PML absorbing boundary condition for seismic numerical modeling by convolutional differentiator in fluid-saturated porous media

Abstract

The perfectly matched layer (PML) was first introduced by Berenger as an absorbing boundary condition for electromagnetic wave propagation. In this article, a method is developed to extend the PML to simulating seismic wave propagation in fluid-saturated porous medium. This nonphysical boundary is used at the computational edge of a Forsyte polynomial convolutional differentiator (FPCD) algorithm as an absorbing boundary condition to truncate unbounded media. The incorporation of PML in Biot’s equations is given. Numerical results show that the PML absorbing boundary condition attenuates the outgoing waves effectively and eliminates the reflections adequately.

Keywords

seismic wave numerical modeling / convolutional differentiator / PML absorbing boundary condition / fluid-saturated porous medium

References

[1] Berenger J. P.. A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. J. Comput. Phys., 1994, 114(2): 185-200.

[2] Biot M. A.. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range. J. Acoust. Soc. Am., 1956, 28(2): 168-178.

[3] Biot M. A.. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher-Frequency Range. J. Acoust. Soc. Am., 1956, 28(2): 179-191.

[4] Cerjan C., Kosloff D., Kosloff R., . A Nonreflecting Boundary Condition for Discrete Acoustic and Elastic Wave Equations. Geophysics, 1985, 50(4): 705-708.

[5] Chew W. C., Liu Q. H.. Perfectly Matched Layers for Elastodynamics: A New Absorbing Boundary Condition. J. Comp. Acoust., 1996, 4(4): 341-359.

[6] Chew W. C., Weedon W. H.. A 3-D Perfectly Matched Medium from Modified Maxwell’s Equations with Stretched Coordinates. Microw. Opt. Technol. Lett., 1994, 7(13): 599-604.

[7] Clayton R., Engquist B.. Absorbing Boundary Conditions for Acoustic and Elastic Wave Equations. Bull. Seism. Soc. Am., 1977, 67: 1529-1540.

[8] Dai N., Vafidis A., Kanasewieh E. R.. Wave Propagation in Heterogeneous, Porous Media: A Velocity-Stress, Finite Difference Method. Geophysics, 1995, 60(2): 327-340.

[9] He J. Q., Liu Q. H.. A Nonuniform Cylindrical FDTD Algorithm with Improved PML and Quasi-PML Absorbing Boundary Conditions. IEEE Trans. Geosci. Remote Sensing, 1999, 37(2): 1066-1072.

[10] Kosloff R., Kosloff D.. Absorbing Boundary for Wave Propagation Problems. J. Comp. Phys., 1986, 63: 363-376.

[11] Li X. F., Li X. F.. Numerical Simulation of Seismic Wave Propagation in Complex Media by Convolutional Differentiator. Acta Seismologica Sinica, 2008, 21(4): 380-385.

[12] Liao Z. P., Wong H. L.. A Transmitting Boundary for the Numerical Simulation of Elastic Wave Analysis. International Journal of Soil Dynamic, 1984, 3(4): 174-183.

[13] Liu Q. H.. An FDTD Algorithm with Perfectly Matched Layers for Conductive Media. Microw. Opt. Technol. Lett., 1997, 14(2): 134-137.

[14] Liu Q. H.. Perfectly Matched Layers for Elastic Waves in Cylindrical and Spherical Coordinates. J. Acoust. Soc. Am., 1999, 105(4): 2075-2084.

[15] Liu Q. H., Tao J. P.. The Perfectly Matched Layer for Acoustic Waves in Absorptive Media. J. Acoust. Soc. Am., 1997, 102(4): 2072-2082.

[16] Pei Z. L.. Two-Dimensional Numerical Simulation of Elastic Wave Propagation in 2-D Anisotropic Two-Phase Media with Staggered-Grid High-Order Difference Method. Journal of China University of Petroleum (Edition of Natural Science), 2006, 30(2): 16-20.

[17] Smith W. D.. A Nonreflecting Plane Boundary for Wave Propagation Problems. J. Comp. Phys., 1974, 15(4): 492-503.