起伏地表条件下地震波数值模拟方法综述
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摘要
起伏地表地震波数值模拟中,如何选择适合地表的数值计算方法以及更好地实现起伏自由边界条件是2个关键问题。为此,就前一个关键问题所涉及的方法、原理以及发展状况进行了详细的阐述分析;而对后一个问题,就近年来发展的主要实现方法进行了详细的论述。目的在于选择适当的实现方法解决相应的问题,以达到满意的模拟效果。
Numerical simulation of seismic waves from irregular topography is a hot issue. In this area there are two key aspects controlling the success of the simulation. The first is how to select appropriate numerical simulation method. The second is how to realize free boundary conditions. This paper reviewed the first issue in terms of methodology, principles, and current situations and discussed in detail the realization methods for the second issue.
Numerical simulation of seismic waves from irregular topography is a hot issue. In this area there are two key aspects controlling the success of the simulation. The first is how to select appropriate numerical simulation method. The second is how to realize free boundary conditions. This paper reviewed the first issue in terms of methodology, principles, and current situations and discussed in detail the realization methods for the second issue.
引文
1 Jamstram C, Tessmer E. Elastic modeling on a grid with vertically varying spacing[J]. Geophysics Prospecting,1994,42(4) :357-370
2 Hayashi K, Burns D, Variable grid finite-difference modeling including surface topography[J]. Expanded Abstracts of 69th Annual International SEG Meeting, 1999, 523-527
3 Oprsal I, Zahradnik J. Elastic finite-difference method for irregular grids [J]. Geophysics, 1999, 64 (1): 240-250
4 Nordstrom J, Carpenter M H. High-order finite difference methods, multidimensional linear problems and curvilinear coordinates[J]. Journal of Computational Physics, 2001,173(1):149-174
5 Tessmer E, Kessler D, Kosloff D, et al. Multi-domain Chebyshev-Fourier method for the solution of the equations of motion of dynamic elasticity[J]. Journal of Computational Physics,1992,100(2):355-363
6 Tessmer E, Kosloff D. 3D elastic modeling with surface topography by Chebychev spectral method[J]. Geophysics, 1994, 59(3): 464-473
7 Gottlieb D, Gunzburger M, Turkel E. On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods[J]. SIAM J Nu-mer Anal,1982,19(4).671-682
8 Hestholm S, Ruud B. 2D finite-difference elastic wave modeling including surface topography[J]. Geophysics Prospecting, 1994,42(5): 371-390
9 Hestholm S, Ruud B, Husebye E. 3-D versus 2-D finite-difference seismic synthetics including real surface topography [J]. Physics of the Earth and Planetary Interiors,1999,113(1): 339-354
10 Hestholm S. 3-D finite-difference elastic wave modeling including surface topography [J]. Geophysics, 1998, 63(2):613-622
11 Hestholm S. Elastic wave modeling with free surfaces: Stability of long simulation[J]. Expanded Abstracts of 71st Annual International SEG Meeting, 2001, 1159-1163
12董良国．复杂地表条件下地震波传播数值模拟[J]．勘探地球物理进展,2005,28(3):631～445
13裴正林．任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟[J]．石油地球物理勘探,2004,39(6): 629～634
14 Moczo P, Bystricky E, Kristek J, et al. Hybrid modeling of P-SV seismic motion at inhomogeneous viscoe-lastic topographic structures[J]. Bull Seism Soc Am, 1997, 87(6): 1305-1323
15黄自萍,张铭,吴文青等．弹性波传播数值模拟的区域分裂法[J]．地球物理学报,2004,47(6):1 094-2 000
16马德堂,朱光明．有限元与伪普法混合求解弹性波动方程[J]．地球科学与环境学报,2004,26(1):61-64
17 Komatitsch D, Tromp J, Vilotte J. The spectral element method for elastic wave equations: Application to 2D and 3D seismic problems[J]. Expanded Abstracts of 68th Annual International SEG Meeting, 1998, 1 460-1 463
18 Komatitsch D, Tromp J. The spectral element method for three-dimensional seismic wave propagation [J]. Expanded Abstracts of 70th Annual International SEG Meeting, 2000,2 197-2 200
19 Pedersen H A, Sanchez-Sesma F J, Campillo M. Three-dimensional scattering by two-dimensional topographies[J]. Bull Seism Soc Am, 1994, 84(4): 1 169-1 183
20 Bouchon M, Schultz C, Toksoz M N. Effect of three-dimensional topography on seismic motion[J]. Journal of Geophysical Research,1996,101(B3) :5 835-5 846
21 Durand S, Gaffet S, Virieux J. Seismic diffracted waves from topography using 3D discrete wave number-boundary intergral equation simulation[J]. Geophysics, 1999,64(2): 572-578
22 Wu R S, Fu L Y. A hybrid method for wave propagation simulation in near-surface regions[J]. Expanded Abstracts of 68th Annual International SEG Meeting, 1998,1456-1459
23 Crase E. High-order (space and time) finite-difference modeling of elastic wave equation[J]. Expanded Abstracts of 60th Annual International SEG Meeting, 1990, 987- 991
24 Vidale J E, Clayton R W. A stable free-surface boundary condition for 2D elastic FD wave simulation [J]. Geophysics, 1986, 51(12): 2 247-2 249
25王雪秋,孙建国．复杂地表地质条件下地震波数值模拟综述[J]．吉林大学学报(地球科学版),2005,35(3): 315～322
26 Robertsson J O. A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography[J]. Geophysics, 1996, 61(6): 1921-1934
27 Jih R S, McLaughlin K L, Zoltan A. Free-boundary conditions of arbitrary polygonal topography in a two-dimensional explicit elastic finite-difference scheme [J]. Geophysics, 1988,53 (8): 1 045 -1 055
28王秀明,张海澜．用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法[J]．中国科学G辑:物理学、力学、天文学,2004,34(5):481～493
29 Kosloff D, Reshef M, Lowenthal D. Elastic wave calculations by the fourier transform[J]. Bull Seism Soc Am,1984,74(4) :875-891
30陈伟．起伏地表条件下二维地震波场的数值模拟[J]．勘探地球物理进展,2005,28(6):631～669
31 Boris J P, Book D L. Flux-corrected transportⅠ. SHASTA, A fluid tansport algorithm that works [J]. Journal of Computational Physics, 1973, 11 (1): 38-69
32 Book D L, Boris J P,Hain K. Flux-corrected tansportⅡ: generalization of the method [J]. Journal of Computational Physics, 1975, 18(2):248-283
33杨顶辉,滕吉文．各向异性介质中三分量地震记录的FCT有限差分模拟[J]．石油地球物理勘探,1997,32 (2):181～191
34吴国忱,王华忠．波场模拟中的数值频散分析与校正策略[J]．地球物理学进展,2005,20(1):58-65
2 Hayashi K, Burns D, Variable grid finite-difference modeling including surface topography[J]. Expanded Abstracts of 69th Annual International SEG Meeting, 1999, 523-527
3 Oprsal I, Zahradnik J. Elastic finite-difference method for irregular grids [J]. Geophysics, 1999, 64 (1): 240-250
4 Nordstrom J, Carpenter M H. High-order finite difference methods, multidimensional linear problems and curvilinear coordinates[J]. Journal of Computational Physics, 2001,173(1):149-174
5 Tessmer E, Kessler D, Kosloff D, et al. Multi-domain Chebyshev-Fourier method for the solution of the equations of motion of dynamic elasticity[J]. Journal of Computational Physics,1992,100(2):355-363
6 Tessmer E, Kosloff D. 3D elastic modeling with surface topography by Chebychev spectral method[J]. Geophysics, 1994, 59(3): 464-473
7 Gottlieb D, Gunzburger M, Turkel E. On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods[J]. SIAM J Nu-mer Anal,1982,19(4).671-682
8 Hestholm S, Ruud B. 2D finite-difference elastic wave modeling including surface topography[J]. Geophysics Prospecting, 1994,42(5): 371-390
9 Hestholm S, Ruud B, Husebye E. 3-D versus 2-D finite-difference seismic synthetics including real surface topography [J]. Physics of the Earth and Planetary Interiors,1999,113(1): 339-354
10 Hestholm S. 3-D finite-difference elastic wave modeling including surface topography [J]. Geophysics, 1998, 63(2):613-622
11 Hestholm S. Elastic wave modeling with free surfaces: Stability of long simulation[J]. Expanded Abstracts of 71st Annual International SEG Meeting, 2001, 1159-1163
12董良国．复杂地表条件下地震波传播数值模拟[J]．勘探地球物理进展,2005,28(3):631～445
13裴正林．任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟[J]．石油地球物理勘探,2004,39(6): 629～634
14 Moczo P, Bystricky E, Kristek J, et al. Hybrid modeling of P-SV seismic motion at inhomogeneous viscoe-lastic topographic structures[J]. Bull Seism Soc Am, 1997, 87(6): 1305-1323
15黄自萍,张铭,吴文青等．弹性波传播数值模拟的区域分裂法[J]．地球物理学报,2004,47(6):1 094-2 000
16马德堂,朱光明．有限元与伪普法混合求解弹性波动方程[J]．地球科学与环境学报,2004,26(1):61-64
17 Komatitsch D, Tromp J, Vilotte J. The spectral element method for elastic wave equations: Application to 2D and 3D seismic problems[J]. Expanded Abstracts of 68th Annual International SEG Meeting, 1998, 1 460-1 463
18 Komatitsch D, Tromp J. The spectral element method for three-dimensional seismic wave propagation [J]. Expanded Abstracts of 70th Annual International SEG Meeting, 2000,2 197-2 200
19 Pedersen H A, Sanchez-Sesma F J, Campillo M. Three-dimensional scattering by two-dimensional topographies[J]. Bull Seism Soc Am, 1994, 84(4): 1 169-1 183
20 Bouchon M, Schultz C, Toksoz M N. Effect of three-dimensional topography on seismic motion[J]. Journal of Geophysical Research,1996,101(B3) :5 835-5 846
21 Durand S, Gaffet S, Virieux J. Seismic diffracted waves from topography using 3D discrete wave number-boundary intergral equation simulation[J]. Geophysics, 1999,64(2): 572-578
22 Wu R S, Fu L Y. A hybrid method for wave propagation simulation in near-surface regions[J]. Expanded Abstracts of 68th Annual International SEG Meeting, 1998,1456-1459
23 Crase E. High-order (space and time) finite-difference modeling of elastic wave equation[J]. Expanded Abstracts of 60th Annual International SEG Meeting, 1990, 987- 991
24 Vidale J E, Clayton R W. A stable free-surface boundary condition for 2D elastic FD wave simulation [J]. Geophysics, 1986, 51(12): 2 247-2 249
25王雪秋,孙建国．复杂地表地质条件下地震波数值模拟综述[J]．吉林大学学报(地球科学版),2005,35(3): 315～322
26 Robertsson J O. A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography[J]. Geophysics, 1996, 61(6): 1921-1934
27 Jih R S, McLaughlin K L, Zoltan A. Free-boundary conditions of arbitrary polygonal topography in a two-dimensional explicit elastic finite-difference scheme [J]. Geophysics, 1988,53 (8): 1 045 -1 055
28王秀明,张海澜．用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法[J]．中国科学G辑:物理学、力学、天文学,2004,34(5):481～493
29 Kosloff D, Reshef M, Lowenthal D. Elastic wave calculations by the fourier transform[J]. Bull Seism Soc Am,1984,74(4) :875-891
30陈伟．起伏地表条件下二维地震波场的数值模拟[J]．勘探地球物理进展,2005,28(6):631～669
31 Boris J P, Book D L. Flux-corrected transportⅠ. SHASTA, A fluid tansport algorithm that works [J]. Journal of Computational Physics, 1973, 11 (1): 38-69
32 Book D L, Boris J P,Hain K. Flux-corrected tansportⅡ: generalization of the method [J]. Journal of Computational Physics, 1975, 18(2):248-283
33杨顶辉,滕吉文．各向异性介质中三分量地震记录的FCT有限差分模拟[J]．石油地球物理勘探,1997,32 (2):181～191
34吴国忱,王华忠．波场模拟中的数值频散分析与校正策略[J]．地球物理学进展,2005,20(1):58-65
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