Boundary conditions for Time-Domain Finite-Difference Elastic Wave Modeling in Anisotropic Media

이방성을 고려한 시간영역 유한차분법 탄성파 모델링에서의 경계조건

  • Lee, Ho-Yong (Dept. of Earth Science Education, Seoul National Univ.) ;
  • Min, Dong-Joo (Dept. of Energy System Engineering, Seoul National Univ.) ;
  • Kwoon, Byung-Doo (Dept. of Earth Science Education, Seoul National Univ.) ;
  • Lim, Seung-Chul (Dept. of Earth Science Education, Seoul National Univ.) ;
  • Yoo, Hai-Soo (Korea Ocean Research and Development Institute)
  • 이호용 (서울대학교 사범대학 지구과학교육과) ;
  • 민동주 (서울대학교 공과대학 에너지시스템공학부) ;
  • 권병두 (서울대학교 사범대학 지구과학교육과) ;
  • 임승철 (서울대학교 사범대학 지구과학교육과) ;
  • 유해수 (한국해양연구원 해양자원연구본부)
  • Published : 2008.05.31


Seismic modeling is used to simulate wave propagation in the earth. Although the earth's subsurface is usually semi-infinite, we cannot handle the semi-infinite model in seismic modeling because of limited computational resources. For this reason, we usually assume a finite-sized model in seismic modeling. In that case, we need to eliminate the edge reflections arising from the artificial boundaries introducing a proper boundary condition. In this study, we changed three kinds of boundary conditions (sponge boundary condition, Clayton and Engquist's absorbing boundary condition, and Higdon's transparent boundary condition) so that they can be applied in elastic wave modeling for anisotropic media. We then apply them to several models whose Poisson's ratios are different. Clayton and Engquist's absorbing boundary condition is unstable in both isotropic and anisotropic media, when Poisson's ratio is large. This indicates that the absorbing boundary condition can be applied in anisotropic media restrictively. Although the sponge boundary condition yields good results for both isotropic and anisotropic media, it requires too much computational memory and time. On the other hand, Higdon's transparent boundary condition is not only inexpensive, but also reduce reflections over a wide range of incident angles. We think that Higdon's transparent boundary condition can be a method of choice for anisotropic media, where Poisson's ratio is large.


  1. Cerjan, C., Kosloff, E., Kosloff, R., and Reshef, M., 1985, A nonreflecting boundary condition for discrete acoustic and elastic wave equations, Geophysics, 50, pp. 705-708
  2. Clayton, R., and Engquist, B., 1977, Absorbing boundary conditions for acoustic and elastic wave equations, Bull. Seis. Soc. Am., 67, pp. 1529-1540
  3. Emerman, S. H., and Stephen, R. A., 1983, Comment on 'Absorbing boundary conditions for acoustic and elastic wave equations' by Clayton, R. and Engquist, B., Bull. Seis. Soc. Am., 73, pp. 661-665
  4. Faria, E. L., and Stoffa, P. L., 1994, Finite-difference modeling in transversely isotropic media, Geophysics, 43, pp. 1099-1110
  5. Igel, H., Mora, P., and Riollet, B., 1995, Anisotropic wave propagation through finite-difference grids, Geophysics, 60, pp. 1203-1216
  6. Higdon, R. L., 1991, Absorbing boundary conditions for elastic waves, Geophysics, 56, pp. 231-241
  7. Juhlin, C., 1995, Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media, Geopysical Prospecting, 43, pp. 843-858
  8. Lysmer, J., and Kuhlemeyer, R. L., 1969, Finite dynamic model for infinite media, J.Eng.Mech.Div., ASCE 95 EM4, pp. 859-877
  9. Reynolds, A. C., 1978, Boundary conditions for the numerical solution of wave propagation problems, Geophysics, 59, pp. 282-289
  10. Shin, C., 1995, Sponge boundary condition for frequencydomain modeling, Geophysics, 60, pp. 1870-1874
  11. Thomsen, L., 1986, Weak elastic anisotropy, Geophysics, 51, pp. 1954-1966
  12. Tsingas, C., Vafidis, A., and Kanasewich, E. R., 1990, Elastic wave propagation in transversely isotropic media using finite differences, Geophysical Prospecting, 38, pp. 933-949