一种层状介质条件下射线的全路径迭代追踪法
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摘要
从射线在整条路径上满足Fermat原理出发 ,采用一阶Taylor展开等办法 ,推出一个适用于任意层状地质结构下近似求解射线路径的对称正定三对角矩阵方程 ,通过求解该方程并结合迭代技术 ,从而实现对整条射线路径的全路径迭代计算。模型计算表明 ,本方法对于任意复杂结构和随机速度分布情况 ,其计算速度比传统的打靶法快 ,精度可根据需要预先确定 ,为复杂结构的地震偏移和层析成像提供了一种有效的射线追踪方法
It starts in this paper from the fact that the ray-path satisfies the Fermat's principal in the whole ray-path. By use of one order Taylor expansion,a well-posed symmetry tridiagonal matrix equation that fits to approximately calculate ray-path adjustment is obtained.Then,combining solving this matrix equation and iterative technique,a whole-path iterative ray-tracing method is fulfilled.The procedure of the ray tracing is ended when the adjustments on the whole ray-path satisfy the preset precision.Numerical tests indicate that this algorithm is faster than traditional shooting method in the arbitrary interface velocity distribution and the precision can be predetermined.It offers a new kind of efficient ray-tracing method for seismic migration and tomography in complex structure.
It starts in this paper from the fact that the ray-path satisfies the Fermat's principal in the whole ray-path. By use of one order Taylor expansion,a well-posed symmetry tridiagonal matrix equation that fits to approximately calculate ray-path adjustment is obtained.Then,combining solving this matrix equation and iterative technique,a whole-path iterative ray-tracing method is fulfilled.The procedure of the ray tracing is ended when the adjustments on the whole ray-path satisfy the preset precision.Numerical tests indicate that this algorithm is faster than traditional shooting method in the arbitrary interface velocity distribution and the precision can be predetermined.It offers a new kind of efficient ray-tracing method for seismic migration and tomography in complex structure.
引文
[1] 杨文采,李幼铭应用地震层析成像[M]北京:地质出版社,1993
[2] UmJ,ThurberCH .Afastalgorithmfortwo-pointseismicraytracing[J],Bull.Seis.Soc.Am.,1987,(77):927-986.
[3] CassellBR .Amethodforcalculatingsyntheticseismogramsinlaterallyvaryingmedia[J].Geophys.J.R .Astron.Soc.,1982,(69):339-354.
[4] ChanderR .Ontracingseismicrayswithspecifiedendpointsinlayersofconstantvelocityandplaneinterface[J],GeophysProsp.,1997,(25):120-124.
[5] FarraV .Bendingmethodrevisited:aHamilitonianapproach[J]Ge ophysJ.Int.,1992,(109):138-150.
[6] 高尔根,徐果明,赵炎炎一种任意截面的逐段迭代射线追踪方法[J]石油地球物理勘探,1998,33:54-60
[7] 高尔根,徐果明二维速度随机分布逐步迭代射线追踪方法[J]地球物理学报,1996,39(增刊):302-308
[8] LanganRT ,LercheI,CutlerRT .Tracingofraysthroughheteroge neousmedia:Anaccurateandefficientprocedure[J].Geophysics,1985,(50):1456-1465.
[9] 黄联捷,李幼铭,吴如山用于图像重建的波前法射线追踪[J]地球物理学报,1992,35:223-233
[10] 刘洪,孟凡林,李幼铭计算最小走时和射线路径的界面网全局方法[J]地球物理学报,1995,38:823-832
[11] VidaleJE .Finitedifferencecalculationoftraveltime[J].Bull.Seis.Soc.Am,1988,(78):2062-2076.
[12] VidaleJE .Finitedifferencecalculationoftraveltimesinthreedimen sion[J].Geophysics,1990,55:521-526.
[13] 刘家琦走时地震层析成像的方法技术[A]应用地震层析成像[M]北京:地质出版社,199336-69
[14] JulianBR ,GubbinsD .Three dimensionalseismicraytracing[J].J.Geophys,1997,(43):95-114.
[15] HanygaA .Numericalmethodsfortracingraysandwavefronts[M ].SeismologicalAlgorithm:ComputationalMethodsandBomputerPro grams.AcademicPress,London,1988.
[16] KellerHB ,PerozziDS .Fastseismicraytracing[J].Soc.IndAppl.Math.J .Appl.Math,1983,(43):981-992.
[17] PereyraV ,LeeWHK ,KellerHB .Solvingtwo pointseismictay tracingproblemsinaheterogeneousmedium[J].Bull.Seis.Soc.Am.,1980,(70):79-99.
[18] PodvinP ,LecomteI.Finitedifferencecomputationoftraveltimeinverycontrastedvelocitymodels:Amassivelyparallelapproachanditsassociatedtools[J].GeophysJ.Int,1991,(105):271-284.
[19] SambridgeMS ,KennettBLN .Boundaryvalueraytracinginhetero geneousmedium:asimpleandversatilealgorithm[J].GeophyJ.Int.,1990,(101):157-168.
[20] 徐果明,卫山,高尔根等二维复杂介质的块状建模及射线追踪[J]石油地球物理勘探,2001,36:213-219
[2] UmJ,ThurberCH .Afastalgorithmfortwo-pointseismicraytracing[J],Bull.Seis.Soc.Am.,1987,(77):927-986.
[3] CassellBR .Amethodforcalculatingsyntheticseismogramsinlaterallyvaryingmedia[J].Geophys.J.R .Astron.Soc.,1982,(69):339-354.
[4] ChanderR .Ontracingseismicrayswithspecifiedendpointsinlayersofconstantvelocityandplaneinterface[J],GeophysProsp.,1997,(25):120-124.
[5] FarraV .Bendingmethodrevisited:aHamilitonianapproach[J]Ge ophysJ.Int.,1992,(109):138-150.
[6] 高尔根,徐果明,赵炎炎一种任意截面的逐段迭代射线追踪方法[J]石油地球物理勘探,1998,33:54-60
[7] 高尔根,徐果明二维速度随机分布逐步迭代射线追踪方法[J]地球物理学报,1996,39(增刊):302-308
[8] LanganRT ,LercheI,CutlerRT .Tracingofraysthroughheteroge neousmedia:Anaccurateandefficientprocedure[J].Geophysics,1985,(50):1456-1465.
[9] 黄联捷,李幼铭,吴如山用于图像重建的波前法射线追踪[J]地球物理学报,1992,35:223-233
[10] 刘洪,孟凡林,李幼铭计算最小走时和射线路径的界面网全局方法[J]地球物理学报,1995,38:823-832
[11] VidaleJE .Finitedifferencecalculationoftraveltime[J].Bull.Seis.Soc.Am,1988,(78):2062-2076.
[12] VidaleJE .Finitedifferencecalculationoftraveltimesinthreedimen sion[J].Geophysics,1990,55:521-526.
[13] 刘家琦走时地震层析成像的方法技术[A]应用地震层析成像[M]北京:地质出版社,199336-69
[14] JulianBR ,GubbinsD .Three dimensionalseismicraytracing[J].J.Geophys,1997,(43):95-114.
[15] HanygaA .Numericalmethodsfortracingraysandwavefronts[M ].SeismologicalAlgorithm:ComputationalMethodsandBomputerPro grams.AcademicPress,London,1988.
[16] KellerHB ,PerozziDS .Fastseismicraytracing[J].Soc.IndAppl.Math.J .Appl.Math,1983,(43):981-992.
[17] PereyraV ,LeeWHK ,KellerHB .Solvingtwo pointseismictay tracingproblemsinaheterogeneousmedium[J].Bull.Seis.Soc.Am.,1980,(70):79-99.
[18] PodvinP ,LecomteI.Finitedifferencecomputationoftraveltimeinverycontrastedvelocitymodels:Amassivelyparallelapproachanditsassociatedtools[J].GeophysJ.Int,1991,(105):271-284.
[19] SambridgeMS ,KennettBLN .Boundaryvalueraytracinginhetero geneousmedium:asimpleandversatilealgorithm[J].GeophyJ.Int.,1990,(101):157-168.
[20] 徐果明,卫山,高尔根等二维复杂介质的块状建模及射线追踪[J]石油地球物理勘探,2001,36:213-219
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