Abstract When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly Matched Layers (PML) are deduced and their Crank-Nicolson scheme are presented in this paper. We use the second-, sixth-, and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives. Two numerical models, a homogeneous isotropic medium and a multi-layer model with a cave, are designed to investigate how the absorbing boundary width and the algorithms determine PML effects. Numerical results show that, for PML, the low-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin, whereas, high-order algorithms always have good absorption when the boundary is thick. Finally, we discuss the reflection coefficient and point out its shortcomings, which is why we use the SNR to quantitatively scale the PML effects.
The research is supported jointly by the 973 Program (Grant No. 2007CB209505), the National Natural Science Fund (Grant No. 40704019, 40674061), the School Basic Research Fund of Tsinghua University (JC2007030), PetroChina Innovation Fund (Grant No. 060511-1-1).
Cite this article:
LIU Jiong,MA Jian-Wei,YANG Hui-Zhu. The study of perfectly matched layer absorbing boundaries for SH wave fields[J]. APPLIED GEOPHYSICS, 2009, 6(3): 267-274.
[1]
Berenger, J. P., 1994, A perfectly matched layer for the absorption of electromagnetics waves: Journal of Computational Physics., 114, 185 - 200.
[2]
Blaschak, J. and Kriegsmann, G., 1988, A comparative study of absorbing boundary conditions: Journal of Computational Physics, 77, 109 - 139.
[3]
Cerjan, C., Kosloff, D., Kosloff, R., and Reshef, M., 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equation: Geophysics, 50(4), 705 - 708.
[4]
Chew, W. C., and Liu, Q. H., 1996, Using perfectly matched layers for elastodynamics: in Proceedings of the IEEE Antennas Propagation Society International Symposium, 1, 366 - 369.
[5]
Collino, F., and Tsogka, C., 2001, Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media: Geophysics, 66(1), 294 - 30.
[6]
Engquist, B., and Majda, A., 1977, Absorbing boundary conditions for the numerical simulation of waves: Mathematics of Computation, 31, 629 - 651.
[7]
He, F. J., Tao, G., and Wang, X. L., 2006, Finite difference modeling of the acoustic field by sidewall logging devices: Chinese Journal of Geophysics, 49(3), 923 - 928.
[8]
Mur, G., 1988, The modeling of Singularities in the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations: IEEE Trans. Microwave Theory and Techniques, 29(10), 1073 - 1077.
[9]
Ozdenvar, T., and McMechan, G., 1996, Causes and reduction of numerical artifacts in pseudo-spectral wavefield extrapolation: Geophysical Journal International, 126, 819 - 828.
[10]
Song, R. L., Ma, J., and Wang, K. X., 2005, The application of the nonsplitting perfectly matched layer in numerical modeling of wave propagation in poroelastic media: Applied Geophysics, 12(4), 216 - 222.
[11]
Wang, S. D., 2003, Absorbing boundary condition for acoustic wave equation by perfectly matched layer: Oil Geophysical Prospecting, 38(1), 31 - 34.
[12]
Wang, T., and Tang, X., 2003, Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach: Geophysics, 68, 1749 - 1755.
[13]
Wang, C. Q, and Zhu, X. L., 1994, Finite-difference time-domain method of electromagnetic field: Peking University Press, 47 - 57.
[14]
Zhao, H. B., Wang, X. M., Wang, D., and Chen, H., 2007, Applications of the boundary absorption using a perfectly matched layer for elastic wave simulation in poroelastic media: Chinese Journal of Geophysics, 50(2), 581 - 591.
2009, Vol. 6 
