变换坐标系下相移法起伏地表地震波场延拓
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摘要
为解决地表起伏变化对地震波场的影响问题,本文提出将(x-z)域的曲网格映射成(ζ-η)域的矩形网格,推导出(ζ-η)域中的标量声波方程,根据推导出来的波动方程采用双平方根法将地表采集到的地震波场在(ζ-η)域中向下延拓,以解决地表起伏带来的负面影响.通过对模型的计算,该方法取得了一定的效果.
In order to solve the effect of surface topography,this article presents the method of transforming the curved grids of(x-z)-coordinate system into rectangular grids of(ζ-η)-coordinate system.Then we derive the wave equation in the(ζ-η)-coordinate system.At last we continue the wave field downward using phase shift technique in the transformed coordinate system.Through calculating the model,we conclude that this method can achieve some good results.
In order to solve the effect of surface topography,this article presents the method of transforming the curved grids of(x-z)-coordinate system into rectangular grids of(ζ-η)-coordinate system.Then we derive the wave equation in the(ζ-η)-coordinate system.At last we continue the wave field downward using phase shift technique in the transformed coordinate system.Through calculating the model,we conclude that this method can achieve some good results.
引文
[1][美]J F.克莱鲍特.地震成象理论及方法[M].北京:石油工业出版社,1991.
[2]马在田.地震成象技术[M].北京:石油工业出版社,1989.
[3]赵景霞,张叔伦,孙沛勇.曲网格伪谱法二维声波模拟[J].石油物探,2003,42(1):1~5.
[4]李录明,罗省贤.波场延拓表层模型校正[J].石油地球物理勘探,2001,36(5):573~577.
[5]李志明,刘春玲.一种理想的二维波场深度延拓法[J].石油地球物理勘探,1990,25(5):519~528.
[6]Fornberg E.The pseudospetral method:Accurate representa-tion of interfaces in elastic wave calculation[J].Geophysics,1998,53(5):625~637.
[7]Reshef M.Depth migration from irregular surfaces with depthextrapolation methods[J].Geophysics,1991,56(1):119~112.
[8]Beasley C,Lynn W.The zero-velocity layer:Migration fromirregular surfaces[j].Geophysics,1992,57(11):1435~1443.
[9]徐士良,编著.FORTRAN常用算法程序集[M].北京:清华大学出版社,1995.
[10]程佩青.数字信号处理教程[M].北京:清华大学出版社,1995.
[11]钱荣钧.复杂地表区偏移基准面问题研究[J].石油地球物理勘探,1996,31(1):41~54.
[12]耿建华,等.波动方程有限差分法叠前深度偏移[J].地球物理学报,1998,41(3):393~399.
[13]艾印双,郑天愉.波场延拓深度滤波方法[J].地球物理学报,1998,41(3):400~407.
[14]程玖兵,王华忠,马在田.频率-空间域有限差分法叠前深度偏移[J].地球物理学报,2001,44(3):390~395.
[15]王建民,王丽娜,裴江云,陈湛文.波场延拓速度分析[J].地球物理学进展,2004,19(2):420~423.
[16]陈树文,刘洪.可用于复杂地质体的波动方程基准面技术[J].地球物理学进展,2002,17(3):365~369.
[17]陈必远,马在田.三维叠前偏移新技术[J].地球物理学报,1994,37(3):400~407.
[18]王振华.常速叠加-DMO-叠后偏移等效叠前偏移[J].地球物理学报,1994,37(6):795~803.
[19]刘超颖,王成祥.非稳态相移法叠前深度偏移[J].地球物理学进展,2004,19(3):543~546.
[20]崔兴福,张关泉,吴雅丽.三维非均匀介质中真振幅地震偏移算子研究[J].地球物理学报,2004,47(3):509~513.
[21]陈中州,常旭,王红落.天然地震转换波偏移成像方法[J].地球物理学进展,2004,19(1):148~153.
[22]刘喜武,刘洪.波动方程地震偏移成像方法的现状与进展[J].地球物理学进展,2002,17(4):582~591.
[23]刘礼农,周立宏,朱振宇,刘洪,李幼铭.复杂观测系统下的三维波动方程叠前深度偏移[J].地球物理学进展,2002,17(4):658~662.
[24]王玉学,张关泉,周瑞芬.非规则测区三维地震偏移的边界吸收层法[J].地球物理学报,2002,45(5):702~706.
[25]陈树文,刘洪,李幼铭.三维叠前深度偏移的准三维算法研究[J].地球物理学进展,2001,16(4):23~28.
[26]Flemming lf N,Berg P,Skovgaard O.Using the pseudospec-tral technique on curved grids for 2D acoustic forward model-ing[J].Geophysical Prospecting,1994,42:321~341.
[27]Tessmer E,Kosloff D,Behle A.Elastic wave propagationsimulation in the presence of surface topography[J].Geo-physics J Int,1992,108:621~632.
[28]Hestholm S,Ruud B.2D finite-difference elastic wave mod-eling including surface topograph[J].Geophysical Prospec-ting,1994,42:371~390.
[2]马在田.地震成象技术[M].北京:石油工业出版社,1989.
[3]赵景霞,张叔伦,孙沛勇.曲网格伪谱法二维声波模拟[J].石油物探,2003,42(1):1~5.
[4]李录明,罗省贤.波场延拓表层模型校正[J].石油地球物理勘探,2001,36(5):573~577.
[5]李志明,刘春玲.一种理想的二维波场深度延拓法[J].石油地球物理勘探,1990,25(5):519~528.
[6]Fornberg E.The pseudospetral method:Accurate representa-tion of interfaces in elastic wave calculation[J].Geophysics,1998,53(5):625~637.
[7]Reshef M.Depth migration from irregular surfaces with depthextrapolation methods[J].Geophysics,1991,56(1):119~112.
[8]Beasley C,Lynn W.The zero-velocity layer:Migration fromirregular surfaces[j].Geophysics,1992,57(11):1435~1443.
[9]徐士良,编著.FORTRAN常用算法程序集[M].北京:清华大学出版社,1995.
[10]程佩青.数字信号处理教程[M].北京:清华大学出版社,1995.
[11]钱荣钧.复杂地表区偏移基准面问题研究[J].石油地球物理勘探,1996,31(1):41~54.
[12]耿建华,等.波动方程有限差分法叠前深度偏移[J].地球物理学报,1998,41(3):393~399.
[13]艾印双,郑天愉.波场延拓深度滤波方法[J].地球物理学报,1998,41(3):400~407.
[14]程玖兵,王华忠,马在田.频率-空间域有限差分法叠前深度偏移[J].地球物理学报,2001,44(3):390~395.
[15]王建民,王丽娜,裴江云,陈湛文.波场延拓速度分析[J].地球物理学进展,2004,19(2):420~423.
[16]陈树文,刘洪.可用于复杂地质体的波动方程基准面技术[J].地球物理学进展,2002,17(3):365~369.
[17]陈必远,马在田.三维叠前偏移新技术[J].地球物理学报,1994,37(3):400~407.
[18]王振华.常速叠加-DMO-叠后偏移等效叠前偏移[J].地球物理学报,1994,37(6):795~803.
[19]刘超颖,王成祥.非稳态相移法叠前深度偏移[J].地球物理学进展,2004,19(3):543~546.
[20]崔兴福,张关泉,吴雅丽.三维非均匀介质中真振幅地震偏移算子研究[J].地球物理学报,2004,47(3):509~513.
[21]陈中州,常旭,王红落.天然地震转换波偏移成像方法[J].地球物理学进展,2004,19(1):148~153.
[22]刘喜武,刘洪.波动方程地震偏移成像方法的现状与进展[J].地球物理学进展,2002,17(4):582~591.
[23]刘礼农,周立宏,朱振宇,刘洪,李幼铭.复杂观测系统下的三维波动方程叠前深度偏移[J].地球物理学进展,2002,17(4):658~662.
[24]王玉学,张关泉,周瑞芬.非规则测区三维地震偏移的边界吸收层法[J].地球物理学报,2002,45(5):702~706.
[25]陈树文,刘洪,李幼铭.三维叠前深度偏移的准三维算法研究[J].地球物理学进展,2001,16(4):23~28.
[26]Flemming lf N,Berg P,Skovgaard O.Using the pseudospec-tral technique on curved grids for 2D acoustic forward model-ing[J].Geophysical Prospecting,1994,42:321~341.
[27]Tessmer E,Kosloff D,Behle A.Elastic wave propagationsimulation in the presence of surface topography[J].Geo-physics J Int,1992,108:621~632.
[28]Hestholm S,Ruud B.2D finite-difference elastic wave mod-eling including surface topograph[J].Geophysical Prospec-ting,1994,42:371~390.
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