Elastic modelling in tilted transversely isotropic media with convolutional perfectly matched layer boundary conditions

Article

<< Previous

Next >>

Contents Vol 43(2)

doi:10.1071/EG12015

The Bulletin of the Australian Society of Exploration Geophysicists

	Search




	Advanced Search



	Journal Home

	About the Journal

	Editorial Committee

	Contacts

	For Advertisers



	Content

	Online Early

	Current Issue

	Just Accepted

	All Issues

	Sample Issue

	Call for Papers



	For Authors

	General Information

	Instructions to Authors

	Submit Article

	Open Access



	For Referees

	Referee Guidelines

	Review Article

	Annual Referee Index



	For Subscribers

	Subscription Prices

	Customer Service

	Print Publication Dates

e-Alerts

Subscribe to our Email Alert or

feeds for the latest journal papers.

Connect with us

Submit Article

Use the online submission system to send us your paper.

Call for Papers

We are preparing a themed issue. More...

Preview

Preview, the Magazine of the Australian Society of Exploration Geophysicists, is also available online.

ASEG Extended Abstracts

ASEG Extended Abstracts, drawn from the ASEG´s conferencces, is also available online.

Elastic modelling in tilted transversely isotropic media with convolutional perfectly matched layer boundary conditions

Byeongho Han ¹ Soon Jee Seol ¹ ² Joongmoo Byun ¹

¹ Department of Natural Resources and Geoenvironmental Engineering, Hanyang University, Seoul, Korea, 133-791.
² Corresponding author. Email: ssjdoolly@hanyang.ac.kr

Exploration Geophysics 43(2) 77-86 http://dx.doi.org/10.1071/EG12015
Submitted: 22 February 2012 Accepted: 6 March 2012 Published: 26 April 2012





	PDF (1.2 MB) $25



	Export Citation

Print

Abstract

To simulate wave propagation in a tilted transversely isotropic (TTI) medium with a tilting symmetry-axis of anisotropy, we develop a 2D elastic forward modelling algorithm. In this algorithm, we use the staggered-grid finite-difference method which has fourth-order accuracy in space and second-order accuracy in time. Since velocity-stress formulations are defined for staggered grids, we include auxiliary grid points in the z-direction to meet the free surface boundary conditions for shear stress. Through comparisons of displacements obtained from our algorithm, not only with analytical solutions but also with finite element solutions, we are able to validate that the free surface conditions operate appropriately and elastic waves propagate correctly. In order to handle the artificial boundary reflections efficiently, we also implement convolutional perfectly matched layer (CPML) absorbing boundaries in our algorithm. The CPML sufficiently attenuates energy at the grazing incidence by modifying the damping profile of the PML boundary. Numerical experiments indicate that the algorithm accurately expresses elastic wave propagation in the TTI medium. At the free surface, the numerical results show good agreement with analytical solutions not only for body waves but also for the Rayleigh wave which has strong amplitude along the surface. In addition, we demonstrate the efficiency of CPML for a homogeneous TI medium and a dipping layered model. Only using 10 grid points to the CPML regions, the artificial reflections are successfully suppressed and the energy of the boundary reflection back into the effective modelling area is significantly decayed.

Key words: anisotropy, boundary condition, elastic modelling, TTI media.

References

Alkhalifah, T., 2000, An acoustic wave equation for anisotropic media: Geophysics, 65, 1239–1250
| CrossRef |

Bécache, E., Fauqueux, S., and Joly, P., 2003, Stability of perfectly matched layers, group velocities and anisotropic waves: Journal of Computational Physics, 188, 399–433
| CrossRef |

Bérenger, J. P., 1994, A perfectly matched layer for the absorption of electromagnetic waves: Journal of Computational Physics, 114, 185–200
| CrossRef |

Cerjan, C., Kosloff, D., Kosloff, R., and Reshef, M., 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equation: Geophysics, 50, 705–708
| CrossRef |

Clayton, R., and Engquist, B., 1977, Absorbing boundary conditions for acoustic and elastic wave equations: Bulletin of the Seismological Society of America, 67, 1529–1540

Collino, F., and Tsogka, C., 2001, Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media: Geophysics, 66, 294–307
| CrossRef |

Elapavuluri, P., and Bancroft, J. C., 2005, Finite difference modeling in structurally complex anisotropic medium: 75th Ann. Internat. Mtg. Soc. Explor. Geophys., Expanded Abstracts, 100–103.

Engquist, B., and Majda, A., 1977, Absorbing boundary conditions for the numerical simulation of waves: Bulletin of the Seismological Society of America, 31, 629–651

Ewing, W. M., Tardetzky, W. S., and Press, F., 1957, Elastic waves in layered media: McGraw–Hill.

Faria, E. L., and Stoffa, P. L., 1994, Finite-difference modeling in transversely isotropic media: Geophysics, 59, 282–289
| CrossRef |

Graves, R. W., 1996, Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences: Bulletin of the Seismic Society of America, 86, 1091–1106

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: The Journal of the Acoustical Society of America, 100, 3061–3069
| CrossRef |

Higdon, R. L., 1991, Absorbing boundary conditions for elastic waves: Geophysics, 56, 231–241
| CrossRef |

Igel, H., Mora, P., and Riollet, B., 1995, Anisotropic wave propagation through finite-difference grids: Geophysics, 60, 1203–1216
| CrossRef |

Juhlin, C., 1995, Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media: Geophysical Prospecting, 43, 843–858
| CrossRef |

Komatitsch, D., and Martin, R., 2007, An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation: Geophysics, 72, SM155–SM167
| CrossRef |

Komatitsch, D., and Tromp, J., 2003, A Perfectly Matched Layer (PML) absorbing condition for the second-order elastic wave equation: Geophysical Journal International, 154, 146–153
| CrossRef |

Komatitsch, D., Barnes, C., and Tromp, J., 2000, Simulation of anisotropic wave propagation based upon a spectral element method: Geophysics, 65, 1251–1260
| CrossRef |

Levander, A. R., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53, 1425–1436
| CrossRef |

Martin, R., Komatitsch, D., and Ezziani, A., 2008, An unsplit convolutional perfectly matched layer improved at grazing incidence for seismic wave propagation in poroelastic media: Geophysics, 73, T51–T61
| CrossRef |

Mur, G., 1981, Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations: Electromagnetic Compatibility, 23, 377–382
| CrossRef |

Operto, S., Virieux, J., Ribodetti, A., and Anderson, J. E., 2009, Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media: Geophysics, 74, T75–T95
| CrossRef |

Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P., 1992, Numerical recipes in Fortran: the art of scientific computing: Cambridge University Press.

Reynolds, A. C., 1978, Boundary conditions for the numerical solution of wave propagation problems: Geophysics, 43, 1099–1110
| CrossRef |

Roden, J. A., and Gedney, S. D., 2000, Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media: Microwave and Optical Technology Letters, 27, 334–339
| CrossRef |

Shin, C., 1995, Sponge boundary condition for frequency-domain modelling: Geophysics, 60, 1870–1874
| CrossRef |

Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966
| CrossRef |

Virieux, J., 1984, SH-wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 49, 1933–1957
| CrossRef |

Virieux, J., 1986, P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method: Geophysics, 51, 889–901
| CrossRef |

Subscriber Login

	Username: Password:

Legal & Privacy | Contact Us | Help