二维起伏地形瑞利面波速度频散特性数值模拟研究
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摘要
瑞利面波在起伏地形下传播的特性不仅与介质性质有关,而且与地形起伏程度有关.目前,国内外对水平地形下瑞利面波频散特性研究较为成熟,但对起伏地形下瑞利面波的频散研究较少.由于地形影响,面波和体波是耦合在一起的,完备的理论尚在探索中.本文以水平地形瑞利面波传播理论为基础展开起伏地形下瑞利面波传播特性研究.首先应用二维有限元数值模拟方法,基于波场快照和合成地表地震记录研究了起伏地形条件下瑞利面波波场的传播特征.在此基础上,研究了起伏地形引起的波场畸变对多道瑞利面波速度频散分析的影响.研究表明:由于起伏地形对波场能量的散射和反射产生传播波的模式转换,导致起伏地形远场为瑞利面波和转换S波叠加的复杂波场,该复杂波场会影响多道瑞利面波的速度频散特征.当地形高差小于0.2个优势波长时,地形影响较小可以近似忽略;而当地形高差接近或大于面波的优势波长时,地形影响较大,在资料解释需考虑.
The propagation characteristics of Rayleigh waves trvalling along topographies are not only with the medium, but also with the extent of varying topographies. Currently, the researches related to the dispersion characteristics of Rayleigh waves are mainly focused on the half-space with a horizontal surface. Then, the research to the that of Rayleigh waves under topography condition is not well established. Due to the effects of topography, Rayleigh waves and body waves are usually coupling together. And complete theory is still under exploration. In the paper, based on the dispersion characteristics of Rayleigh waves under the condition of a half-space with a horizontal surface, a study for the dispersion characteristics of Rayleigh waves trvalling along topographies is conducted. At first, by using the 2 D finite element numerical method, the propagation characteristics of Rayleigh waves along varying topography based upon the snapshots and synthetic recordings are studied. Then, the effects of distorted wave field caused by the topography to the velocity dispersion of Rayleigh waves are analyzed and discussed. The results show that the reflection and refraction being caused by topography can rise the converted waves, mainly as converted S-wave, which complicate the Rayleigh wave field. Then, the dispersion characteristics of Rayleigh waves can be effected by the complicated wave field. When the topography difference is less than the 0.2 main wavelength, the effects of topography on the dispersion of Rayleigh waves approximately can be neglected, while the topography effects must be considered when the difference is close or over the main wavelength.
The propagation characteristics of Rayleigh waves trvalling along topographies are not only with the medium, but also with the extent of varying topographies. Currently, the researches related to the dispersion characteristics of Rayleigh waves are mainly focused on the half-space with a horizontal surface. Then, the research to the that of Rayleigh waves under topography condition is not well established. Due to the effects of topography, Rayleigh waves and body waves are usually coupling together. And complete theory is still under exploration. In the paper, based on the dispersion characteristics of Rayleigh waves under the condition of a half-space with a horizontal surface, a study for the dispersion characteristics of Rayleigh waves trvalling along topographies is conducted. At first, by using the 2 D finite element numerical method, the propagation characteristics of Rayleigh waves along varying topography based upon the snapshots and synthetic recordings are studied. Then, the effects of distorted wave field caused by the topography to the velocity dispersion of Rayleigh waves are analyzed and discussed. The results show that the reflection and refraction being caused by topography can rise the converted waves, mainly as converted S-wave, which complicate the Rayleigh wave field. Then, the dispersion characteristics of Rayleigh waves can be effected by the complicated wave field. When the topography difference is less than the 0.2 main wavelength, the effects of topography on the dispersion of Rayleigh waves approximately can be neglected, while the topography effects must be considered when the difference is close or over the main wavelength.
引文
Chen W, Xu Y X, Zhang Y, 2009. Study of Transmission Characteristics of Rayleigh Waves on an Elastic Wedge [J] Chinese Journal of Engineering Geophysics (in Chinese), 6(2):143-149.
Dong L G. 2005. The simulation of seismic wave propagation in Complex surface conditions [J]. Progress in Exploration GeoPhysics, 28(3): 187-194.
Fujii K, Takeuchi S, Okano Y, et al. 1984. Rayleigh wave scattering at various wedge corners [J]. Bull. Seism. Soc. Am., 74: 41- 60.
Park C, Miller R, Xia J. 1999, Multichannel analysis of surface waves [J]. Geophysics 64: 800-808.
Sanchez-Sesma F J, Campillo M. 1991. Diffraction of P, SV, and Rayleigh waves by topographic features: A boundary integral formulation.Bull [J]. Seism. Soc. Am., 81: 2234-2253.
Zhang B X, Lu L Y. 2005. Investigation on the dispersion curves of rayleigh wave by frequency-wavenumber analysis method [J]. Chinese Journal of Engineering Geophysics, 2(4): 245-255.
Zhang B X, Lu Li Y, Bao G S. 2002. A Study On Zigzag Dispersion Curves In Rayleigh Wave Exploration [J]. Chinese Journal of Geophysics (in Chinese), 45(2): 263-274, doi: 10.3321/j.issn:0001-5733.2002.02.013.
Zhang K, Liu Z P, Xiong Z Y, et al. 2015. Application of seismoelectric effect to the experiment measurememt of Rayleigh surface waves [J]. Progress in Geophysics(in chinese), 30(6): 2955-2962, doi: 10.6038/pg20150665.
Zhou H, Chen X F. 2006, The study on the frequency responses of topography with different scales due to incident SH wave [J]. Chinese J.Geophys. (in Chinese) ,49(1):208-214, doi: 10.3321/j.issn:0001-5733.2006.01.027.
Zhou H, Chen X F. 2007. A study on the effect of depressed topography on Rayleigh surface wave [J]. Chinese J.Geophys. (in Chinese), 50(4): 1182-1189, doi: 10.3321/j.issn:0001-5733.2007.04.027.
陈伟, 徐义贤, 张煜. 2009. 瑞雷面波在弹性楔状体中的传播特性研究[J]. 工程地球物理学报 , 6(2):143-149.
董良国. 2005. 复杂地表条件下地震波传播数值模拟[J]. 勘探地球物理进展,28(3): 187-194.
张碧星, 鲁来玉, 鲍光淑. 2002. 瑞利波勘探中“之”字形频散曲线研究[J]. 地球物理学报, 45(2): 263-274, doi: 10.3321/j.issn:0001-5733.2002.02.013.
张凯, 刘争平, 熊自英, 等. 2015. 声电效应在瑞利面波频散特性物理模拟中的应用[J]. 地球物理学进展, 30(6): 2955-2962, doi: 10.6038/pg20150665.
周红, 陈晓非. 2006. 不同尺度地形的SH波频率域响应特征研究[J]. 地球物理学报, 49(1): 205-211, doi: 10.3321/j.issn:0001-5733.2006.01.027.
周红, 陈晓非. 2007. 凹陷地形对Rayleigh面波传播影响的研究[J]. 地球物理学报, 50(4): 1182-1189, doi: 10.3321/j.issn:0001-5733.2007.04.027.
(1)1)汪利民. 2015. 三维多道面波分析技术及基于三维矢量波动方程的面波数值模拟技术研究[R]. 武汉:中国地质大学(武汉), 38-49.
Dong L G. 2005. The simulation of seismic wave propagation in Complex surface conditions [J]. Progress in Exploration GeoPhysics, 28(3): 187-194.
Fujii K, Takeuchi S, Okano Y, et al. 1984. Rayleigh wave scattering at various wedge corners [J]. Bull. Seism. Soc. Am., 74: 41- 60.
Park C, Miller R, Xia J. 1999, Multichannel analysis of surface waves [J]. Geophysics 64: 800-808.
Sanchez-Sesma F J, Campillo M. 1991. Diffraction of P, SV, and Rayleigh waves by topographic features: A boundary integral formulation.Bull [J]. Seism. Soc. Am., 81: 2234-2253.
Zhang B X, Lu L Y. 2005. Investigation on the dispersion curves of rayleigh wave by frequency-wavenumber analysis method [J]. Chinese Journal of Engineering Geophysics, 2(4): 245-255.
Zhang B X, Lu Li Y, Bao G S. 2002. A Study On Zigzag Dispersion Curves In Rayleigh Wave Exploration [J]. Chinese Journal of Geophysics (in Chinese), 45(2): 263-274, doi: 10.3321/j.issn:0001-5733.2002.02.013.
Zhang K, Liu Z P, Xiong Z Y, et al. 2015. Application of seismoelectric effect to the experiment measurememt of Rayleigh surface waves [J]. Progress in Geophysics(in chinese), 30(6): 2955-2962, doi: 10.6038/pg20150665.
Zhou H, Chen X F. 2006, The study on the frequency responses of topography with different scales due to incident SH wave [J]. Chinese J.Geophys. (in Chinese) ,49(1):208-214, doi: 10.3321/j.issn:0001-5733.2006.01.027.
Zhou H, Chen X F. 2007. A study on the effect of depressed topography on Rayleigh surface wave [J]. Chinese J.Geophys. (in Chinese), 50(4): 1182-1189, doi: 10.3321/j.issn:0001-5733.2007.04.027.
陈伟, 徐义贤, 张煜. 2009. 瑞雷面波在弹性楔状体中的传播特性研究[J]. 工程地球物理学报 , 6(2):143-149.
董良国. 2005. 复杂地表条件下地震波传播数值模拟[J]. 勘探地球物理进展,28(3): 187-194.
张碧星, 鲁来玉, 鲍光淑. 2002. 瑞利波勘探中“之”字形频散曲线研究[J]. 地球物理学报, 45(2): 263-274, doi: 10.3321/j.issn:0001-5733.2002.02.013.
张凯, 刘争平, 熊自英, 等. 2015. 声电效应在瑞利面波频散特性物理模拟中的应用[J]. 地球物理学进展, 30(6): 2955-2962, doi: 10.6038/pg20150665.
周红, 陈晓非. 2006. 不同尺度地形的SH波频率域响应特征研究[J]. 地球物理学报, 49(1): 205-211, doi: 10.3321/j.issn:0001-5733.2006.01.027.
周红, 陈晓非. 2007. 凹陷地形对Rayleigh面波传播影响的研究[J]. 地球物理学报, 50(4): 1182-1189, doi: 10.3321/j.issn:0001-5733.2007.04.027.
(1)1)汪利民. 2015. 三维多道面波分析技术及基于三维矢量波动方程的面波数值模拟技术研究[R]. 武汉:中国地质大学(武汉), 38-49.