Time-Domain Elastic Wave Modeling in Anisotropic Media using Cell-Based Finite-Difference Method

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2008 Vol.45, Issue 5 Preview Page Next Page

Time-Domain Elastic Wave Modeling in Anisotropic Media using Cell-Based Finite-Difference Method 셀 기반 유한차분법을 이용한 이방성 매질에서의 시간영역 탄성파 모델링: 이호용, 민동주, 권병두, 유해수
Ho-Yong Lee, Dong-Joo Min, Byung-Doo Kown and Hai-Soo Yoo

31 October 2008. pp. 536-545

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Abstract

Since seismic anisotropy often appears in geological media, which may result from various causes, we need to describe anisotropic features in seismic modeling and inversion. Although a number of modeling algorithms were developed to describe seismic anisotropy, we still need to develop a simple but accurate modeling algorithm to simulate geological scale models. For such a modeling algorithm for anisotropic media, we extend a time-domain cell-based finite-difference method to anisotropic media. Since the cell-based finite-difference scheme only employs displacements, we can expect that our anisotropic modeling algorithm is computationally more efficient than the staggered-grid finite-difference method. Because our algorithm does not require any interpolations, it’s possible to simulate a model whose material properties abruptly change. In order to suppress artificial reflections originating from the outer boundaries of a given model, we apply Higdon’s absorbing boundary conditions. Numerical examples show that our modeling algorithm can properly describe anisotropic features.

Keywords

Anisotropy

Seismic modeling

Time domain cell-based FDM

Absorbing boundary

지하 내부에 존재하는 암석은 여러 가지 원인에 의해 이방성을 지니므로 탄성파 모델링이나 실제 자료의 역산에서 이방성 구조를 고려해야 한다. 이를 위해 많은 탄성파 모델링 방법들이 시도되었으나, 적용하기 쉽고 실제 지하구조를 정확하게 표현할 수 있는 방법이 필요하다. 본 연구에서는 시간영역 변위근사 셀 기반 유한차분법을 이방성 매질에 적용하였다. 셀 기반 유한차분법은 변위자체를 사용하기 때문에 메모리와 계산시간이 엇격자법에 비해 매우 적게 소요된다. 또한 이 방법은 물성의 평균값을 사용하지 않기 때문에 매질의 성질이 급변하는 경계에서도 정확한 해를 제시할 수 있다. 모형경계에서 발생하는 인공적인 반사파를 제거하기 위해서 등방성 매질에서 고안되었던 Higdon의 흡수경계조건을 이방성 매질에 적용하였다. 셀 기반 유한차분법은 등방성 매질의 자유면 경계조건뿐만 아니라 이방성 매질을 포함하는 여러 가지 모형에서 매우 정확한 해를 제시함을 확인할 수 있었다.

키워드

이방성

탄성파 모델링

유한차분법

시간영역 셀 기반 유한차분법

흡수경계조건

References

민동주, 유해수, 2003, “시간영역 변위근사 유한차분법의자유면 경계조건,” 물리탐사, 제 6권 2호, pp. 77-86.
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.
Clayton, R. and Engquist, B., 1977, “Absorbing boundary conditions for acoustic and elastic wave equations,” Bulletin of the Seismological Society of America, 67, pp. 1529-1540.
Kelly, K. R., Ward, R. W., Treitel, S. and Alford, R. M., 1976, “Synthetic seismograms: A finite-difference approach,” Geophysics, 53, pp. 1045-1055.
Faria, E. L. and Stoffa, P. L., 1994, “Finite-difference modeling in transversely isotropic media,” Geophysics, 59, pp. 282-289.
Gao, H. and Zhang, J., 2006, “Parallel 3-D simulation of seismic wave propagation in heterogeneous anisotropic media: a grid method approach,” Geophys. J. International, 165, pp. 875-888.
Graves, R. W., 1996, “Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences,” Bull. Seism. Soc. Am., 86, pp. 1091-1106.
Igel, H., Mora, P. and Riollet, B., 1995, “Anisotropic wave propagation through finite-difference grids,” Geophysics, 60, pp. 1203-1216.
Higdon, R. L., 1991, “Absorbing boundary conditions for elastic waves,” Geophysics, 56, pp. 231-241.
Juhlin, C., 1995, “Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media,” Geopysical Prospecting, 43, pp. 843-858.
Min, D. -J., Shin, C., and Yoo, H. S., 2004, “Free-surface boundary condition in finite-difference elastic wave modeling,” Bulletin of the Seismological Society of America, 94, pp. 237-250.
Randall, C. J., 1988, “Absorbing boundary condition for the elastic wave equation,” Geophysics, 53, pp. 611-624.
Saenger, E. H., Gold, N. and Shapiro, S. A., 2000, “Modeling the propagation of elastic waves using a modified finite-difference grid,” Wave motion, 31, pp. 77-92.
Saenger, E. H. and Bohlen, T., 2004, “Finite-difference modling of viscoelastic and anisotropic wave propagation using the rotated staggered grid,” Geophysics, 69, pp. 583-591.
Shin, C., 1995, “Sponge boundary condition for frequency-domain modeling,” Geophysics, 60, pp. 1870-1874.
Thomsen, L., 1986, “Weak elastic anisotropy,” Geophysics, 51, pp. 1954-1966.
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.
Vidale J. E., Clayton R. W., 1986, “A stable free-surface boundary condition for two-dimensional elastic finite-difference wave simulation”, Geophysics, 51, pp. 2247-2249.
Write, J., 1987, “The effects of transverse isotropy on reflection amplitude versus offset,” Geophysics, 52, pp. 564-567.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society for Geosystem Engineering
Journal Title(Ko) :한국지구시스템공학회지
Volume : 45
No :5
Pages :536-545

[1] 민동주, 유해수, 2003, “시간영역 변위근사 유한차분법의자유면 경계조건,” 물리탐사, 제 6권 2호, pp. 77-86.

[2] 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.

[3] Clayton, R. and Engquist, B., 1977, “Absorbing boundary conditions for acoustic and elastic wave equations,” Bulletin of the Seismological Society of America, 67, pp. 1529-1540.

[4] Kelly, K. R., Ward, R. W., Treitel, S. and Alford, R. M., 1976, “Synthetic seismograms: A finite-difference approach,” Geophysics, 53, pp. 1045-1055.

[5] Faria, E. L. and Stoffa, P. L., 1994, “Finite-difference modeling in transversely isotropic media,” Geophysics, 59, pp. 282-289.

[6] Gao, H. and Zhang, J., 2006, “Parallel 3-D simulation of seismic wave propagation in heterogeneous anisotropic media: a grid method approach,” Geophys. J. International, 165, pp. 875-888.

[7] Graves, R. W., 1996, “Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences,” Bull. Seism. Soc. Am., 86, pp. 1091-1106.

[8] Igel, H., Mora, P. and Riollet, B., 1995, “Anisotropic wave propagation through finite-difference grids,” Geophysics, 60, pp. 1203-1216.

[9] Higdon, R. L., 1991, “Absorbing boundary conditions for elastic waves,” Geophysics, 56, pp. 231-241.

[10] Juhlin, C., 1995, “Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media,” Geopysical Prospecting, 43, pp. 843-858.

[11] Min, D. -J., Shin, C., and Yoo, H. S., 2004, “Free-surface boundary condition in finite-difference elastic wave modeling,” Bulletin of the Seismological Society of America, 94, pp. 237-250.

[12] Randall, C. J., 1988, “Absorbing boundary condition for the elastic wave equation,” Geophysics, 53, pp. 611-624.

[13] Saenger, E. H., Gold, N. and Shapiro, S. A., 2000, “Modeling the propagation of elastic waves using a modified finite-difference grid,” Wave motion, 31, pp. 77-92.

[14] Saenger, E. H. and Bohlen, T., 2004, “Finite-difference modling of viscoelastic and anisotropic wave propagation using the rotated staggered grid,” Geophysics, 69, pp. 583-591.

[15] Shin, C., 1995, “Sponge boundary condition for frequency-domain modeling,” Geophysics, 60, pp. 1870-1874.

[16] Thomsen, L., 1986, “Weak elastic anisotropy,” Geophysics, 51, pp. 1954-1966.

[17] 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.

[18] Vidale J. E., Clayton R. W., 1986, “A stable free-surface boundary condition for two-dimensional elastic finite-difference wave simulation”, Geophysics, 51, pp. 2247-2249.

[19] Write, J., 1987, “The effects of transverse isotropy on reflection amplitude versus offset,” Geophysics, 52, pp. 564-567.

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