Constrain low-velocity layer using higher-mode Rayleigh waves
-
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，通过数值模拟和实例分析发现：如果观测的基阶模式频散曲线不包含对低速层深度灵敏的频段，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 range. 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 multimode Rayleigh waves are conducted in this paper based on seismic reflection data. 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.
-
图 1 跨天津北断裂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）
图 2 天津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 reflection data for an active fault collected in Tianjin
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
图 4 基于多模式瑞雷面波频散曲线的反演（左）及与观测频散曲线的拟合（右）
（a） 仅用基阶模式；（b） 基阶、1阶高阶模式联合；（c） 基阶、1阶高阶和2阶高阶模式联合
Figure 4. The inversion based on multimode 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 higher modes；（c） Using the fundamental，the first higher and the second higher modes
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
图 6 基于模型1多模式瑞雷面波频散曲线的反演（左）及与观测频散曲线的拟合（右）
（a） 仅用基阶模式；（b） 基阶和1阶高阶模式联合；（c） 基阶、1阶高阶和2阶高阶模式联合
Figure 6. The inversion based on multimode 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 higher modes；（c） Using the fundamental，the first higher and the second higher modes；
8 基于模型2多模式瑞雷面波频散曲线的反演（左）及与观测频散曲线的拟合 （右）
（a） 仅用基阶模式；（b） 基阶、1阶高阶模式联合
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）
（a） Using only the fundamental mode；（b） Using the fundamental and the first higher modes
图 8 基于模型2多模式瑞雷面波频散曲线的反演（左）及与观测频散曲线的拟合 （右）
（c） 基阶、1阶高阶和2阶高阶模式联合；（d） 基阶、1阶高阶和2阶高阶模式联合，其中初始模型为（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 higher and the second higher modes；（d） Using the fundamental，the first higher and the second higher modes，and the initial model is the final model of fig. c；
图 9 基于模型2多模式瑞雷面波频散曲线的反演 （左） 及与观测频散曲线的拟合 （右）
（a） 基阶、1阶高阶和2阶高阶模式联合（仅使用部分2阶高阶频散数据）；（b） 基阶、1阶高阶和2阶高阶模式联合，其中初始模型为图8b的最终模型（仅使用部分2阶高阶频散数据）
Figure 9. The inversion based on multimode 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 higher and the second higher modes，and the initial model is the final model of fig. 8b （only part of the second higher mode dispersion data are used）
图 11 模型1 （a）和模型2 （b）中不同频率和不同模式的相速度对S波速度的灵敏度
Figure 11. The sensitivity analysis of the multimode Rayleigh-wave phase velocities at different frequencies for models 1 （a） and 2 （b）
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）频带范围的频散曲线的反演结果
Figure 12. Inversed results for models 1 （a） and 2 （b） using different modes at narrower （left） and wider （right） frequency bands
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S波速度
Table 1. The parameters of the initial model and the S-wave velocities inverted from multimode dispersion curves
层数 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 
下载: 导出CSV
表 2 模型1和模型2的模型参数
Table 2. The parameters of models 1 and 2
层数 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
下载: 导出CSV
-
陈宇坤,李振海,邵永新,王志胜,高武平,杨绪连. 2008. 天津地区第四纪年代地层剖面研究[J]. 地震地质,30(2):383–399. doi: 10.3969/j.issn.0253-4967.2008.02.005 Chen Y K,Li Z H,Shao Y X,Wang Z S,Gao W P,Yang X L. 2008. Study on the Quaternary chronostratigraphic section in Tianjin area[J]. Seismology and Geology,30(2):383–399 (in Chinese). 陈宇坤, 赵国敏, 闫成国, 李振海, 杨菲, 杨绪连, 王志胜, 刘芳, 刘红艳, 任峰, 纪静, 张春丽, 杨港生, 李文栋. 2013. 天津市活动断层探测与地震危险性评价[M]. 北京: 科学出版社: 171–175. Chen Y K, Zhao G M, Yan C G, Li Z H, Yang F, Yang X L, Wang Z S, Liu F, Liu H Y, Ren F, Ji J, Zhang C L, Yang G S, Li W D. 2013. Detection on Active Faults and Assessment on Seismic Risk in Tianjin[M]. Beijing: Science Press: 171–175 （in Chinese）. 凡友华,刘雪峰,陈晓非,刘家琦. 2009. 瑞雷波勘探的f-k域能量最大模方法[J]. 哈尔滨工业大学学报,41(1):105–107. doi: 10.3321/j.issn:0367-6234.2009.01.024 Fan Y H,Liu X F,Chen X F,Liu J Q. 2009. Max-mode method of Rayleigh wave prospecting in frequency-wavenumber domain[J]. Journal of Harbin Institute of Technology,41(1):105–107 (in Chinese). 李建平. 2018. 浅层地震反射资料的多阶振型面波反演[J]. 地震学报,40(1):24–31. doi: 10.11939/jass.20170116 Li J P. 2018. Inversion of multi-mode surface waves extracted from the shallow seismic reflection data[J]. Acta Seismologica Sinica,40(1):24–31 (in Chinese). 鲁来玉,张碧星,汪承灏. 2006. 基于瑞利波高阶模式反演的实验研究[J]. 地球物理学报,49(4):1082–1091. doi: 10.3321/j.issn:0001-5733.2006.04.021 Lu L Y,Zhang B X,Wang C H. 2006. Experiment and inversion studies on Rayleigh wave considering higher modes[J]. Chinese Journal of Geophysics,49(4):1082–1091 (in Chinese). 鲁来玉,丁志峰,何正勤. 2011. 浅层有限频率面波成像中的3D灵敏度核分析[J]. 地球物理学报,54(1):55–66. doi: 10.3969/j.issn.0001-5733.2011.01.007 Lu L Y,Ding Z F,He Z Q. 2011. Analysis of 3D sensitivity kernels of the finite frequency surface wave tomography in shallow subsurface[J]. Chinese Journal of Geophysics,54(1):55–66 (in Chinese). doi: 10.1002/cjg2.1586 罗银河,夏江海,刘江平,刘庆生. 2008. 基阶与高阶瑞利波联合反演研究[J]. 地球物理学报,51(1):242–249. doi: 10.3321/j.issn:0001-5733.2008.01.030 Luo Y H,Xia J H,Liu J P,Liu Q S. 2008. Joint inversion of fundamental and higher mode Rayleigh waves[J]. Chinese Journal of Geophysics,51(1):242–249 (in Chinese). 王辉,丁志峰. 2006. 浅层地震勘探资料处理中的速度分析参数选取[J]. 地震地质,28(4):597–603. doi: 10.3969/j.issn.0253-4967.2006.04.007 Wang H,Ding Z F. 2006. Parameters selection for velocity analysis in shallow seismic data processing[J]. Seismology and Geology,28(4):597–603 (in Chinese). 夏江海. 2015. 高频面波方法[M]. 武汉: 中国地质大学出版社: 85–86. Xia J H. 2015. High-Frequency Surface-Wave Method[M]. Wuhan: China University of Geosciences Press: 85–86 （in Chinese）. 尹晓菲,胥鸿睿,郝晓菡,孙石达,王芃. 2020. 水平层状模型中多模式瑞雷波和拉夫波相速度频散曲线的灵敏度分析[J]. 石油地球物理勘探,55(1):136–146. Yin X F,Xu H R,Hao X H,Sun S D,Wang P. 2020. Sensitivity analysis of multi-mode Rayleigh and Love wave phase-velocity dispersion curves in horizontal layered models[J]. Oil Geophysical Prospecting,55(1):136–146 (in Chinese). 张碧星,鲁来玉. 2002. 层状半空间中导波的传播[J]. 声学学报,27(4):295–304. doi: 10.3321/j.issn:0371-0025.2002.04.002 Zhang B X,Lu L Y. 2002. Propagation of guided waves in stratified half space[J]. Acta Acustica,27(4):295–304 (in Chinese). Alleyne D,Cawley P. 1991. A two-dimensional Fourier transform method for the measurement of propagating multimode signals[J]. J Acoust Soc Am,89(3):1159–1168. doi: 10.1121/1.400530 Forbriger T. 2003a. Inversion of shallow-seismic wavefields:I. Wavefield transformation[J]. Geophys J Int,153(3):719–734. doi: 10.1046/j.1365-246X.2003.01929.x Forbriger T. 2003b. Inversion of shallow-seismic wavefields:II. Inferring subsurface properties from wavefield transforms[J]. Geophys J Int,153(3):735–752. doi: 10.1046/j.1365-246X.2003.01985.x Forchap E A,Schmid G. 1998. Experimental determination of Rayleigh-wave mode velocities using the method of wave number analysis[J]. Soil Dyn Earthq Eng,17(3):177–183. Foti S. 2000. Multistation Methods for Geotechnical Characterization Using Surface Waves[D]. Turin: Politecnico di Torino: 63–65, 109–127. Gabriels P,Snieder R,Nolet G. 1987. In situ measurements of shear-wave velocity in sediments with higher-mode Rayleigh waves[J]. Geophys Prospect,35(2):187–196. doi: 10.1111/j.1365-2478.1987.tb00812.x Gao L L,Xia J H,Pan Y D. 2014. Misidentification caused by leaky surface wave in high-frequency surface wave method[J]. Geophys J Int,199(3):1452–1462. doi: 10.1093/gji/ggu337 Ikeda T,Matsuoka T,Tsuji T,Hayashi K. 2012. Multimode inversion with amplitude response of surface waves in the spatial autocorrelation method[J]. Geophys J Int,190(1):541–552. doi: 10.1111/j.1365-246X.2012.05496.x Liang Q,Chen C,Zeng C,Luo Y H,Xu Y X. 2008. Inversion stability analysis of multimode Rayleigh-wave dispersion curves using low-velocity-layer models[J]. Near Surf Geophys,6(3):157–165. doi: 10.3997/1873-0604.2007040 Lu L Y,Zhang B X. 2004. Analysis of dispersion curves of Rayleigh waves in the frequency-wavenumber domain[J]. Can Geotech J,41(4):583–598. doi: 10.1139/t04-005 Lu L Y,Zhang B X. 2006. Inversion of Rayleigh waves using a genetic algorithm in the presence of a low-velocity layer[J]. Acoust Phys,52(6):701–712. doi: 10.1134/S106377100606011X Lu L Y,Wang C H,Zhang B X. 2007. Inversion of multimode Rayleigh waves in the presence of a low-velocity layer:Numerical and laboratory study[J]. Geophys J Int,168(3):1235–1246. doi: 10.1111/j.1365-246X.2006.03258.x Luo Y H,Xia J H,Liu J P,Liu Q S,Xu S F. 2007. Joint inversion of high-frequency surface waves with fundamental and higher modes[J]. J Appl Geophys,62(4):375–384. Maraschini M,Ernst F,Foti S,Socco L V. 2010. A new misfit function for multimodal inversion of surface waves[J]. Geophysics,75(4):G31–G43. doi: 10.1190/1.3436539 Maraschini M,Foti S. 2010. A Monte Carlo multimodal inversion of surface waves[J]. Geophys J Int,182(3):1557–1566. doi: 10.1111/j.1365-246X.2010.04703.x Matsuzawa H,Yoshizawa K. 2019. Array-based analysis of multimode surface waves:Application to phase speed measurements and modal waveform decomposition[J]. Geophys J Int,218(1):295–312. doi: 10.1093/gji/ggz153 Mcmechan G A,Yedlin M J. 1981. Analysis of dispersive waves by wave field transformation[J]. Geophysics,46(6):869–874. doi: 10.1190/1.1441225 Socco L V,Foti S,Boiero D. 2010. Surface-wave analysis for building near-surface velocity models:Established approaches and new perspectives[J]. Geophysics,75(5):75A83–75A102. doi: 10.1190/1.3479491 Tokimatsu K,Tamura S,Kojima H. 1992. Effects of multiple modes on Rayleigh wave dispersion characteristics[J]. J Geotech Eng,118(10):1529–1543. doi: 10.1061/(ASCE)0733-9410(1992)118:10(1529) Wang J N,Wu G X,Chen X F. 2019. Frequency-Bessel transform method for effective imaging of higher-mode Rayleigh dispersion curves from ambient seismic noise data[J]. J Geophys Res:Solid Earth,124(4):3708–3723. doi: 10.1029/2018JB016595 Xia J H,Miller R D,Park C B. 1999. Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves[J]. Geophysics,64(3):659–992. doi: 10.1190/1.1444578 Xia J H,Miller R D,Park C B,Tian G. 2003. Inversion of high frequency surface waves with fundamental and higher modes[J]. J Appl Geophys,52:45–57. doi: 10.1016/S0926-9851(02)00239-2 Xu Y X,Xia J H,Miller R D. 2006. Quantitative estimation of minimum offset for multichannel surface-wave survey with attively exciting source[J]. J Appl Geophys,59(2):117–125. doi: 10.1016/j.jappgeo.2005.08.002 Zhang S X,Chan L S. 2003. Possible effects of misidentified mode number on Rayleigh wave inversion[J]. J Appl Geophys,53(1):17–29. doi: 10.1016/S0926-9851(03)00014-4 -
查看大图
计量
- 文章访问数: 30
- HTML全文浏览量: 10
- PDF下载量: 22
- 被引次数: 0