Abstract
In elastic wave forward modeling, absorbing boundary conditions (ABC) are used to mitigate undesired reflections from the model truncation boundaries. The perfectly matched layer (PML) has proved to be the best available ABC. However, the traditional splitting PML (SPML) ABC has some serious disadvantages: for example, global SPML ABCs require much more computing memory, although the implementation is easy. The implementation of local SPML ABCs also has some difficulties, since edges and corners must be considered. The traditional non-splitting perfectly matched layer (NPML) ABC has complex computation because of the convolution. In this paper, based on non-splitting perfectly matched layer (NPML) ABCs combined with the complex frequency-shifted stretching function (CFS), we introduce a novel numerical implementation method for PML absorbing boundary conditions with simple calculation equations, small memory requirement, and easy programming.
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References
Appelö, D., and Kreiss, G., 2006, A new absorbing layer for elastic waves: Journal of Computational Physics, 215(2), 642–660.
Basu, U., and Chopra, A. K., 2004, Perfectly matched layers for transient elastodynamics of unbounded domains: International Journal for Numerical Methods in Engineering, 59(8), 1039–1074.
Bérenger, J. P., 1994, A perfectly matched layer for absorption of electromagnetic waves: Journal of Computational Physics, 114(2), 185–200.
Chen, Y. H., Chew, W. C., and Oristaglio, M. L., 1997, Application of perfectly matched layers to the transient modeling of subsurface EM problems: Geophysics, 62(6), 1730–1736.
Chew, W. C., and Weedon, W. H., 1994, A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates: Microwave and Optical Technology Letters, 7(13), 599–604
Chew, W. C., and Liu, Q. H., 1996, Perfectly matched layers for elastodynamics: A new absorbing boundary condition: Journal of Computational Acoustics, 4(4), 341–359.
Cohen, G., and Fauqueux, S., 2005, Mixed spectral finite elements for the linear elasticity system in unbounded domains: SIAM Journal on Scientific Computing, 26(3), 864–884.
Collino, F., and Tsogka C., 2001, Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media: Geophysics, 66(1), 294–307.
Drossaert, F. H. and Giannopoulos, A., 2007, A nonsplit complex frequency-shifted PML based on recursive integration for FDTD modeling of elastic waves: Geophysics, 72(2), T9–T17.
Festa, G., and Nielsen S., 2003, PML absorbing boundaries: Bulletin of the Seismological Society of America, 93(2), 891–903.
Festa, G., and Vilotte, J. P., 2005, The Newmark scheme as velocity-stress time-staggering: An efficient PML implementation for spectral-element simulations of elastodynamics: Geophysical Journal International, 161(3), 789–812.
Hastings, F. D., Schneider, J. B., and Broschat, S. L., 1996, Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation: Journal of the Acoustical Society of America, 100(5), 3061–3069.
Higdon, R. L., 1991, Absorbing boundary condition for elastic waves: Geophysics, 56(2), 231–241.
Komatitsch, D., and Martin, R., 2007, An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation: Geophysics, 72(5), SM155–SM167
Komatitsch, D., and Tromp J., 1999, Introduction to the spectral-element method for 3-D seismic wave propagation: Geophysical Journal International, 139(3), 806–822.
Kuzuoglu, M., and Mittra, R., 1996, Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers: IEEE Microwave and Guided Wave Letters, 6(2), 447–449.
Liao, Z. P., Wong, H. L., and Yuan, Y. F., 1984, A transmitting boundary for transient wave analysis: Scientia Sinica, 27(6), 1063–1076.
Ma, S., and Liu, P., 2006, Modeling of the perfectly matched layer absorbing boundaries and intrinsic attenuation in explicit finite-element methods: Bulletin of the Seismological Society of America, 96(5), 1779–1794.
Marfurt, K. J., 1984, Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equation: Geophysics, 49(5), 533–549.
Rappapport, C. M., 1995, Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space: IEEE Microwave Guided Wave Lett., 5(3), 90–92.
Shin, C., 1995, Sponge boundary condition for frequency-domain modeling: Geophysics, 60(6), 1870–1874.
Song R. L., Ma J., and Wang K. X., 2005, The application of non-splitting perfectly matched layer in numerical modeling of wave propagation in poroelastic media: Applied geophysics, 2(4), 216–222.
Teixeira, F. L., and Chew, W. C., 1999, On causality and dynamic stability of perfectly matched layers for FDTD simulations: IEEE Transactions on Microwave Theory and Techniques, 47(6), 775–785.
Tsili, W. and Tang, X. M., 2003, Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach: Geophysics, 68(5), 1749–1755.
Wang, T., and Oristaglio, M. L., 2000, 3-D simulation of GPR surveys over pipes in dispersive soils: Geophysics, 65(5), 1560–1568.
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This research was sponsored by the Chinese National Development and Reform Commission (No. [2005]2372) and the Innovative Technological Research Foundation of PetroChina Company Limited (No. 060511-1-3).
Qin Zhen received his master from Jianghan Petroleum University in 2004 and received his PhD from the China University of Geosciences in Wuhan in 2008. Currently, he is a post-doctor at the Research Institute of Petroleum Exploration & Development. His research work mainly focus on seismic pre-stack denoising, geophysical forward modeling, and geophysical inverse problems.
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Qin, Z., Lu, M., Zheng, X. et al. The implementation of an improved NPML absorbing boundary condition in elastic wave modeling. Appl. Geophys. 6, 113–121 (2009). https://doi.org/10.1007/s11770-009-0012-3
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DOI: https://doi.org/10.1007/s11770-009-0012-3