优化的三维地震波旁轴近似吸收边界条件
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摘要
三维地震波数值模拟中的吸收边界如果采用镶边处理(如最佳匹配层吸收边界条件(PML)或阻尼吸收边界条件),会大幅度增加计算量和计算时间,若增加旁轴近似阶数,则会增加数值实现的复杂度,甚至会导致计算过程的不稳定。为解决上述问题,提出优化的三维声波旁轴近似吸收边界条件,并做了相应的理论推导和数值分析,只需合理地调节加权因子,就可拓宽边界处的完全吸收角度,且其反射系数误差很小。数值实例表明,该方法不增加计算空间,算法简单且易于实现,能够获得比常规旁轴近似吸收边界条件更好的边界吸收效果,是一种有效的三维地震波数值模拟吸收边界条件。
Computational cost increase greatly in numerical simulation of 3-D seismic waves if padding processing such as PML or damping absorbing boundary condition is adopted in handling of absorbing boundary conditions.These algorithms of the simulation are complicated,even become instable if increasing the order of paraxial approximation.Optimized dual absorbing boundary condition was proposed and formulae were derived.Theoretical analysis showed that if proper weighting factor is used,the complete absorbing angle is enlarged at the boundary and the errors in reflectance are small.Numerical examples showed that the proposed method does not increase the computational cost.It is easy to implement and yields better results compared to conventional paraxial approximation.
Computational cost increase greatly in numerical simulation of 3-D seismic waves if padding processing such as PML or damping absorbing boundary condition is adopted in handling of absorbing boundary conditions.These algorithms of the simulation are complicated,even become instable if increasing the order of paraxial approximation.Optimized dual absorbing boundary condition was proposed and formulae were derived.Theoretical analysis showed that if proper weighting factor is used,the complete absorbing angle is enlarged at the boundary and the errors in reflectance are small.Numerical examples showed that the proposed method does not increase the computational cost.It is easy to implement and yields better results compared to conventional paraxial approximation.
引文
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2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
3Hastings F,Schneider J B,Broschat S L.Application of the perfectly matched layer(PML)absorbing bounda-ry condition to elastic wave propagation[J].Journal of the Acoustic Society of America,1996,100(5):3061～3069
4Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastody-namic problemin anisotropic heterogeneous media[J].Geophysics,2001,66(1):294～307
5Zeng Y Q,He J Q,Liu Q H.The application of the perfectly matched layer in numerical modeling of wave propagationin poroelastic media[J].Geophysics,2001,66(4):1258～1266
6Komatitsch D,Tromp J.Aperfectly matchedlayer ab-sorbing boundary condition for the second-order seis-mic wave equation[J].Geophysical Journal Internation-al,2003,154:146～150
7Clayton R.Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations[J].The Bulle-tin of the Seismological Society of America,1977,67:1529～1540
8Reynolds A C.Boundary conditions for the numerical solution of wave propagation problems[J].Geophys-ics,1978,43(6):1099～1110
9Liao Z P,Wong H L.Atransmitting boundary for the numerical si mulation of elastic wave propagation[J].Soil Dynamics and Earthquake Engineering,1984,3(4):174～183
10Liao Z P.Transmitting boundary and radiation condi-tions at infinity[J].Science in China(Series E),2001,44(2):67～76
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12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
13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
14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):32～35
15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
16佘德平.数值模拟技术的发展现状[J].勘探地球物理进展,2003,26(5):407～412
17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(1):25～31
18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):187～194
19王珺,杨长春,冯英杰.用优化通量校正传输技术压制数值模拟的频散[J].勘探地球物理进展,2007,30(4):16～21
2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
3Hastings F,Schneider J B,Broschat S L.Application of the perfectly matched layer(PML)absorbing bounda-ry condition to elastic wave propagation[J].Journal of the Acoustic Society of America,1996,100(5):3061～3069
4Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastody-namic problemin anisotropic heterogeneous media[J].Geophysics,2001,66(1):294～307
5Zeng Y Q,He J Q,Liu Q H.The application of the perfectly matched layer in numerical modeling of wave propagationin poroelastic media[J].Geophysics,2001,66(4):1258～1266
6Komatitsch D,Tromp J.Aperfectly matchedlayer ab-sorbing boundary condition for the second-order seis-mic wave equation[J].Geophysical Journal Internation-al,2003,154:146～150
7Clayton R.Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations[J].The Bulle-tin of the Seismological Society of America,1977,67:1529～1540
8Reynolds A C.Boundary conditions for the numerical solution of wave propagation problems[J].Geophys-ics,1978,43(6):1099～1110
9Liao Z P,Wong H L.Atransmitting boundary for the numerical si mulation of elastic wave propagation[J].Soil Dynamics and Earthquake Engineering,1984,3(4):174～183
10Liao Z P.Transmitting boundary and radiation condi-tions at infinity[J].Science in China(Series E),2001,44(2):67～76
11Higdon R L.Absorbing boundary condition for elastic waves[J].Geophysics,1991,56(2):231～241
12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
13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
14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):32～35
15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
16佘德平.数值模拟技术的发展现状[J].勘探地球物理进展,2003,26(5):407～412
17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(1):25～31
18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):187～194
19王珺,杨长春,冯英杰.用优化通量校正传输技术压制数值模拟的频散[J].勘探地球物理进展,2007,30(4):16～21
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