非均匀介质交错网格高阶差分地震波数值模拟
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摘要
地震波数值模拟是解决地震正反演问题的重要手段和了解地下地质构造的有力工具。从波动方程出发建立一阶速度-应力方程组,用Taylor级数和交错网格差分技术对方程组进行高阶差分离散,避免了直接对波动方程二阶导数进行差分带来运算量大的问题;采用特征分析法处理边界问题,对边界反射进行很好的吸收。文中给出了相应差分精度的稳定性条件,并用高阶交错网格有限差分法对非均匀介质模型进行了数值模拟。计算结果表明,该方法具有较高的稳定性和精度,适合于复杂介质的弹性波场模拟。
Seismic wave numerical simulation was an important means to solve the problem of the seismic inversion and also a powerful tool to recognize the underground geological structure. One-order velocity-stress equations were established based on the elastic wave equation. The velocity-stress equations were replaced with high-order finite-difference by using Taylor series and staggered grid technique,by which the large computation problems resulted from differentiating the two-order derivate in the wave equation were avoided. Feature analysis method was adopted to solve boundary condition. The boundary reflection was absorbed effectively by this method. The stability conditions of the differential accuracy were given. The geology models were numerically simulated by high-order staggered grid difference method. The results show that the method is of high stability and accuracy,and suitable for elastic wave simulation of complex media.
Seismic wave numerical simulation was an important means to solve the problem of the seismic inversion and also a powerful tool to recognize the underground geological structure. One-order velocity-stress equations were established based on the elastic wave equation. The velocity-stress equations were replaced with high-order finite-difference by using Taylor series and staggered grid technique,by which the large computation problems resulted from differentiating the two-order derivate in the wave equation were avoided. Feature analysis method was adopted to solve boundary condition. The boundary reflection was absorbed effectively by this method. The stability conditions of the differential accuracy were given. The geology models were numerically simulated by high-order staggered grid difference method. The results show that the method is of high stability and accuracy,and suitable for elastic wave simulation of complex media.
引文
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[6]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分法稳定性研究[J].地球物理学报,2000,43(6):856~864.
[7]董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1):46~56.
[8]董良国,马在田.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411~419.
[9]刘洋,李承楚,牟永光.任意偶数阶精度的有限差分法数值模拟[J].石油地球物理勘探,1998,33(1):1~10.
[10]董良国,马在田.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):856~864.
[2]Virieux J.SH wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1984,49(11):1933~1957.
[3]Virieux J.P-SV wave propagationin heterogeneous media:Velocity-stress finite-difference method[J].Geophysics,1986,51(4):889~901.
[4]Dablain M.A The application of high-order differencing to the scalar wave equation[J].Geophysics,1986,51(1):54~66.
[5]Levander A R.Fourth-order finite-difference P-SVseismograms[J].Geophysics,1988,53(11):1425~1436.
[6]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分法稳定性研究[J].地球物理学报,2000,43(6):856~864.
[7]董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1):46~56.
[8]董良国,马在田.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411~419.
[9]刘洋,李承楚,牟永光.任意偶数阶精度的有限差分法数值模拟[J].石油地球物理勘探,1998,33(1):1~10.
[10]董良国,马在田.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):856~864.
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