τ-p变换在隧道反射地震超前预报波场分离中应用的数值模拟研究
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摘要
本文基于二维有限元数值方法,模拟了复杂条件下隧道内的地震全波波场,分析了隧道地震超前预报中的反射记录中的多方向和多波反射波特征,证实了分离前方有效反射波和其它方向的干扰反射波,以及有效反射波的P波、S波分离在预报准确性中的重要性.基于多个数值模型,研究了τ-p变换进行波场分离的有效性和影响因素.研究结果表明:在隧道前方反射层倾向与隧道轴线交角变化较大范围内(90°～45°),τ-p变换都可以有效的分离多方向和多波反射事件,提取主要来自掌子面前方的有效反射波剖面.来自隧道顶、底的缓倾界面的具有双曲时距曲线特征的干扰波和S波的高视速度会对P波的波场分离产生较大干扰;而由于S波的低速和强能量特征,其波场分离受具有双曲时距曲线特征的干扰波的视速度影响较小,且不受P波的影响.
This article presents the simulation of tunnel seismic wave field under complex conditions by using the finite element method.The importance of the separation of interested reflected seismic wave ahead of tunnel face from other directions and that of interested P-wave and S-wave are showed based on the characteristic analysis of the multi-directions and multi-components of the reflection records.in tunnel seismic records,Based on several numerical models,the flexibility of the τ-p transformation for the wave field separation are studied and the results show that τ-p transformation is effective in the separation of the multi-directions and multi-components of the reflection records from the wave ahead of tunnel face,even if the dips of reflector ahead of tunnel are varying widely(90°~45°).Because of the high apparent velocity effects due to the interference waves with hyperbola time-distance relationship and S-wave,the separation of interested S-wave is usually clearly,whereas that of P-wave has more interference waves.Therefore,in the subsequent processing,it should be separated as the main basis for S-wave profile.For the angle of reflection layer <45°,due to its time-distance relationship is not linear relationship,the difference between the designed filter of apparent velocity which based on the linear relationship of the direct wave and actual relationship is too large for pressure or shear waves,therefore errors of separation are large,so adopted migration processing before the τ-p transformation for the flat dipping fault.
This article presents the simulation of tunnel seismic wave field under complex conditions by using the finite element method.The importance of the separation of interested reflected seismic wave ahead of tunnel face from other directions and that of interested P-wave and S-wave are showed based on the characteristic analysis of the multi-directions and multi-components of the reflection records.in tunnel seismic records,Based on several numerical models,the flexibility of the τ-p transformation for the wave field separation are studied and the results show that τ-p transformation is effective in the separation of the multi-directions and multi-components of the reflection records from the wave ahead of tunnel face,even if the dips of reflector ahead of tunnel are varying widely(90°~45°).Because of the high apparent velocity effects due to the interference waves with hyperbola time-distance relationship and S-wave,the separation of interested S-wave is usually clearly,whereas that of P-wave has more interference waves.Therefore,in the subsequent processing,it should be separated as the main basis for S-wave profile.For the angle of reflection layer <45°,due to its time-distance relationship is not linear relationship,the difference between the designed filter of apparent velocity which based on the linear relationship of the direct wave and actual relationship is too large for pressure or shear waves,therefore errors of separation are large,so adopted migration processing before the τ-p transformation for the flat dipping fault.
引文
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[19]李彦鹏马在田.坐标拉伸后的线性拉冬变换法波场分离[J].石油地球物理勘探,1998,33(5):611-624.Li Yanpeng,Ma Zaitian.Wave field separation by linearRadon transform after coordinate stretch[J].Oil GeophysicalProspecting,1998,33(5):611-624.
[20]牛滨华孙春岩张中杰沈操李英才吕景贵王宏语.多项式Radon变换[J].地球物理学报,2001,44(2):263-271.Niu Binhua,Sun Chunyan.et.al.Polynomial radon transform[J].Chinese J.Geophys.(in Chinese):2001,44(2):263-271.
[21]刘喜武刘洪李幼铭.高分辨率Radon变换方法及其在地震信号处理中的应用[J].地球物理学进展,2004,19(1):8-15.Liu Xiwu,Liu Hong,Li Youming.High resolution radontransform and its application in seismic signal processing[J].Progress in Geophysics,2004,19(1):8-15.
[22]王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建[J].地球物理学报,2007,50(3):851-859.Wang Weihong,Pei Jiangyun,Zhang Jianfeng.Prestackseismic data reconstruction using weighted parabolic Radontransform[J].Chinese J.Geophys.(in Chinese),2007,50(3):851-859.
[23]熊登,赵伟,张剑锋.混合域高分辨率抛物Radon变换及在衰减多次波中的应用[J].地球物理学报,2009,52(4):1068-1077.Xiong Deng,Zhao Wei,Zhang Jianfeng.Hybrid-domain highresolution parabolic Radon transform and its application todemultiple[J].Chinese J.Geophys.(in Chinese),2009,52(4):1068-1077.
[24]冯晅,张先武,刘财,王典,杨庆节.带有多道相关的抛物线Radon变换法分离P—P,P—SV波[J].地球物理学报,2011,54(2):304-309.Feng Xuan,Zhang Xianwu,Liu Cai,et al.Separating P-P andP-SV wave by parabolic Radon transform with multiplecoherence[J].Chinese J.Geophys.(in Chinese),2011,54(2):304-309.
[25]黄新武吴律牛滨华李丽吴亚东.抛物线Radon变换中的参数采样与假频[J].石油大学学报(自然科学版),2003,27(2):27-31.Huang Xinwu,Wu Lu,et al.Sampling and aliasing ofparameters in parabolic radon transform[J].Journal of theUniversity of Petroleum,China(Edition of Natural Science),2003,27(2):27-31.
[26]朱生旺,魏修成,李锋.用抛物线Radon变换稀疏解分离和压制多次波[J].石油地球物理勘探,2002,37(2):110-115.Zhu Shengwang,Wei Xiucheng,et al.Separating andsuppressing multiples by sparse solution of parabolic Radontransform[J].Oil Geophysical Prospecting,2002,37(2):110-115.
[27]李远钦,刘雯林.n维广义Radon变换[J].地球物理学进展,1997,12(4):59-66.Li Yuanqin,Liu Wenlin.General N-D Random Transform[J].Progress in Geophysics,1997,12(4):59-66.
[28]Kappus M.E.,Harding A.J.,Orcutt J.A.A comparison oftau-p transform methods[J].Geophysics,1990,55(9):1202-1215.
[29]张保卫.Radon变换及其在地震数据处理中的应用[D].西安:长安大学,硕士论文,2007.Zhang Baowei.Radon Transform and its application inseismic data processing[D].Xi’an:Changan University,Master,2007.
[30]王维红,首皓,刘洪,等.线性同相轴波场分离的高分辨率τ-p变换法[J].地球物理学进展,2006,21(1):74-78.Wang Weihong,Shou Hao,Liu Hong,et al.High resolutionτ-p transform in linear events wavefield separation.Progressin Geophysics,2006,21(1):74-78.
[31]Sacchi Mauricio D.,Porsani Milton.Fast high resolutionparabolic Radon transform[J].SEG Technical ProgramExpanded Abstracts,1999,18(1):1477-1480.
[2]Helgason S.The radon transform[M].Birkhauser,1999,1-169.
[3]Doherty S.M.,Claerbout J.F.Structure independent velocityestimation[J].Geophysics,1976,41(5):850-881.
[4]Phinney R.A.Inversion for sediment structure using multichanneldata[J].The Journal of the Acoustical Society of America,1982,72(1):96.
[5]Durrani TS,Bisset D.The Radon transform and its properties[J].Geophysics,1984,49(8):1180-1187.
[6]Tatham R.H.,Goolsbee D.V.Separation of S-wave and P-wave reflections offshore western Florida[J].Geophysics,1984,49(5):493-508.
[7]Chapman CH.Generalized Radon transforms and slant stacks[J].Geophysical Journal of the Royal Astronomical Society,1981,66(2):445-453.
[8]Thorson J.R.,Claerbout J.F.Velocity-stack and slant-stackstochastic inversion[J].Geophysics,1985,50(12):2727-2741.
[9]Hampson D.Inverse velocity stacking for multiple elimination[J].Geophysics,1986,22(1):44-55.
[10]Beylkin Gregory,Burridge Robert.Multiparameter inversionfor acoustic and elastic media[J].Geophysics,1987,6(1):747-749.
[11]Kostov C.Toeplitz structure in slant-stack inversion[J].SEGTechnical Program Expanded Abstracts 2005,1618(9):1618-1621.
[12]Foster D.J.,Mosher C.C.Suppression of multiple reflectionsusing the Radon transform[J].Geophysics,1992,57(3):386-395.
[13]Zhou B.Z,Greenhalgh S.A.Linear and parabolic tau-ptransforms revisited[J].Geophysics,1994,59(7):1133-1149.
[14]吴律.论Radon变换在地球物理勘探中应用的可能性[J].石油地球物理勘探,1985,20(3):235-241.Wu Lu,On the possibility of using Radon transform ingeophysical prospecting[J].Oil Geophysical Prospecting,1985,20(3):235-241.
[15]李世雄.Radon变换的抽样取值与小波[J].地球物理学报,1993,36(2):233-241.Li Shixiong.Sampling of Radon transform and wavelet[J].Chinese J.Geophys.(in Chinese),1993,36(2):233-241.
[16]沈源杨文采.广义Radon变换与叠前地震数据处理[J].地球物理学报,1992,35(3):369-379.Shen Yuan,Yang Wencai.Generalized Radon transform andforestack data processing[J].Chinese J.Geophys.(inChinese),1992,35(3):369-379.
[17]李世雄,叶雅梅,李嘉禹.数据严重缺少的Radon变换的反演[J].地球物理学报,1995,38(3):367-377.Li Shixiong,Ye Yamei,Li Jiayu.Inversion of Radon transformwith extremely incomplete data[J].Chinese J.Geophys.(inChinese),1995,38(3):367-377.
[18]李世雄,林其彭,李嘉禹.分区连续函数的Radon变换的高精度反演法[J].地球物理学报,1996,39(2):251-264.Li Shixiong,Lin Qipeng,Li Jiayu.High precisionreconstruction methods for Radon transform of piecewisesmooth functions[J].Chinese J.Geophys.(in Chinese),1996,39(2):251-264.
[19]李彦鹏马在田.坐标拉伸后的线性拉冬变换法波场分离[J].石油地球物理勘探,1998,33(5):611-624.Li Yanpeng,Ma Zaitian.Wave field separation by linearRadon transform after coordinate stretch[J].Oil GeophysicalProspecting,1998,33(5):611-624.
[20]牛滨华孙春岩张中杰沈操李英才吕景贵王宏语.多项式Radon变换[J].地球物理学报,2001,44(2):263-271.Niu Binhua,Sun Chunyan.et.al.Polynomial radon transform[J].Chinese J.Geophys.(in Chinese):2001,44(2):263-271.
[21]刘喜武刘洪李幼铭.高分辨率Radon变换方法及其在地震信号处理中的应用[J].地球物理学进展,2004,19(1):8-15.Liu Xiwu,Liu Hong,Li Youming.High resolution radontransform and its application in seismic signal processing[J].Progress in Geophysics,2004,19(1):8-15.
[22]王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建[J].地球物理学报,2007,50(3):851-859.Wang Weihong,Pei Jiangyun,Zhang Jianfeng.Prestackseismic data reconstruction using weighted parabolic Radontransform[J].Chinese J.Geophys.(in Chinese),2007,50(3):851-859.
[23]熊登,赵伟,张剑锋.混合域高分辨率抛物Radon变换及在衰减多次波中的应用[J].地球物理学报,2009,52(4):1068-1077.Xiong Deng,Zhao Wei,Zhang Jianfeng.Hybrid-domain highresolution parabolic Radon transform and its application todemultiple[J].Chinese J.Geophys.(in Chinese),2009,52(4):1068-1077.
[24]冯晅,张先武,刘财,王典,杨庆节.带有多道相关的抛物线Radon变换法分离P—P,P—SV波[J].地球物理学报,2011,54(2):304-309.Feng Xuan,Zhang Xianwu,Liu Cai,et al.Separating P-P andP-SV wave by parabolic Radon transform with multiplecoherence[J].Chinese J.Geophys.(in Chinese),2011,54(2):304-309.
[25]黄新武吴律牛滨华李丽吴亚东.抛物线Radon变换中的参数采样与假频[J].石油大学学报(自然科学版),2003,27(2):27-31.Huang Xinwu,Wu Lu,et al.Sampling and aliasing ofparameters in parabolic radon transform[J].Journal of theUniversity of Petroleum,China(Edition of Natural Science),2003,27(2):27-31.
[26]朱生旺,魏修成,李锋.用抛物线Radon变换稀疏解分离和压制多次波[J].石油地球物理勘探,2002,37(2):110-115.Zhu Shengwang,Wei Xiucheng,et al.Separating andsuppressing multiples by sparse solution of parabolic Radontransform[J].Oil Geophysical Prospecting,2002,37(2):110-115.
[27]李远钦,刘雯林.n维广义Radon变换[J].地球物理学进展,1997,12(4):59-66.Li Yuanqin,Liu Wenlin.General N-D Random Transform[J].Progress in Geophysics,1997,12(4):59-66.
[28]Kappus M.E.,Harding A.J.,Orcutt J.A.A comparison oftau-p transform methods[J].Geophysics,1990,55(9):1202-1215.
[29]张保卫.Radon变换及其在地震数据处理中的应用[D].西安:长安大学,硕士论文,2007.Zhang Baowei.Radon Transform and its application inseismic data processing[D].Xi’an:Changan University,Master,2007.
[30]王维红,首皓,刘洪,等.线性同相轴波场分离的高分辨率τ-p变换法[J].地球物理学进展,2006,21(1):74-78.Wang Weihong,Shou Hao,Liu Hong,et al.High resolutionτ-p transform in linear events wavefield separation.Progressin Geophysics,2006,21(1):74-78.
[31]Sacchi Mauricio D.,Porsani Milton.Fast high resolutionparabolic Radon transform[J].SEG Technical ProgramExpanded Abstracts,1999,18(1):1477-1480.
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