适用于VTI介质地震波方程的PML吸收边界
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摘要
正演模拟计算的一个关键是在有限空间中模拟地震波在无限空间中的传播。要消除由于把地震波的传播设定在有限区域而产生的边界反射,需要引入吸收边界条件。本文研究的完全匹配层(PM L)吸收边界条件是Berenger在1994年提出的一种新的人工边界条件,从横向各相同性(VT I)介质的一阶弹性波方程出发,给出方程在交错网格空间的高阶有限差分格式,并推导出适用于其的PM L吸收边界条件及边界的交错网格高阶有限差分格式。计算结果表明,PM L吸收边界条件可以完全吸收外行波场。
The key point of modeling simulation is simulating the propagation of seismic wave in the limit space instead of in the infinite space.To eliminate the propagation of seismic waves generated in a certain area to set the boundary reflection,need to introduce absorbing boundary conditions.In this paper,the writer discussed the new artificial boundary conditions——perfectly matched layer(PML) absorbing boundary condition proposed by Berenger in 1994.Based on the seismic wave equation of VTI media,the thesis gave the high-order finite-difference scheme of the equation in the space of staggered-grid and pushed to the corresponding PML absorbing boundary condition and the staggered-grid high-order finite-difference scheme of the absorbing boundary.The results show that,PML absorbing boundary condition can almost completely absorb the wave that propagates out of the simulation field.
The key point of modeling simulation is simulating the propagation of seismic wave in the limit space instead of in the infinite space.To eliminate the propagation of seismic waves generated in a certain area to set the boundary reflection,need to introduce absorbing boundary conditions.In this paper,the writer discussed the new artificial boundary conditions——perfectly matched layer(PML) absorbing boundary condition proposed by Berenger in 1994.Based on the seismic wave equation of VTI media,the thesis gave the high-order finite-difference scheme of the equation in the space of staggered-grid and pushed to the corresponding PML absorbing boundary condition and the staggered-grid high-order finite-difference scheme of the absorbing boundary.The results show that,PML absorbing boundary condition can almost completely absorb the wave that propagates out of the simulation field.
引文
[1]Berenger J P.A perfectly matched layer forthe absorption of electro-magnetic waves[J].J.Comput.Phys.1994,114:185-200.
[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]李景叶,陈小宏.TI介质地震波场数值模拟边界条件处理[J].西安石油大学学报.2006,21(4):20-23.
[4]牟永光,裴正林著.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[5]Abarbanel S,&Gottlieb D.A mathematicalanalysis of the PML method[J].J.Comput.Phys.1997,134:357-363.
[6]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.
[7]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005:14~32.
[8]Collino F,Tsogka C.Application of thePML absorbing layer model to the linear e-lastodynamic problem in anisotropic hetero-geneous media[J].Geophysics,2001,9(1):294~307.
[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]李景叶,陈小宏.TI介质地震波场数值模拟边界条件处理[J].西安石油大学学报.2006,21(4):20-23.
[4]牟永光,裴正林著.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[5]Abarbanel S,&Gottlieb D.A mathematicalanalysis of the PML method[J].J.Comput.Phys.1997,134:357-363.
[6]董良国,马在田,曹景忠等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.
[7]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005:14~32.
[8]Collino F,Tsogka C.Application of thePML absorbing layer model to the linear e-lastodynamic problem in anisotropic hetero-geneous media[J].Geophysics,2001,9(1):294~307.
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