交错网格高阶差分法三维弹性波数值模拟(英文)
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摘要
本文应用交错网格高阶有限差分方法模拟弹性波在三维各向同性介质中的传播。采用时间上二阶、空间上高阶近似的交错网格高阶差分公式求解三维弹性波位移-应力方程,并在计算边界处应用基于傍轴近似法得到的三维弹性波方程吸收边界条件。在此基础上进行了三维盐丘地质模型的地震波传播数值模拟试算。试算结果表明该方法模拟精度高,在很大程度上减小了数值频散,绕射波更加丰富,而且适用于介质速度具有纵向变化和横向变化的情况。
This article provides the application of the high-order, staggered-grid, finite-difference scheme to model elastic wave propagation in 3-D isotropic media. Here, we use second-order, tempo- ral- and high-order spatial finite-difference formulations with a staggered grid for discretization of the 3-D elastic wave equations of motion. The set of absorbing boundary conditions based on paraxial approximations of 3-D elastic wave equations are applied to the numerical boundaries. The trial re- sults for the salt model show that the numerical dispersion is decreased to a minimum extent, the accuracy high and diffracted waves abundant. It also shows that this method can be used for modeling wave propagation in complex media with the lateral variation of velocity.
This article provides the application of the high-order, staggered-grid, finite-difference scheme to model elastic wave propagation in 3-D isotropic media. Here, we use second-order, tempo- ral- and high-order spatial finite-difference formulations with a staggered grid for discretization of the 3-D elastic wave equations of motion. The set of absorbing boundary conditions based on paraxial approximations of 3-D elastic wave equations are applied to the numerical boundaries. The trial re- sults for the salt model show that the numerical dispersion is decreased to a minimum extent, the accuracy high and diffracted waves abundant. It also shows that this method can be used for modeling wave propagation in complex media with the lateral variation of velocity.
引文
Alford, R.M., Kelly, K.R., and Boore, D.M., 1974, Accu-racy of finite-difference modeling of the acoustic wave equation: Geophysics, 39, 834-852.
Carcione, J.M., Herman, G.C., and ten Kroode, A.P.E., 2002, Seismic modeling: Geophysics, 67, 1304-1325.
Crase, E., 1990, High-order (space and time) finite-differ- ence modeling of the elastic wave equation: 60th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 987-991.
Dabiain, M.A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51, 54-66.
Dong L.G, Ma Z.T., Cao J.Z., 2000, The staggered-grid, high- order, difference method of one-order elastic equation: Chinese J. Geophys.: 43(3), 411-419.
Graves, R.W., 1996, Simulating seismic wave propagation in 3D elastic media using staggered grid finite differences: Bull. Seism. Soc. Am., 88, 881-897.
Kelly, K.R., Ward, R.W., Treitel, S., and Alford, R.M., 1976, Synthetic seismograms: A finite-difference approach: Geophysics, 41, 2-27.
Kneib, G., and Kerner, C., 1993, Accurate and efficient seis- mic modeling in random media: Geophysics, 58, 576-588.
Kosloff, D., Reshef, M., and Loewenthal, D., 1984, Elastic wave calculations by the Fourier method: Bull. Seism. Soc. Am., 74, 875-891.
Levander, A.R., 1988, Fourth-order finite difference P-SV seismograms: Geophysics, 53, 1425-1436.
Madariaga, R., 1976, Dynamics of an expanding circular fault: Bull. Seism. Soc. Am., 66, 163-182.
Ma Z.T., Cao J.Z., Wang J.L. et al., 1997, Conspectus of com- putational geophysics (in Chinese): Tongji University press.
Virieux, J., 1984, SH wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 49, 1933-1957.
Virieux, J., 1986, P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 51, 889-901.
Xia F., Dong L.G., Ma Z.T., 2004, Absorbing boundary con- ditions in 3D elastic-wave numerical modeling: Chinese J. Geophys., 47(1), 132-
Carcione, J.M., Herman, G.C., and ten Kroode, A.P.E., 2002, Seismic modeling: Geophysics, 67, 1304-1325.
Crase, E., 1990, High-order (space and time) finite-differ- ence modeling of the elastic wave equation: 60th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 987-991.
Dabiain, M.A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51, 54-66.
Dong L.G, Ma Z.T., Cao J.Z., 2000, The staggered-grid, high- order, difference method of one-order elastic equation: Chinese J. Geophys.: 43(3), 411-419.
Graves, R.W., 1996, Simulating seismic wave propagation in 3D elastic media using staggered grid finite differences: Bull. Seism. Soc. Am., 88, 881-897.
Kelly, K.R., Ward, R.W., Treitel, S., and Alford, R.M., 1976, Synthetic seismograms: A finite-difference approach: Geophysics, 41, 2-27.
Kneib, G., and Kerner, C., 1993, Accurate and efficient seis- mic modeling in random media: Geophysics, 58, 576-588.
Kosloff, D., Reshef, M., and Loewenthal, D., 1984, Elastic wave calculations by the Fourier method: Bull. Seism. Soc. Am., 74, 875-891.
Levander, A.R., 1988, Fourth-order finite difference P-SV seismograms: Geophysics, 53, 1425-1436.
Madariaga, R., 1976, Dynamics of an expanding circular fault: Bull. Seism. Soc. Am., 66, 163-182.
Ma Z.T., Cao J.Z., Wang J.L. et al., 1997, Conspectus of com- putational geophysics (in Chinese): Tongji University press.
Virieux, J., 1984, SH wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 49, 1933-1957.
Virieux, J., 1986, P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 51, 889-901.
Xia F., Dong L.G., Ma Z.T., 2004, Absorbing boundary con- ditions in 3D elastic-wave numerical modeling: Chinese J. Geophys., 47(1), 132-
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