Matlab环境下瑞利波有限差分正演与曲线绘制
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摘要
以瑞利波频散方程为出发点的Abo-Zena传递矩阵等方法,只能研究层状介质中瑞利波的传播特性,对于非层状介质,传递矩阵无能为力。因此,不得不考虑有限元、有限差分等方法。根据弹性动力学方程,采用交错网格有限差分方法对均匀弹性半空间介质进行全波场模拟,并在Matlab环境下实现编程计算,再现了瑞利波在近地表的传播状态,实现了地震剖面曲线的正振幅充填问题,从而获得了类似野外地震勘探的剖面记录。模拟结果表明,采用一阶差分格式所得到的地震记录存在较严重的数值频散,在采用有限差分法研究瑞利波"之"字形成因时,须尽量压制数值频散现象,才能获得更接近实际情况的频散曲线。
The propagator matrix approach Abo-Zena based on the dispersion equation of Rayleigh wave could only be used for studying dispersion characteristics of layered media.For non-layered media,the propagator matrix approach was useless,and the finite-element method and the finite-difference method had to be considered.The authors applied the finite-difference method to simulate full-wave-fields in an infinite half-space filled with homogeneous elastic solid medium.The modeling program was written out in Matlab environment.The propagation characteristics of Rayleigh wave reappeared in snaps.A kind of algorithm to draw and fill the wiggle curves of the seismic synthetic records was also achieved,and more realistic seismograms were obtained.According to the modeling results,there is serious numerical dispersion by using one order finite-difference method,and the numerical dispersion must be suppressed when zigzag dispersion will be studied by finite-difference method in the future.Then,more realistic dispersion curves can be obtained.
The propagator matrix approach Abo-Zena based on the dispersion equation of Rayleigh wave could only be used for studying dispersion characteristics of layered media.For non-layered media,the propagator matrix approach was useless,and the finite-element method and the finite-difference method had to be considered.The authors applied the finite-difference method to simulate full-wave-fields in an infinite half-space filled with homogeneous elastic solid medium.The modeling program was written out in Matlab environment.The propagation characteristics of Rayleigh wave reappeared in snaps.A kind of algorithm to draw and fill the wiggle curves of the seismic synthetic records was also achieved,and more realistic seismograms were obtained.According to the modeling results,there is serious numerical dispersion by using one order finite-difference method,and the numerical dispersion must be suppressed when zigzag dispersion will be studied by finite-difference method in the future.Then,more realistic dispersion curves can be obtained.
引文
[1]丛皖平,张鹏,王继矿.多道瑞利波在矿井独头巷道超前探测中的应用[J].煤田地质与勘探,2008,36(4):67-69.
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[3]夏宇靖.稳态瑞雷波实测洞穴D-vR曲线的类型[J].煤田地质与勘探,1996,24(1):50-55.
[4]杨天春,吴燕清,刘新华.对瑞利波频散曲线计算中高频数值溢出的处理[J].煤炭学报,2007,32(10):1041-1045.
[5]THOMAS B,ULRICH L,WOLFGANG R,et al.Rayleigh-to-shear wave conversion at the tunnel face—From 3D-FD model-ing to ahead-of-drill exploration[J].Geophysics,2008,72(6):67-79.
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[7]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波在有限差分正演模拟[J].地球物理学报,2007,50(2):567-573.
[8]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):824-830.
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[10]刘彩云,陈忠,熊杰.地震剖面图Wiggle曲线绘制与正振幅填充算法[J].成都大学学报(自然科学版),2008,27(4):320-321.
[2]谢昭晖,钟和,陈昌彦.瑞利波勘探技术在岩土工程勘察中应用[J].物探与化探,2007,31(3):279-282.
[3]夏宇靖.稳态瑞雷波实测洞穴D-vR曲线的类型[J].煤田地质与勘探,1996,24(1):50-55.
[4]杨天春,吴燕清,刘新华.对瑞利波频散曲线计算中高频数值溢出的处理[J].煤炭学报,2007,32(10):1041-1045.
[5]THOMAS B,ULRICH L,WOLFGANG R,et al.Rayleigh-to-shear wave conversion at the tunnel face—From 3D-FD model-ing to ahead-of-drill exploration[J].Geophysics,2008,72(6):67-79.
[6]郭君.地下洞穴的瑞利面波波场特征有限元数值模拟研究[D].成都:西南交通大学,2008.
[7]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波在有限差分正演模拟[J].地球物理学报,2007,50(2):567-573.
[8]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):824-830.
[9]马在田,曹景忠,王家林,等.计算地球物理学概论[M].上海:同济大学出版社,1997:20-27.
[10]刘彩云,陈忠,熊杰.地震剖面图Wiggle曲线绘制与正振幅填充算法[J].成都大学学报(自然科学版),2008,27(4):320-321.
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