加权吸收边界条件的优化设计
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摘要
基于声波波动方程的旁轴近似吸收边界条件可以通过提高泰勒级数展开的旁轴近似阶数获得更好的吸收效果,但这样不仅增加了差分计算的复杂性,同时还导致计算过程不稳定。针对这一问题,提出了优化加权吸收边界条件。首先从理论上讨论了优化加权吸收边界条件,提出了加权因子概念,通过调节加权因子来拓展边界反射完全吸收角度;然后利用脉冲响应和数值模拟对优化加权吸收边界条件的吸收效果进行了分析。结果表明,选择合适的加权因子可以将边界处的完全吸收角度拓宽到60°以上,反射系数误差不超过2.5%。该方法简单易行,计算量小,而吸收效果比常规旁轴近似吸收边界条件更好。
Paraxial approximation absorption boundary condition based on acoustic wave equation can obtain better absorption results by increasing paraxial approximation order of Taylor series.However, this kind of operation will increase the complexity of difference computation,and result in instability of computation process.In order to solve the problem,we proposed optimized weighted absorption boundary condition.Firstly,optimized weighted absorption boundary condition was discussed theoretically,the concept of weighted factor was proposed,and the perfect absorption angle of boundary reflection was extended by adjusting weighted factor. Then,impulse response and numerical simulation were used to analyze the absorption effect of optimized weighted absorption boundary condition.Results showed that properly selected weighted factor can extend the perfect absorption angle at boundary to more than 60°,and the error of reflection coefficient is no more than 2.5%. The method is easily realized with small computation amount,and its absorption effect is better than conventional paraxial approximation absorption boundary condition.
Paraxial approximation absorption boundary condition based on acoustic wave equation can obtain better absorption results by increasing paraxial approximation order of Taylor series.However, this kind of operation will increase the complexity of difference computation,and result in instability of computation process.In order to solve the problem,we proposed optimized weighted absorption boundary condition.Firstly,optimized weighted absorption boundary condition was discussed theoretically,the concept of weighted factor was proposed,and the perfect absorption angle of boundary reflection was extended by adjusting weighted factor. Then,impulse response and numerical simulation were used to analyze the absorption effect of optimized weighted absorption boundary condition.Results showed that properly selected weighted factor can extend the perfect absorption angle at boundary to more than 60°,and the error of reflection coefficient is no more than 2.5%. The method is easily realized with small computation amount,and its absorption effect is better than conventional paraxial approximation absorption boundary condition.
引文
1 Berenger J P.A perfectly matched layer for the absorption of electromagnetic waves[J].Journal of Computational Physics,1994,114(2):185-200
2 Hastings F,Schneider J B,Broschat S L.Application of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation[J]. Journal of the Acoustic Society of America,1996, ??100(5):3061-3069
3 Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J]. Geophysics,2001,66(1):294-307
4 Zeng Y Q,He J Q,Liu Q H.The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media[J].Geophysics, 2001,66(4):1258-1266
5 Komatitsch D,Tromp J.A perfectly matched layer absorbing boundary condition for the second -order seismic wave equation[J].Geophysical Journal International, 2003,154(1):146-150
6陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79
7 Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,67(6):1529-1540
8 Reynolds A C.Boundary conditions for the numerical solution of wave propagation problems[J].Geophysics, 1978,43(6):1099-1110
9 Liao Z P,Wong H L.A transmitting boundary for the numerical simulation of elastic propagation[J].Soil Dynamics and Earthquake Engineering,1984,3(4): 174-183
10 Liao Z P.Transmitting boundary and radiation conditions at infinity[J].Science in China(Series E),2001, 44(2):67-76
11 Higdon R L.Absorbing boundary condition for elastic waves[J].Geophysics,1991,56(2):231-241
12王华忠,马在田.优化系数的吸收边界条件方程[J].石油地球物理勘探,1997,32(5):628-636
13罗大清,宋炜,吴律,等.加权方向校正及插值预测吸收边界条件的三维波动方程叠前数值模拟[J].石油地球物理勘探,1999,34(3):275-284
14崔兴福,张关泉.地震波方程人工边界的两种处理方??法[J].石油物探,2003,42(4):452-455
15李文杰,魏修成,刘洋.声波正演中一种新的边界条件——双重吸收边界条件[J].石油物探,2004,43(6): 528-531
16陈可洋,刘洪林,杨微,等.随机介质模型的改进方法及应用[J].大庆石油地质与开发,2008,27(5):124- 126,131
2 Hastings F,Schneider J B,Broschat S L.Application of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation[J]. Journal of the Acoustic Society of America,1996, ??100(5):3061-3069
3 Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J]. Geophysics,2001,66(1):294-307
4 Zeng Y Q,He J Q,Liu Q H.The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media[J].Geophysics, 2001,66(4):1258-1266
5 Komatitsch D,Tromp J.A perfectly matched layer absorbing boundary condition for the second -order seismic wave equation[J].Geophysical Journal International, 2003,154(1):146-150
6陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79
7 Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,67(6):1529-1540
8 Reynolds A C.Boundary conditions for the numerical solution of wave propagation problems[J].Geophysics, 1978,43(6):1099-1110
9 Liao Z P,Wong H L.A transmitting boundary for the numerical simulation of elastic propagation[J].Soil Dynamics and Earthquake Engineering,1984,3(4): 174-183
10 Liao Z P.Transmitting boundary and radiation conditions at infinity[J].Science in China(Series E),2001, 44(2):67-76
11 Higdon R L.Absorbing boundary condition for elastic waves[J].Geophysics,1991,56(2):231-241
12王华忠,马在田.优化系数的吸收边界条件方程[J].石油地球物理勘探,1997,32(5):628-636
13罗大清,宋炜,吴律,等.加权方向校正及插值预测吸收边界条件的三维波动方程叠前数值模拟[J].石油地球物理勘探,1999,34(3):275-284
14崔兴福,张关泉.地震波方程人工边界的两种处理方??法[J].石油物探,2003,42(4):452-455
15李文杰,魏修成,刘洋.声波正演中一种新的边界条件——双重吸收边界条件[J].石油物探,2004,43(6): 528-531
16陈可洋,刘洪林,杨微,等.随机介质模型的改进方法及应用[J].大庆石油地质与开发,2008,27(5):124- 126,131
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