigh waves are conducted in this paper based on seismic reflection data. The studies show that if the observed fundamental-mode dispersion curve does not include the frequency band sensitive to the depth of the low-velocity layer, the inversion based on the fundamental-mode alone may not be able to recover the low-velocity characteristics of the model. But the low-velocity layer can be reconstructed accurately by inversion considering both the fundamental and higher mode Rayleigh waves even the observed fundamental mode dispersion curve has no obvious indication of low-velocity characteristics.
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图 1 跨天津北断裂的地震勘探测线及钻孔位置示意图（陈宇坤等，2013）
Figure 1. Schematic diagram of seismic survey line and borehole location across the north fault of Tianjin （Chen et al，2013）
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图 2 跨天津北某活动断层浅层地震勘探数据的时间序列
Figure 2. Time series of the shallow seismic exploration data across the north fault of Tianjin
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图 3 图2所示时间序列在频率-波数域和频率-相速度域中的能量分布
（a） 未剔除体波的结果；（b） 剔除体波后的结果；（c） 提取的三个模式的频散点
Figure 3. The energy distribution in the frequency-wavenumber and frequency-phase velocity domains for the time series shown in Fig.2
（a） The result before removing body waves；（b） The result after removing body waves； （c） The extraction of surface-wave dispersion curves for three modes
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图 4 基于多模式瑞雷面波频散曲线的反演（左）及其最终模型理论频散曲线与观测频散曲线的拟合（右）
（a） 仅用基阶模式；（b） 基阶、一阶模式联合；（c） 基阶、一阶和二阶模式联合
Figure 4. The inversion based on multi-mode Rayleigh-wave dispersion curves （left） and the fitting between the theoretical and observed dispersion curves （right）
（a） Using only the fundamental mode；（b） Using the fundamental and the first modes；（c） Using the fundamental，the first and the second modes
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图 5 表2中两个模型的理论频散曲线
红点表示的频率范围与本文实际数据采集得到的观测频散曲线的频带范围相同，如图3c所示（a） 模型1：速度递增模型；（b） 模型2：含有低速层的模型
Figure 5. The theoretical dispersion curves calculated from two models 1 and 2 listed in Table 2
The red dots indicate the theoretical dispersion curves with the same frequency range as the observed dispersion curves shown in Fig. 3c （a） Model 1：A normal layered model with S-wave velocity increasing with depth； （b） Model 2：A model with a low-velocity layer
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图 6 基于模型1多模式瑞雷面波频散曲线的反演（左）及其最终模型理论频散曲线与观测频散曲线的拟合（右）
（a） 仅用基阶模式；（b） 基阶和一阶模式联合；（c） 基阶、一阶和二阶模式联合
Figure 6. The inversion based on multi-mode Rayleigh-wave dispersion curves of model 1 （left） and the fitting between the theoretical and observed dispersion curves （right）
（a） Using only the fundamental mode；（b） Using the fundamental and the first modes；（c） Using the fundamental，the first and the second modes
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图 8 基于模型2多模式瑞雷面波频散曲线的反演（左）及其最终模型理论频散曲线与观测频散曲线的拟合 （右）
（a） 仅用基阶模式；（b） 基阶和一阶模式联合
Figure 8. The inversion based on multi-mode Rayleigh-wave dispersion curves of model 2 （left） and the fitting between the theoretical and observed dispersion curves （right）
（a） Using only the fundamental mode；（b） Using the fundamental and the first modes
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图 8 基于模型2多模式瑞雷面波频散曲线的反演（左）及其最终模型理论频散曲线与观测频散曲线的拟合 （右）
（c） 基阶、一阶和二阶模式联合；（d） 基阶、一阶和二阶模式联合，其中初始模型为图（c）的最终模型
Figure 8. The inversion based on multimode Rayleigh-wave dispersion curves of model 2 （left） and the fitting between the theoretical and observed dispersion curves （right）
（c） Using the fundamental，the first and the second modes；（d） Using the fundamental， the first and the second modes，and the initial model is the final model of Fig.c；
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图 9 基于模型2多模式瑞雷面波频散曲线的反演 （左） 及其最终模型理论频散曲线与观测频散曲线的拟合 （右）
（a） 基阶、一阶和二阶模式联合（仅使用部分二阶频散数据）；（b） 基阶、一阶和二阶模式联合，其中初始模型为图8b的最终模型（仅使用部分二阶频散数据）
Figure 9. The inversion based on multi-mode Rayleigh-wave dispersion curves of model 2 （left） and the fitting between the theoretical and observed dispersion curves （right）
（a） Using the fundamental，the first higher and the second higher modes （only part of the second higher mode dispersion data are used）；（b） Using the fundamental，the first and the second modes，and the initial model is the final model of Fig.8b （only part of the second mode dispersion data are used）
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图 11 模型1 （a）和模型2 （b）在不同频率和不同模式下瑞雷波相速度的S波速度深度敏感核
Figure 11. The sensitivity analysis of the multimode Rayleigh-wave phase velocities at different frequencies for models 1 （a） and 2 （b）
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图 12 模型1 （a）和模型2 （b）中采用不同模式基于较窄（左）和较宽（右）频段的频散曲线的反演结果
Figure 12. Inversion results of dispersion curves based on narrower （left） and wider （right） frequency bands using different modes for models 1 （a） and 2 （b）
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图 13 S波速度剖面 （a）及钻孔土层 （b）
Figure 13. S-wave velocity profile （a） and borehole soil layer （b）
表 1 初始模型参数和各模式频散曲线联合反演的S波速度
Table 1 The parameters of the initial model and the S-wave velocities inverted from multi-mode dispersion curves
层序 层厚/m 深度/m ρ/（g·cm−3） vP/（m·s−1） 初始vS/（m·s−1） 反演vS/（m·s−1） 1 1.0 1.0 1.60 300 152 135.4 2 1.0 2.0 1.73 400 156 145.3 3 1.0 3.0 1.77 470 163 200.8 4 1.0 4.0 1.79 550 165 221.5 5 1.0 5.0 1.79 570 170 195.4 6 1.0 6.0 1.79 590 180 169.6 7 1.0 7.0 1.79 600 185 155.3 8 1.0 8.0 1.79 700 190 102.4 9 2.0 10.0 1.79 800 200 152.8 10 3.0 13.0 1.79 900 210 254.6 11 4.0 17.0 1.80 1 100 220 259.3 半空间 $ \infty $ $ \infty $ 1.80 1 200 230 250.1 
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表 2 模型1和模型2的模型参数
Table 2 The parameters of models 1 and 2
层序 层厚/m 深度/m 模型1 模型2 $\mathrm{\rho }/ （ \mathrm{g}\cdot {\mathrm{c}\mathrm{m} }^{-3} ） $ ${v}_{{\rm{P}}}/ （ {\rm{m}}\cdot {{\rm{s}}}^{-1} ） $ ${{v} }_{{{\rm{S}}} }/ （ \mathrm{m}\cdot {\mathrm{s} }^{-1} ） $ $\mathrm{\rho }/ （ \mathrm{g}\cdot {\mathrm{c}\mathrm{m} }^{-3} ） $ ${v}_{{\rm{P}}}/ （ {\rm{m}}\cdot {{\rm{s}}}^{-1} ） $ ${{v} }_{{{\rm{S}}} }/ （ \mathrm{m}\cdot {\mathrm{s} }^{-1} ） $ 1 1.0 1.0 1.581 7 249.1 126.5 1.605 3 266.2 135.4 2 1.0 2.0 1.654 6 399.7 156.0 1.629 7 373.2 145.3 3 1.0 3.0 1.728 3 556.2 192.9 1.724 1 580.1 200.8 4 1.0 4.0 1.735 2 659.8 196.8 1.776 2 738.1 221.5 5 1.0 5.0 1.739 5 646.0 199.2 1.732 7 654.9 195.4 6 1.0 6.0 1.739 5 664.8 199.3 1.683 6 554.8 169.6 7 1.0 7.0 1.739 7 653.0 199.4 1.653 0 505.1 155.3 8 1.0 8.0 1.742 1 739.8 200.8 1.508 2 376.8 102.4 9 2.0 10.0 1.754 8 832.9 208.2 1.647 2 611.3 152.8 10 3.0 13.0 1.767 5 926.3 216.0 1.824 7 1 089.9 254.6 11 4.0 17.0 1.780 3 1 120.5 224.1 1.831 0 1 297.7 259.3 半空间 $ \infty $ $ \infty $ 1.792 9 1 210.7 232.3 1.818 5 1 303.7 250.1
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