起伏地表有限元叠前逆时偏移完全匹配层
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摘要
在地震波传播的数值模拟中,用有限区域代替求解无限区域地震波传播规律是一种有效手段。目前完全匹配层吸收边界条件是边界吸收最好的选择。通常正演模拟不考虑自由表面吸收条件,但在逆时偏移中,地表反射的存在会引起假的同相轴。推导了位移形式的有限元二阶声波方程的完全匹配层吸收边界条件公式,并应用于起伏地表声波方程有限元数值模拟与逆时偏移成像;通过数值分析并与传统的Clayton-Engquist吸收边界条件做了比较。计算结果表明,方法取得了理想的边界吸收效果,可以消除起伏地表反射引起的假同相轴。
Boundary reflection is an important problem of numerical simulation in limited domain.Perfectly matched layer(PML) absorbing boundary condition(ABC) is one of the best choices to eliminate boundary reflection.Generally,forward modeling needn’t consider PML ABC in free surface,but in prestack reverse time migration,false events will be existed due to the free surface reflection.The goal is to derive the PML ABC formulas of second-order finite element acoustic wave equation based on rugged topography in displacement form and apply it in finite element numerical simulation in rugged topography.Several numerical modeling results are compared.The numerical results show that PML ABC based on rugged topography obtains a much better boundary absorption effect than that of CE ABC,which shows the advantages of this method.So it will eliminate the fault events result from the free surface reflection in prestack reverse time migration based on rugged topography.
Boundary reflection is an important problem of numerical simulation in limited domain.Perfectly matched layer(PML) absorbing boundary condition(ABC) is one of the best choices to eliminate boundary reflection.Generally,forward modeling needn’t consider PML ABC in free surface,but in prestack reverse time migration,false events will be existed due to the free surface reflection.The goal is to derive the PML ABC formulas of second-order finite element acoustic wave equation based on rugged topography in displacement form and apply it in finite element numerical simulation in rugged topography.Several numerical modeling results are compared.The numerical results show that PML ABC based on rugged topography obtains a much better boundary absorption effect than that of CE ABC,which shows the advantages of this method.So it will eliminate the fault events result from the free surface reflection in prestack reverse time migration based on rugged topography.
引文
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2 Chang W F,McMechan G A.Reverse-time migration of offsetvertical seismic pro?ling data using the excitation-time imaging condition.Geophysics,1986;51(1):67—84
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5 Kaelin B,Guitton A.Imaging condition for reverse time migration.76th Annual International Meeting and Exposition,SEG Expanded Abstracts,New Orleans,2006:2594—2598
6 Sava P,Fomel S.Time-shift imaging condition in seismic migration.Geophysics,2006;71(6):209—217
7 Schleicher,J.,J.Costa,and A.Novais.A comparison of imaging conditions for wave-equation shot-pro?le migration.Geophysics,2008;73(6):219—227
8 Baysal E,Kosloff E D,Sherwood J W C.Reverse time migration.Geophysics,1983;48(11):1514—1524
9 Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Seismological Society of America,1977;66(11):1529—1540
10 Cerjan C,Kosloff D,Kosloff R,et al.A nonre?ecting boundary condition for discrete acoustic and elastic wave equation.Geophys-ics,1985;50(4):705—708
11 Sochacki J,Kubichek R,George,J,et al.Absorbing boundary conditions and surface waves.Geophysics,1987;52(1):60—71
12 Peng C B,Toksoz M N.An optimal absorbing boundary condition for elastic wave modeling.Geophysics,1995;60(1):296—301
13 Grote M J.Nonreflecting boundary conditions for elastodynamics scattering.Journal of Computational Physics,2000;161(1):331—353
14 Berenger J P.Three-dimensional perfectly matched layer for the ab-sorption of electromagnetic waves.Journal of Computational Physics,1996;127:363—379
15 Liu Yang,Sen M K.A hybrid absorbing boundary condition for e-lastic wave modeling with staggered-grid finite difference.SEG An-nual Meeting,Denver,2010;2945—2949
16薛东川,王尚旭,焦淑静.起伏地表复杂介质波动方程有限元数值模拟方法.地球物理学进展,2007;22(2):522—529
17薛东川,王尚旭.波动方程有限元叠前逆时偏移.石油地球物理勘探,2008;43(1):17—21
18王永刚,邢文军,谢万学,等.完全匹配层吸收边界条件的研究.中国石油大学学报,2007;31(1):19—24
19 Chew W C,Liu Q.Perfectly matched layers for the electrodynam-ics:a new absorbing boundary condition.J Comp Acoust,1996;4:341—359
2 Chang W F,McMechan G A.Reverse-time migration of offsetvertical seismic pro?ling data using the excitation-time imaging condition.Geophysics,1986;51(1):67—84
3 Guitton A,Valenciano V,Bevc D,Robust imaging condition for shot-pro?le migration:74thAnnual International Meeting and Expo-sition,SEG,Expanded Abstracts,2006:2519—2523
4 Guitton A,Valenciano A,Bevc D,et al.Smoothing image condition for shot-pro?le migration.Geophysics,2007;72(3):149—154
5 Kaelin B,Guitton A.Imaging condition for reverse time migration.76th Annual International Meeting and Exposition,SEG Expanded Abstracts,New Orleans,2006:2594—2598
6 Sava P,Fomel S.Time-shift imaging condition in seismic migration.Geophysics,2006;71(6):209—217
7 Schleicher,J.,J.Costa,and A.Novais.A comparison of imaging conditions for wave-equation shot-pro?le migration.Geophysics,2008;73(6):219—227
8 Baysal E,Kosloff E D,Sherwood J W C.Reverse time migration.Geophysics,1983;48(11):1514—1524
9 Clayton R,Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Seismological Society of America,1977;66(11):1529—1540
10 Cerjan C,Kosloff D,Kosloff R,et al.A nonre?ecting boundary condition for discrete acoustic and elastic wave equation.Geophys-ics,1985;50(4):705—708
11 Sochacki J,Kubichek R,George,J,et al.Absorbing boundary conditions and surface waves.Geophysics,1987;52(1):60—71
12 Peng C B,Toksoz M N.An optimal absorbing boundary condition for elastic wave modeling.Geophysics,1995;60(1):296—301
13 Grote M J.Nonreflecting boundary conditions for elastodynamics scattering.Journal of Computational Physics,2000;161(1):331—353
14 Berenger J P.Three-dimensional perfectly matched layer for the ab-sorption of electromagnetic waves.Journal of Computational Physics,1996;127:363—379
15 Liu Yang,Sen M K.A hybrid absorbing boundary condition for e-lastic wave modeling with staggered-grid finite difference.SEG An-nual Meeting,Denver,2010;2945—2949
16薛东川,王尚旭,焦淑静.起伏地表复杂介质波动方程有限元数值模拟方法.地球物理学进展,2007;22(2):522—529
17薛东川,王尚旭.波动方程有限元叠前逆时偏移.石油地球物理勘探,2008;43(1):17—21
18王永刚,邢文军,谢万学,等.完全匹配层吸收边界条件的研究.中国石油大学学报,2007;31(1):19—24
19 Chew W C,Liu Q.Perfectly matched layers for the electrodynam-ics:a new absorbing boundary condition.J Comp Acoust,1996;4:341—359
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