Abstract
The nonsplitting perfectly matched layer (NPML) absorbing boundary condition (ABC) was first provided by Wang and Tang (2003) for the finite-difference simulation of elastic wave propagation in solids. In this paper, the method is developed to extend the NPML to simulating elastic wave propagation in poroelastic media. Biot’s equations are discretized and approximated to a staggered-grid by applying a fourth-order accurate central difference in space and a second-order accurate central difference in time. A cylindrical two-layer seismic model and a borehole model are chosen to validate the effectiveness of the NPML. The results show that the numerical solutions agree well with the solutions of the discrete wavenumber (DW) method.
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References
Bayliss, A., Jordan, K. E., LeMesurier, B. J., and Turkel, E., 1986, A fourth-order accurate finite-difference scheme for the computation of elastic waves: Bull., Seis. Soc. Am., 76, 1115–1132.
Berenger, J. P., 1994, A perfectly matched layer for absorption of electromagnetic waves: J. Comput. Phys., 114, 185–200.
Biot, M. A., 1956, Theory of propagation of elastic waves in a fluid-saturated porous solid, II, Higher-frequency range: J. Acoust. Soc. Am., 28, 179–191.
Biot, M. A., 1956, Theory of propagation of elastic waves in a fluid-saturated porous solid, I, Low-frequency range: J. Acoust. Soc. Am., 28, 168–178.
Biot, M. A., 1962, Mechanics deformation and acoustic propagation in porous media: J. Appl. Phys., 33, 1482–1498.
Cerjan, C, Kosloff, D., Kosloff, R., and Reshef, M.., 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equations: Geophysics, 50, 705–708.
Chew, W. C, and Liu, Q. H., 1996, Perfectly matched layers for elastodynamics: A new absorbing boundary condition: J. Computat. Acoustics, 4, 341–359.
Clayton, R., and Engquist, B., 1977, Absorbing boundary conditions for acoustic and elastic wave equations: Bull. Seism. Soc. Am., 67, 1529–1540.
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, 294–307.
Dai, N., Vafidis, A., and Kanasewich, E.R., 1995, Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method: Geophysics, 60, 327–340.
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: J. Acoust. Soc. Am., 100, 3061–3069.
Hou, A.N., and He, Q. D., 1995, Study of an elastic wave high-order difference method and its stability in anisotropic media: Chinese Journal of Geophysics, 38,243–251.
Kosloff, R., and Kosloff, D., 1986, Absorbing boundary for wave propagation problems: J. Comp. Phys., 63, 363–376.
Liu, Q. H., and Tao J., 1997, The perfectly matched layer for acoustic waves in absorptive media: J. Acoust. Soc. Am., 102, 2072–2082.
Lysmer, J., and Kuhlemeyer R.L., 1969, Finite dynamic model for infinite media: J. Eng. Mech. Div., ASCE 95 EM4, 859–877.
Randall, C. J., 1988, Absorbing boundary condition for the elastic wave equation: Geophysics, 53, 611–624.
Randall, C. J., 1989, Absorbing boundary condition for the elastic wave equation: velocity-stress formulation: Geophysics, 54, 1141–1152.
Smith, W. D., 1974, A nonreflecting plane boundary for wave propagation problem: J. Computational Phys., 15,492–503.
Teixeira, F. L., and Chew, W. C, 1997, PML-FDTD in cylindrical and spherical grids: IEEE Microwave and Guided Wave Lett., 7, 285–287.
Wang, Tsili and Tang, Xiaoming, 2003, Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach: Geophysics, 68, 1749–1755.
Wang, X. M., Zhang, H. L. and Wang, D., 2003, Modeling of seismic wave propagation in heterogeneous porous media using a high-order staggered finite-difference method: Chinese Journal of Geophysics, 46, 842–849.
Zeng, Y. Q., and Liu, Q. H., 2001, A staggered-grid finite-difference method with perfectly matched layers for poroelastic wave equations: J. Acoust. Soc. Am., 109,2571–2580.
Zeng, Y. Q., He, J. Q., and Liu, Q. H., 2001, The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media: Geophysics, 66, 1258–1266
Zhang, B. X., Wang, K. X., and Dong, Q. D., 1995, Theory of acoustic multipole logging and analysis of wave components and calculation of fall waveforms for two-phase medium formation: ACTA Geophysic Sinica, Vol.38, Supp.l.
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This research was supported by Natural Science Foundation of China (No. 403740043).
First Author
Song Ruolong, received his BSc (2003) in the College of Physics of Jilin University, studied for his MSc in the Acoustic Department, and now studies for his PhD at Jilin University (2005). He works on the finite-difference simulation of elastic wave propagation of acoustic waves in complex media.
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Song, R., Ma, J. & Wang, K. The application of the nonsplitting perfectly matched layer in numerical modeling of wave propagation in poroelastic media. Appl. Geophys. 2, 216–222 (2005). https://doi.org/10.1007/s11770-005-0027-3
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DOI: https://doi.org/10.1007/s11770-005-0027-3