起伏地表条件下地震波场数值模拟有限积分变换有限差分方法
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摘要
针对起伏地表条件下的地震波数值模拟问题,提出将起伏的地表映射到一个规则的长方形网格坐标系中,并在此基础上推导出变换域中的波动方程。根据导出来的波动方程应用有限余弦变换有限差分方法进行地震波场的数值模拟,以解决起伏地表条件下的数值模拟。
To settle the quession of numerical simulation under the undulating surface,this paper raise a plan undulating surface mapping rules to a rectangular grid coordinate system and based on this,deducing the scalar wave equation in transform domain,According guided the equation we carried out the seismic wave field numerical simulation by using transform of limited cosine and method of finite difference,to complete the undulating surface under the conditions of numerical simulation.
To settle the quession of numerical simulation under the undulating surface,this paper raise a plan undulating surface mapping rules to a rectangular grid coordinate system and based on this,deducing the scalar wave equation in transform domain,According guided the equation we carried out the seismic wave field numerical simulation by using transform of limited cosine and method of finite difference,to complete the undulating surface under the conditions of numerical simulation.
引文
[1]王祥春,刘学伟,变换坐标系下相移法起伏地表地震波场延拓[J].地球物理学进展,2005(3):677-680.
[2]Hesthlom S,Ruud B.2D finite-difference elastic wavemodeling including surface topography[J].Geophysical Prospecting,1994,42:371-390.
[3]Hesthlom S,Ruud B.3-D finite-difference elasticwavemodeling inclding surface topography[J].Geophysics,1998,63(2),613-622.
[4]Tessmer E,Kosloff D.3-D elastic modeling with sur-face topography by a chebychev spectral method[J].Geophysics.1994,59(3),464-473.
[5]Hestholm S,Finite-difference seismic wave modelingincluding surface topography[J].PHD Thesis of RiceUniverity,1999,89(1):54-68.
[6]王雪秋,孙建国,张文志.复杂地表地质条件下地震波数值模拟综述[J].吉林大学学报(地球科学版),2005,35(增刊):12-18.
[7]史奈登I N.富利叶变换[M].北京:科学出版社,1958.
[8]МихайленкоБГ.Методрешениядинамическихзадачсейсмикидлядвумерно-неоднородныхмоделейсред[J].ДАНСССР,1979(1):254.
[9]孙建国.大尺度强变速地震波场数值模拟与偏移成像的有限积分变换方案[J].石油地球物理勘探,2005(2):76-82.
[10]王雪秋,利用有限积分变换—有限差分法模拟地震波场[D].长春:吉林大学,2002.
[11]Kosloff D,Reshef S,Loewenthal D.Elastic wavecalculations by the fourier method[J].Bull Seism SocAm,1984,74(3),875-891.
[12]Fornberg B.The pseudostral method:Accurate representation of interfaces in elastic wave calculations[J].Geophysics,1988,53(5):625-637.
[13]胡健伟,汤怀民.微分方程数值方法[M].北京:科学出版社,2001.
[2]Hesthlom S,Ruud B.2D finite-difference elastic wavemodeling including surface topography[J].Geophysical Prospecting,1994,42:371-390.
[3]Hesthlom S,Ruud B.3-D finite-difference elasticwavemodeling inclding surface topography[J].Geophysics,1998,63(2),613-622.
[4]Tessmer E,Kosloff D.3-D elastic modeling with sur-face topography by a chebychev spectral method[J].Geophysics.1994,59(3),464-473.
[5]Hestholm S,Finite-difference seismic wave modelingincluding surface topography[J].PHD Thesis of RiceUniverity,1999,89(1):54-68.
[6]王雪秋,孙建国,张文志.复杂地表地质条件下地震波数值模拟综述[J].吉林大学学报(地球科学版),2005,35(增刊):12-18.
[7]史奈登I N.富利叶变换[M].北京:科学出版社,1958.
[8]МихайленкоБГ.Методрешениядинамическихзадачсейсмикидлядвумерно-неоднородныхмоделейсред[J].ДАНСССР,1979(1):254.
[9]孙建国.大尺度强变速地震波场数值模拟与偏移成像的有限积分变换方案[J].石油地球物理勘探,2005(2):76-82.
[10]王雪秋,利用有限积分变换—有限差分法模拟地震波场[D].长春:吉林大学,2002.
[11]Kosloff D,Reshef S,Loewenthal D.Elastic wavecalculations by the fourier method[J].Bull Seism SocAm,1984,74(3),875-891.
[12]Fornberg B.The pseudostral method:Accurate representation of interfaces in elastic wave calculations[J].Geophysics,1988,53(5):625-637.
[13]胡健伟,汤怀民.微分方程数值方法[M].北京:科学出版社,2001.
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