用于地震波场模拟的PML边界衰减因子研究(英文)
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摘要
在地震波场数值模拟中,为了消除由人为边界产生的边界反射,需要引进边界吸收条件。本文从声波方程完全匹配层吸收边界的经典方法出发,基于高斯函数任意阶光滑的特点,提出了一种高斯型衰减因子,分析比较该因子与一般衰减因子的性质,并基于均匀与层状速度模型分别进行了数值模拟计算。数值结果显示,当选择相同的PML边界吸收层层数时,高斯型衰减因子的吸收效果明显优于一般的衰减因子,边界反射更少,信噪比更高;对比最近提出的正弦型衰减因子,在信噪比接近的情况下,高斯型衰减因子所需的PML吸收层层数更少。
When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially truncated boundaries. In this paper, a damping factor referred to as the Gaussian damping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers (PMLs). This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models: a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio (SNR) than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR.
When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially truncated boundaries. In this paper, a damping factor referred to as the Gaussian damping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers (PMLs). This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models: a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio (SNR) than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR.
引文
Berenger,J.P.,1994,A perfectly matched layer forthe absorption of electromagnetics waves: JournalComputation Physics,114,185– 200.
Burns,D.R.,1992,Acoustic and elastic scattering fromseamounts in three dimensions-numerical modelingstudy: J.Acoust.Soc.Amer.,92,2784– 2791.
Cerjan,C.,Kosloff,D.,Kosloff,R.,and Reshef,M.,1985,A nonreflecting boundary condition for discrete acousticand elastic wave equations: Geophysics,50(4),705–708.
Clayton,R.,Engquist,B.,1977,Absorbing boundarycondition for acoustic and elastic wave equations: Bull.Sersm.Soc.Am.,67,1529– 1540.
Collino,F.,and Tsogka,C.,2001,Application of theperfectly matched absorbing layer model to the linearelasto-dynamic problem in anisotropic heterogeneous media: Geophysics,66(1),294– 307.
Du,Q.Z.,Sun,R.Y.,Qin,T.,Zhu,Y.T.,and Bi,L.F.,2010,A study of perfectly matched layers for jointmulticomponent reverse-time migration: AppliedGeophysics,7(2),166– 173.
Hastings,F.,Schneider,J.B.,and Broschat,S.L.,1996,Application of the perfectly matched absorbing layer(PML) absorbing boundary condition to elastic wavepropagation: Journal of Acoustic Society of America,100(5),3061– 3069.
Higdon,R.L.,1986,Absorbing boundary conditions fordifference approximations to the multidimensional waveequation: Math.Comp.,47,437– 459.
Higdon,R.L.,1987,Numerical absorbing boundaryconditions for the wave equation: Math.Comp.,49,65–90.
Higdon,R.L.,1991,Absorbing boundary condition forelastic waves: Geophysics,56(2),231– 241.
Komatitsch,D.,Tromp,J.,2003,A perfectly matchedlayer absorbing boundary condition for the second-order seismic wave equation: Geophysical JournalInternational,154(1),146– 150.
Liao,Z.P.,Wong,H.L.,Yang,B.P.,and Yuan,Y.F.,1984,A transmitting boundary for transient wave analysis:Scientia Sinica (Series A),27(10),1063– 1076.
Wang,T.,and Tang,X.M.,2003,Finite-differencemodeling of elastic wave propagation: a nonsplittingperfectly matched layer approach: Geophysics,68(5),1749– 1755.
Wang,Y.G.,Xing,W.J.,Xie,W.X.,and Zhu,Z.L.,2007,Study of absorbing boundary condition by perfectlymatched layer: Journal of China University of Petroleum(In Chinese),31(1),19– 24.
Burns,D.R.,1992,Acoustic and elastic scattering fromseamounts in three dimensions-numerical modelingstudy: J.Acoust.Soc.Amer.,92,2784– 2791.
Cerjan,C.,Kosloff,D.,Kosloff,R.,and Reshef,M.,1985,A nonreflecting boundary condition for discrete acousticand elastic wave equations: Geophysics,50(4),705–708.
Clayton,R.,Engquist,B.,1977,Absorbing boundarycondition for acoustic and elastic wave equations: Bull.Sersm.Soc.Am.,67,1529– 1540.
Collino,F.,and Tsogka,C.,2001,Application of theperfectly matched absorbing layer model to the linearelasto-dynamic problem in anisotropic heterogeneous media: Geophysics,66(1),294– 307.
Du,Q.Z.,Sun,R.Y.,Qin,T.,Zhu,Y.T.,and Bi,L.F.,2010,A study of perfectly matched layers for jointmulticomponent reverse-time migration: AppliedGeophysics,7(2),166– 173.
Hastings,F.,Schneider,J.B.,and Broschat,S.L.,1996,Application of the perfectly matched absorbing layer(PML) absorbing boundary condition to elastic wavepropagation: Journal of Acoustic Society of America,100(5),3061– 3069.
Higdon,R.L.,1986,Absorbing boundary conditions fordifference approximations to the multidimensional waveequation: Math.Comp.,47,437– 459.
Higdon,R.L.,1987,Numerical absorbing boundaryconditions for the wave equation: Math.Comp.,49,65–90.
Higdon,R.L.,1991,Absorbing boundary condition forelastic waves: Geophysics,56(2),231– 241.
Komatitsch,D.,Tromp,J.,2003,A perfectly matchedlayer absorbing boundary condition for the second-order seismic wave equation: Geophysical JournalInternational,154(1),146– 150.
Liao,Z.P.,Wong,H.L.,Yang,B.P.,and Yuan,Y.F.,1984,A transmitting boundary for transient wave analysis:Scientia Sinica (Series A),27(10),1063– 1076.
Wang,T.,and Tang,X.M.,2003,Finite-differencemodeling of elastic wave propagation: a nonsplittingperfectly matched layer approach: Geophysics,68(5),1749– 1755.
Wang,Y.G.,Xing,W.J.,Xie,W.X.,and Zhu,Z.L.,2007,Study of absorbing boundary condition by perfectlymatched layer: Journal of China University of Petroleum(In Chinese),31(1),19– 24.
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