Abstract:
When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially truncated boundaries. In this paper, a damping factor referred to as the Gaussian damping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers (PMLs). This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models: a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio (SNR) than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR.
YANG Hao-Xing,WANG Hong-Xia. A study of damping factors in perfectly matched layers for the numerical simulation of seismic waves[J]. APPLIED GEOPHYSICS, 2013, 10(1): 63-70.
[1]
Berenger, J. P., 1994, A perfectly matched layer for the absorption of electromagnetics waves: Journal Computation Physics, 114, 185 - 200.
[2]
Burns, D. R., 1992, Acoustic and elastic scattering from seamounts in three dimensions-numerical modeling study: J. Acoust. Soc. Amer., 92, 2784 - 2791.
[3]
Cerjan, C., Kosloff, D., Kosloff, R., and Reshef, M., 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equations: Geophysics, 50(4), 705 - 708.
[4]
Clayton, R., Engquist, B., 1977, Absorbing boundary condition for acoustic and elastic wave equations: Bull. Sersm. Soc. Am., 67, 1529 - 1540.
[5]
Collino, F., and Tsogka, C., 2001, Application of the perfectly matched absorbing layer model to the linear elasto-dynamic problem in anisotropic heterogeneous media: Geophysics, 66(1), 294 - 307.
[6]
Du, Q. Z., Sun, R. Y., Qin, T., Zhu, Y. T., and Bi, L. F., 2010, A study of perfectly matched layers for joint multicomponent reverse-time migration: Applied Geophysics, 7(2), 166 - 173.
[7]
Hastings, F., Schneider, J. B., and Broschat, S. L., 1996, Application of the perfectly matched absorbing layer (PML) absorbing boundary condition to elastic wave propagation: Journal of Acoustic Society of America, 100(5), 3061 - 3069.
[8]
Higdon, R. L., 1986, Absorbing boundary conditions for difference approximations to the multidimensional wave equation: Math. Comp., 47, 437 - 459.
[9]
Higdon, R. L., 1987, Numerical absorbing boundary conditions for the wave equation: Math. Comp., 49, 65 - 90.
[10]
Higdon, R. L., 1991, Absorbing boundary condition for elastic waves: Geophysics, 56(2), 231 - 241.
[11]
Komatitsch, D., Tromp, J., 2003, A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation: Geophysical Journal International, 154(1), 146 - 150.
[12]
Liao, Z. P., Wong, H. L., Yang, B. P., and Yuan, Y. F., 1984, A transmitting boundary for transient wave analysis: Scientia Sinica (Series A), 27(10), 1063 - 1076.
[13]
Wang, T., and Tang, X. M., 2003, Finite-difference modeling of elastic wave propagation: a nonsplitting perfectly matched layer approach: Geophysics, 68(5), 1749 - 1755.
[14]
Wang, Y. G., Xing, W. J., Xie, W. X., and Zhu, Z. L., 2007, Study of absorbing boundary condition by perfectly matched layer: Journal of China University of Petroleum (In Chinese), 31(1), 19 - 24.