瑞雷波场正演模拟及频散曲线的提取
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摘要
面波勘探是在近几年才兴起的一种浅层勘探方法。它广泛应用于工程勘探,岩土工程,以及地基评估等方面。在工程物探方法中占据着重要的地位。其原因在于通过所测得面波记录计算出频散曲线就可以直接对场地进行分层,此方法简便、经济、实用。因此,对瑞雷面波的传播规律和机理的认识,和准确的提取出频散曲线就显的尤为重要。
本文阐述了瑞雷波的基本理论及其传播振动特性。通过一阶速度-应力弹性波动方程用交错网格有限差分法,对其进行数值求解,实现了瑞雷面波的数值模拟,得到了其波场快照和面波理论记录,并利用简单模型验证其正确性。在提取频散曲线方面介绍并实现了三种方法：f-k法、τ-p法、相移法。传统的f-k法、τ-p法所提取的频散曲线,速度都是不等距变化的。本文在传统的方法基础上做了改进,能够直接在f-v谱上提取频散曲线,避免了传统的f-k法、τ-p法所提取的频散曲线的突跳现象。首先通过正演数值模拟出理论面波记录,然后利用各种方法在理论记录上提取频散曲线,再用频散曲线的正演验证其所提取频散曲线的正确性,最后比较并分析了各种方法所求出频散曲线的优劣性。发现τ-p法、相移法的效果较f-k法好,更加较为贴近理论正演结果,实际应用中应作为首选方法。
对实测记录提取了频散曲线,指出了论文中需要更加深入研究的内容和方向。
The surface wave exploration is a recently developed shallow exploration methods. It is widely used in engineering exploration, geotechnical engineering, groundwork evaluating, and so on. It plays an important role in engineering geophysical method. Its reason is through dispersion curves can be directly layer explanation. This method is simple, economical and practical. Therefore, Understand the Rayleigh wave propagation mechanism, and accurately extract frequency dispersion curve is significant particularly important.
This thesis expounds the basic theory and the Rayleigh wave propagation characteristics of vibration. Through the first-order speed-stress elastic wave equation with the finite difference method and staggered grids, realized the Rayleigh wave numerical simulation, got the wave field snapshots and wave theory records, and used the simple model to test its true. To extracting frequency dispersion curves, introduced and realized fulfill the three methods: f-k method,τ-p method and phase-shift method. The extraction rate of the frequency dispersion curves which extracted by traditional method is not isometric changes. This thesis modified the traditional method. It can directly extract frequency dispersion curves in the f-v spectrum, avoided jump phenomena of frequency dispersion curves extraction which extracted by f-k method andτ-p method.First, simulated a theory of surface wave record, second, used all sorts of methods on record extracting frequency dispersion curves with, then verified its correctness by theoretical frequency dispersion curves, finally compared and analyzed the frequency dispersion curves. Discoveredτ-p method and phase-shift method effect is good, more close to the theoretical results. These two kinds of methods should be the top-choice in practical application.
Extracted the frequency dispersion curves of field data and pointed out in the thesis to more in-depth study of the content and direction.
本文阐述了瑞雷波的基本理论及其传播振动特性。通过一阶速度-应力弹性波动方程用交错网格有限差分法,对其进行数值求解,实现了瑞雷面波的数值模拟,得到了其波场快照和面波理论记录,并利用简单模型验证其正确性。在提取频散曲线方面介绍并实现了三种方法：f-k法、τ-p法、相移法。传统的f-k法、τ-p法所提取的频散曲线,速度都是不等距变化的。本文在传统的方法基础上做了改进,能够直接在f-v谱上提取频散曲线,避免了传统的f-k法、τ-p法所提取的频散曲线的突跳现象。首先通过正演数值模拟出理论面波记录,然后利用各种方法在理论记录上提取频散曲线,再用频散曲线的正演验证其所提取频散曲线的正确性,最后比较并分析了各种方法所求出频散曲线的优劣性。发现τ-p法、相移法的效果较f-k法好,更加较为贴近理论正演结果,实际应用中应作为首选方法。
对实测记录提取了频散曲线,指出了论文中需要更加深入研究的内容和方向。
The surface wave exploration is a recently developed shallow exploration methods. It is widely used in engineering exploration, geotechnical engineering, groundwork evaluating, and so on. It plays an important role in engineering geophysical method. Its reason is through dispersion curves can be directly layer explanation. This method is simple, economical and practical. Therefore, Understand the Rayleigh wave propagation mechanism, and accurately extract frequency dispersion curve is significant particularly important.
This thesis expounds the basic theory and the Rayleigh wave propagation characteristics of vibration. Through the first-order speed-stress elastic wave equation with the finite difference method and staggered grids, realized the Rayleigh wave numerical simulation, got the wave field snapshots and wave theory records, and used the simple model to test its true. To extracting frequency dispersion curves, introduced and realized fulfill the three methods: f-k method,τ-p method and phase-shift method. The extraction rate of the frequency dispersion curves which extracted by traditional method is not isometric changes. This thesis modified the traditional method. It can directly extract frequency dispersion curves in the f-v spectrum, avoided jump phenomena of frequency dispersion curves extraction which extracted by f-k method andτ-p method.First, simulated a theory of surface wave record, second, used all sorts of methods on record extracting frequency dispersion curves with, then verified its correctness by theoretical frequency dispersion curves, finally compared and analyzed the frequency dispersion curves. Discoveredτ-p method and phase-shift method effect is good, more close to the theoretical results. These two kinds of methods should be the top-choice in practical application.
Extracted the frequency dispersion curves of field data and pointed out in the thesis to more in-depth study of the content and direction.
引文
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[2]Haskell,M.A. The dispersion of surface waves on multilayered media[J].Bulletin of the Seismological Society of America,1953,43(1):17-43
[3]Chang F K. Rayleigh wave dispersion technique for rapid subsurface exploration[A].第42届国际地球物理年会[C],1973
[4]VIC株式会社.佐藤式全自动地下勘察机(GR-810)[M].1986
[5]J.S.Heisey, K.H.Stoke, A.H.Meyer.Muduli of pavement systems from spectralanalysis of surface waves[M].Transfortation Research Record,1982:247-258
[6]S.Nazarian, K.H.Stokoe. In situ determination of elastic moduli of pavement systems by spectral-of-surface-waves method[C].Research Report, Austin, Centerfor Transportation, The University of Texas,1986:437-442.
[7]刘云祯,王振东.瞬态表面波法的数据采集处理系统及其应用实例[J].物探与化探,1996,20(1)：28-33
[8]阮元成,陈宁,常亚屏.瞬态面波法在察汗乌苏水电站坝基测试中的应用[R].福州：第九届岩土工程物探学术交流会,2006
[9]于杰荣,彭皖生,董辉等.瑞雷波勘探技术在海堤工程检测中的应用[R].福州：第九届岩土工程物探学术交流会,2006
[10]黄真萍,罗敏,李堂磊.瑞雷面波在强夯地基效果评价中的研究与应用[R].福州：第九届岩土工程物探学术交流会,2006
[11]蒋婵君.瑞雷波资料处理方法研究[D].中南大学硕士学位论文,2009
[12]刘云祯.工程物探新技术[M].北京地质出版社,2006
[13]崔占荣,张世洪,张俊喻.瞬态瑞雷面波勘探中一些问题讨论[J].物探与化探,1997,
19(5)：369-376
[14]包军强,张学强,刘江干等.浅层多波的分离、识别与提取[J].物探与化探,1998,22(5)：336-376
[15]肖柏勋,柴亚萍,石波.基于扩充Prony法的瞬态瑞利面波的相速度提取.水利水电快报,v20,1999,73-77.
[16]李绵飞.TRES-1型多分量瑞利面波勘探仪的研究应用.物探与化探,22(2),998,129-133
[17]时福荣.互相关分析计算瑞雷面波传播速度的原理和方法[J].物探与化探,1990,12(4)：357-360
[18]任青文.表面波谱分析法及其在工程中的应用[J].河海科技进展.1994,14(2)：7-13
[19]张碧星,鲁来玉.用频率-波数法分析瑞雷面波频散曲线[J].工程地球物理学报.2005,2(4)：245-248
[20]朱晓明,薛家俊,刘喜武等.时频分析在地震数据处理中的应用[J].内蒙古石油化工,2007,33(8)：96-99
[21]陈淑珍,刘怀林.基于τ-p变换的频散曲线及其算法实现[J].武汉大学学报(自然科学版),2000,46(1)：123-126
[22]孙云莲,刘敦敏.时-频分析与小波变换及其应用[J].武汉大学学报(工学版),2003,36(2)： 103-106
[23]Haskell,M.A.The dispersion of surface waves on multilayered media[J].Bulletin[J].Bull Seism Soc Am,1953,43(8):17-34
[24]Knopoff, L.A matrix method for elasticwave propagation[J].Bulletin of the seismological society of America,1964,54:431-438
[25]凡友华,刘家琦,韩波.瑞利面波频散曲线的理论计算研究[J].湖南大学学报,2001,28(3)：10-16
[26]Abo-Zena,A.Dispersion function computations for unlimited frequency values[J]. Geophysical Journal of the Royal Astronomical Society,979,58:91-105
[27]张碧星,兰从庆,喻明等：分层介质中面波能量分布[J].声学学报,1998,23(2)：97-106
[28]凡友华,肖柏勋,刘家琦.计算层状介质中轴对称柱面瑞利面波频散函数的δ矩阵法[J].物探与化探,2001,25(2)：109-116
[29]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟[J].地球物理学报,2007,50(2)：568-573
[30]熊章强,张大洲,肖柏勋等.裂缝介质中瑞雷面波传播的渐变非均匀交错网格数值模拟[J].湖南大学学报(自然科学版),2008,35(8)：24-28
[31]熊章强,张大洲,秦臻等.瑞雷波数值模拟中的边界条件及模拟实例分析[J].中南大学学报(自然科学版),2008,39(4)：825-830
[32]裴云江,吴永刚,刘英杰.近地表低速带反演[J].长春地质学院学报,1994,24(3)：317-320
[33]石耀霖,金文.面波频散反演地球内部构造的遗传算法[J].地球物理学报,1995,38(2)：189-198
[34]肖柏勋.高模式瑞雷面波及其正反演研究[D].中南大学,2000
[35]刘江平,侯卫生,徐顺芳.相邻道瑞雷波法及在防渗墙强度检测中的应用[J].人民长江,2003,34(2)：34-36
[36]鲁来玉等.基于瑞利波高阶模式反演的实验研究[J].地球物理学报,2006,49(4)：1082-1091
[37]R.E.谢里夫,L.P.吉尔达特.勘探地震学[M].石油工业出版社,1994
[38]梁志强.层状介质中多模式面波频散曲线研究[D].长安大学,2006
[39]陆基孟.地震勘探原理[M].东营：石油大学出版社,1993
[40]朱介寿等.地震学中的计算方法[M].北京：地震出版社,1988
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