非均匀介质中交错网格高阶有限差分数值模拟
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摘要
地震波场的数值模拟一直是地球物理学的一个重要的研究领域,而在数值正演模拟方法的研究中,计算精度和计算效率是评价该方法有效性及优越性的二个关键问题。这里从一阶速度—应力弹性波动方程出发,着重介绍如何构造离散化模型的网格,如何求解空间导数,如何选取边界条件等内容,从而更有效地提高数值计算的精度与计算效率。文中构造了不同类型的介质模型,并在交错网格中,利用高阶有限差分模拟非均匀介质的波场传播。模拟结果表明,该方法实现简单,具有很好地稳定性和较高的精度,能够直观、高效地反映出介质中波场的传播规律。
During the forward modeling,the computation precision and the efficiency are two pivotal questions to evaluate the validity and superiority of the method.Based on the one-order velocity-stress elastic wave equation,this paper emphasizes on improving the computation precision and the efficiency from to compartmentalize the discrete grid,solve the spacial derivative and add the boundary condition.The snapshots of the wave-filed of heterogeneous media using the high-order difference forward modeling with staggered-grid show the propagation law of the wave in different media more intuitively and effectively,and furthermore,validate that this method is easy and practical.
During the forward modeling,the computation precision and the efficiency are two pivotal questions to evaluate the validity and superiority of the method.Based on the one-order velocity-stress elastic wave equation,this paper emphasizes on improving the computation precision and the efficiency from to compartmentalize the discrete grid,solve the spacial derivative and add the boundary condition.The snapshots of the wave-filed of heterogeneous media using the high-order difference forward modeling with staggered-grid show the propagation law of the wave in different media more intuitively and effectively,and furthermore,validate that this method is easy and practical.
引文
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[9]CER JAN C,KOSLOFF D,et al.A nonreflectingboundary cond itions for d iscrete acoustic and elasticwave equations[J].Geophysics,1985,50(3):705
[2]佘德平.数值模拟技术的发展现状[J].勘探地球物理进展,2003,26(5):407
[3]单延明,吴清岭,于承业,等.复杂地质构造波动方程数值模拟[J].物探化探计算技术,2002,24(1):
[4]吴永刚,吴清岭.有限差分法弹性波场数值模拟[J].大庆石油地质与开发,1994,13(3):1
[5]VIR IEUX J.P-SV wave propagation in heterogeneousm ed ia:veloc ity-stress fin ite-d ifference m ethod.[J].Geophysics,1986,51(4):889
[6]董良国.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
[7]孙若昧.地震波传播有限差分模拟的人工边界问题[J].地球物理学进展,1996,11(3):53
[8]夏凡,董良国,马在田.三维弹性波数值模拟中的吸收边界条件[J].地球物理学报,2004,47(1):132
[9]CER JAN C,KOSLOFF D,et al.A nonreflectingboundary cond itions for d iscrete acoustic and elasticwave equations[J].Geophysics,1985,50(3):705
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