VTI介质一阶准P波方程正演模拟及边界条件
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摘要
本文根据具有垂直对称轴的横向各向同性(VTI)介质中的一阶准P波方程,构造了该方程在交错网格中求解的高阶有限差分格式,给出了其稳定性条件;重点研究了适用于该方程的完全匹配层(PML)吸收边界条件,在此基础上实现了VTI介质中一阶准P波方程的正演模拟,得到了高精度的波场快照和合成记录,并采用叠前逆时深度偏移算法对复杂模型的合成记录进行偏移成像,得到了较好的成像效果。数值算例表明:准P波方程正演模拟能克服常规弹性波方程正演模拟的某些缺陷,便于研究各向异性介质中纵波的传播机理;叠前逆时深度偏移算法能够对复杂模型准确成像;通过对比分析各向同性与各向异性Marmousi模型的合成记录以及两种偏移算法的成像结果,显示各向异性参数对波场特征(旅行时和振幅)会产生明显影响,在地震资料处理、反演和解释中不可忽略。
Based on the first-order Quasi-P wave equation in VTI medium,the high-order finite difference scheme of the equation which was solved in the staggered grid was constructed in this paper,the stability condition of the equation was also given,the Perfectly Matched Layer(PML)absorbing boundary conditions which fit the equation were thoroughly studied in this paper,based on the studies above the forward modeling was realized for the first-order Quasi-P wave equation in VTI medium,high precision wavefield snapshot and synthetic record were obtained,the pre-stack reverse-time depth migration algorithm was used to conduct migration imaging for the complicated model,then good imaging results were achieved.The numerical experiments show that the Quasi-P wave equation forward modeling can overcome some of the defects of the conventional wave equation modeling,it also can facilitate the research on wave propagation mechanism in the anisotropic medium.The pre-stack reverse-time depth migration algorithm could accurately image the complex models;by comparing and analyzing the synthetic records and imaging results of the two migration algorithms for the isotropic and anisotropic Marmousi model,it can be indicated that the anisotropic parameters will have significant influence on the wave field characteristics(travel time and amplitude),which can not be ignored in the seismic data processing,inversion and interpretation.
Based on the first-order Quasi-P wave equation in VTI medium,the high-order finite difference scheme of the equation which was solved in the staggered grid was constructed in this paper,the stability condition of the equation was also given,the Perfectly Matched Layer(PML)absorbing boundary conditions which fit the equation were thoroughly studied in this paper,based on the studies above the forward modeling was realized for the first-order Quasi-P wave equation in VTI medium,high precision wavefield snapshot and synthetic record were obtained,the pre-stack reverse-time depth migration algorithm was used to conduct migration imaging for the complicated model,then good imaging results were achieved.The numerical experiments show that the Quasi-P wave equation forward modeling can overcome some of the defects of the conventional wave equation modeling,it also can facilitate the research on wave propagation mechanism in the anisotropic medium.The pre-stack reverse-time depth migration algorithm could accurately image the complex models;by comparing and analyzing the synthetic records and imaging results of the two migration algorithms for the isotropic and anisotropic Marmousi model,it can be indicated that the anisotropic parameters will have significant influence on the wave field characteristics(travel time and amplitude),which can not be ignored in the seismic data processing,inversion and interpretation.
引文
[1]Vafidis A,Abramovici F,Kanasewich E R.Elastic wave propagation using fully vectorized high order fi-nite-difference algorithms.Geophysics,1992,57(2):218～232
[2]Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method.Geo-physics,1986,51(4):889～901
[3]Levader A R.Fourth-order finite-difference P-SV seis-mograms.Geophysics,1988,53(11):1425～1436
[4]Hudson J A.Overall properties of a cracked solids.Math Proc Cambridge Philos Soc,1980,88(2):371～384
[5]Hudson J A.Wave speeds and attenuation of elastic waves in material containing cracks.Geophys J R As-tron Soc,1981,64(1):133～150
[6]Cheng C H.Crack models for a transversely aniso-tropic medium.J Geophys Res,1993,98:675～684
[7]Alkhalifah T.An acoustic wave equation for aniso-tropic media.Geophysics,2000,65(4):1239～1250
[8]Hesthol mS.Acoustic VTImodeling using high-order finite-differences.SEG Technical Program Expand-ed Abstracts,2007,26:139～143
[9]Berenger J P.A perfectly matched layer for the ab-sorption of electromagnetics waves.J Comput Phys,1994,114(2):185～200
[10]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954～1966
[11]何兵寿,张会星.VTI介质中准P波方程的数值解法.煤炭学报,2006,31(4):446～450
[12]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.地球物理学报,2000,43(3):411～419
[13]牟永光,裴正林著.三维复杂介质地震数值模拟.北京:石油工业出版社,2005
[14]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856～864
[15]Clayton R,Engquist B.Absorbing boundary condi-tions for acoustic and elastic wave equations.Bull Seismic Society America,1977,67(6):1529～1540
[16]Liao Z P,Wong H L.Atransmitting boundary for the numerical simulation of elastic wave propagation.Soil Dynamics and Earthquake Engineering,1984,3(4):174～183
[17]Hastings F D,Schneider J B,Broschat S L.Applica-tion of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation.Jour-nal Acoustical Society of America,1996,100(5):3061～3069
[18]王守东.声波方程完全匹配层吸收边界.石油地球物理勘探,2003,38(1):31～34
[19]裴正林.三维各向异性介质中弹性波方程交错网格高阶有限差分法数值模拟.石油大学学报(自然科学版),2004,28(5):23～29
[20]何兵寿.矢量波场叠前逆时深度偏移方法研究[博士论文].北京:石油大学(北京),2002
[21]Alkhalifah T.Ananisotropic Marmousimodel.SEP-95,1997,265～283
[22]Whitemore N D.Migration:Fundamental issues and future developments.Presented at Soc.Explor.Geophs.Research workshop4,52nd Ann.Internet.Mtg.,Dallas,1982
[23]Loewenthal D,Mulfti I R.Reverse time migrationin spatial frequency domain.Geophysics,1983,48(5):627～635
[24]Mc Mechan G A.Migration by extrapolation of time-dependent boundary values.Geophys.Prosp,1983,31(2):413～420
[25]何兵寿,张会星.多分量波场的矢量法叠前逆时深度偏移技术.石油地球物理勘探,2006,41(4):369～374
[26]何兵寿,张会星,韩令贺等.两种声波方程的叠前逆时深度偏移及比较.石油地球物理勘探,2008,43(6):656～661
[2]Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method.Geo-physics,1986,51(4):889～901
[3]Levader A R.Fourth-order finite-difference P-SV seis-mograms.Geophysics,1988,53(11):1425～1436
[4]Hudson J A.Overall properties of a cracked solids.Math Proc Cambridge Philos Soc,1980,88(2):371～384
[5]Hudson J A.Wave speeds and attenuation of elastic waves in material containing cracks.Geophys J R As-tron Soc,1981,64(1):133～150
[6]Cheng C H.Crack models for a transversely aniso-tropic medium.J Geophys Res,1993,98:675～684
[7]Alkhalifah T.An acoustic wave equation for aniso-tropic media.Geophysics,2000,65(4):1239～1250
[8]Hesthol mS.Acoustic VTImodeling using high-order finite-differences.SEG Technical Program Expand-ed Abstracts,2007,26:139～143
[9]Berenger J P.A perfectly matched layer for the ab-sorption of electromagnetics waves.J Comput Phys,1994,114(2):185～200
[10]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954～1966
[11]何兵寿,张会星.VTI介质中准P波方程的数值解法.煤炭学报,2006,31(4):446～450
[12]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.地球物理学报,2000,43(3):411～419
[13]牟永光,裴正林著.三维复杂介质地震数值模拟.北京:石油工业出版社,2005
[14]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究.地球物理学报,2000,43(6):856～864
[15]Clayton R,Engquist B.Absorbing boundary condi-tions for acoustic and elastic wave equations.Bull Seismic Society America,1977,67(6):1529～1540
[16]Liao Z P,Wong H L.Atransmitting boundary for the numerical simulation of elastic wave propagation.Soil Dynamics and Earthquake Engineering,1984,3(4):174～183
[17]Hastings F D,Schneider J B,Broschat S L.Applica-tion of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation.Jour-nal Acoustical Society of America,1996,100(5):3061～3069
[18]王守东.声波方程完全匹配层吸收边界.石油地球物理勘探,2003,38(1):31～34
[19]裴正林.三维各向异性介质中弹性波方程交错网格高阶有限差分法数值模拟.石油大学学报(自然科学版),2004,28(5):23～29
[20]何兵寿.矢量波场叠前逆时深度偏移方法研究[博士论文].北京:石油大学(北京),2002
[21]Alkhalifah T.Ananisotropic Marmousimodel.SEP-95,1997,265～283
[22]Whitemore N D.Migration:Fundamental issues and future developments.Presented at Soc.Explor.Geophs.Research workshop4,52nd Ann.Internet.Mtg.,Dallas,1982
[23]Loewenthal D,Mulfti I R.Reverse time migrationin spatial frequency domain.Geophysics,1983,48(5):627～635
[24]Mc Mechan G A.Migration by extrapolation of time-dependent boundary values.Geophys.Prosp,1983,31(2):413～420
[25]何兵寿,张会星.多分量波场的矢量法叠前逆时深度偏移技术.石油地球物理勘探,2006,41(4):369～374
[26]何兵寿,张会星,韩令贺等.两种声波方程的叠前逆时深度偏移及比较.石油地球物理勘探,2008,43(6):656～661
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