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.
引文
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