PML吸收边界条件影响因素分析
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摘要
影响完全匹配层方法吸收效果的主要因素有吸收层厚度和衰减系数,笔者通过地震波场数值模拟,讨论了吸收层厚度和衰减系数对吸收效果的影响。研究表明,在衰减系数一定时,吸收层厚度越大,边界反射越弱。吸收层的厚度一般在12～20道较为适当,在吸收层的厚度比较小时,随着衰减系数的增大,边界反射逐渐减弱甚至完全没有边界反射,但是若再进一步增大衰减系数则又会逐步出现边界反射。因此,在实际应用中应该注意衰减系数的选择,衰减系数一般在500～2 000之间,衰减系数较大反而影响其效果。
The main factors which influence the absorbing effects of the perfectly matched layer(PML) method are the thickness of absorbing layer and the attenuation coefficient.Based on the numerical simulation of the seismic wave field,the author discusses the impact of the thickness of absorption layer and the attenuation coefficient on the absorption effect.The results show that,under the condition of constant attenuation coefficient,the larger the thickness of the absorption layer is,the weaker the boundary reflection becomes.The absorption layer thickness of 12～20 traces is fairly appropriate.When the thickness of the absorption layer is smaller,the boundary reflection gets more and more weaker or even becomes zero with increasing attenuation coefficient.Nevertheless,if the attenuation coefficient is further enlarged,the boundary reflection will gradually appear again.Therefore,we must pay attention to the choice of attenuation coefficient in practice.The attenuation coefficient is generally between 500 and 2000.If the attenuation coefficient is larger than 3000,the absorption effect is not satisfactory.
The main factors which influence the absorbing effects of the perfectly matched layer(PML) method are the thickness of absorbing layer and the attenuation coefficient.Based on the numerical simulation of the seismic wave field,the author discusses the impact of the thickness of absorption layer and the attenuation coefficient on the absorption effect.The results show that,under the condition of constant attenuation coefficient,the larger the thickness of the absorption layer is,the weaker the boundary reflection becomes.The absorption layer thickness of 12～20 traces is fairly appropriate.When the thickness of the absorption layer is smaller,the boundary reflection gets more and more weaker or even becomes zero with increasing attenuation coefficient.Nevertheless,if the attenuation coefficient is further enlarged,the boundary reflection will gradually appear again.Therefore,we must pay attention to the choice of attenuation coefficient in practice.The attenuation coefficient is generally between 500 and 2000.If the attenuation coefficient is larger than 3000,the absorption effect is not satisfactory.
引文
[1]Clayton R,Engquist B.Absorbing boundary conditions for acousticand elastic wave equations[J].Bulletin of the Seismological Socie-ty of America,1977,67(6):1529-1540.
[2]王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34.
[3]徐义,张剑锋.地震波数值模拟的非规则网格PML吸收边界[J].地球物理学报,2008,51(5):1520-1526.
[4]赵海波,王秀明,王东,等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报,2007,50(2):581-591.
[5]王永刚,邢文军,谢万学,等.完全匹配层吸收边界条件的研究[J].中国石油大学学报:自然科学版,2007,31(1):19-24.
[6]Berenger J P.A perfectly matched layer for the absorption of elec-tromagnetic waves[J].Journal of Computational Physics,1994,114(2):185-200.
[7]Collino F,Tsogka C.Application of the perfectly matched absorbinglayer model to the linear elastodynamic problem in anisotropic het-erogeneous media[J].Geophysics,2001,66(1):294-307.
[8]Hastings F D,Schneider J B,Broschat S L.Application of the per-fectly matched layer(PML)absorbing boundary condition to e-lastic wave propagation[J].Journal Acoustical Society of America,1996,100(5):3061-3069.
[2]王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34.
[3]徐义,张剑锋.地震波数值模拟的非规则网格PML吸收边界[J].地球物理学报,2008,51(5):1520-1526.
[4]赵海波,王秀明,王东,等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报,2007,50(2):581-591.
[5]王永刚,邢文军,谢万学,等.完全匹配层吸收边界条件的研究[J].中国石油大学学报:自然科学版,2007,31(1):19-24.
[6]Berenger J P.A perfectly matched layer for the absorption of elec-tromagnetic waves[J].Journal of Computational Physics,1994,114(2):185-200.
[7]Collino F,Tsogka C.Application of the perfectly matched absorbinglayer model to the linear elastodynamic problem in anisotropic het-erogeneous media[J].Geophysics,2001,66(1):294-307.
[8]Hastings F D,Schneider J B,Broschat S L.Application of the per-fectly matched layer(PML)absorbing boundary condition to e-lastic wave propagation[J].Journal Acoustical Society of America,1996,100(5):3061-3069.
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