一阶弹性波方程的变网格高阶有限差分数值模拟
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摘要
使用可变网格的有限差分法进行地震模拟有许多独特的优点,主要表现为对地质模型的离散化更为合理,在低速带和复杂构造区域,可将局部网格划分得相对精细些,不仅提高了模拟精度,消除了因采样不足导致的频散现象,而且可以减少计算机内存需求,保持模型计算的灵活性。本文提出一种新的基于高阶交错网格技术的弹性波数值模拟方法,通过改变网格的空间步长实现了局部网格加密技术,弥补了常规网格的缺陷和不足。试算结果表明,本文提出的算法稳定性较好,且能够提高模拟精度,减少计算时间,提高计算效率。
Using variable-grid finite-difference algorithm to carry out the seismic simulation has many unique advantages that mainly are more reasonable for discretization of geologic model,and relatively fine division of local grid can be implemented in low-velocity zone and complex structural area,which not only improves the simulated precision and eliminates the dispersion resulted from insufficient sampling,but also can reduce the requirement of computer memory,keeping the flexibility of model computation.The paper presented a new elastic wave numeric simulation method based on high-order staggered-gird technique,which realized the technique densifying local grid by changing the spatial step of grid,remedying the defect and shortcoming of ordinary grid.The testing results showed that the algorithm presented by the paper is characterized by good stability,improved precision of simulation,reducing computational time and improving computational efficiency.
Using variable-grid finite-difference algorithm to carry out the seismic simulation has many unique advantages that mainly are more reasonable for discretization of geologic model,and relatively fine division of local grid can be implemented in low-velocity zone and complex structural area,which not only improves the simulated precision and eliminates the dispersion resulted from insufficient sampling,but also can reduce the requirement of computer memory,keeping the flexibility of model computation.The paper presented a new elastic wave numeric simulation method based on high-order staggered-gird technique,which realized the technique densifying local grid by changing the spatial step of grid,remedying the defect and shortcoming of ordinary grid.The testing results showed that the algorithm presented by the paper is characterized by good stability,improved precision of simulation,reducing computational time and improving computational efficiency.
引文
[1]Virieux J.P-SV wave propagation in heterogeneousmedia:velocity-stress finite-difference method.Geo-physics,1986,51,88~901
[2]Jastram C and Behle A.Acoustic modeling on a verti-cally verying grid.Geophys Prosp,1992,40,157~169
[3]Jastram C and Tessmer E.Elastic modeling on a grid ofvertically varying spacing.Geophys Prosp,1994,42,357~370
[4]Falk J,Tessmer E and Gajewski D.Tube wave model-ing by the finite-difference method with varying gridspacing.Prosp,1996,148,77~93
[5]Pitarka A.3D elastic finite-difference modeling of seis-mic motion using staggered grids with nonuniformspacing.Bulletin of Seismological of America,1999,89,54~68
[6]Graves R W.Simulating seismic wave propagationin 3D elastic using staggered-grid finite-differences.Bull Seism Soc Am,1996,86,1091~1107
[7]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411~419
[8]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现.地球物理学报,2002,45(4):534~545
[9]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856~864
[2]Jastram C and Behle A.Acoustic modeling on a verti-cally verying grid.Geophys Prosp,1992,40,157~169
[3]Jastram C and Tessmer E.Elastic modeling on a grid ofvertically varying spacing.Geophys Prosp,1994,42,357~370
[4]Falk J,Tessmer E and Gajewski D.Tube wave model-ing by the finite-difference method with varying gridspacing.Prosp,1996,148,77~93
[5]Pitarka A.3D elastic finite-difference modeling of seis-mic motion using staggered grids with nonuniformspacing.Bulletin of Seismological of America,1999,89,54~68
[6]Graves R W.Simulating seismic wave propagationin 3D elastic using staggered-grid finite-differences.Bull Seism Soc Am,1996,86,1091~1107
[7]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411~419
[8]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现.地球物理学报,2002,45(4):534~545
[9]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856~864
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