基于双线性插值的三维地震波旅行时计算
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摘要
针对地震波射线追踪方法中有效计算地震波旅行时及提高计算精度的问题,为克服传统射线追踪算法(即初值问题的试射法和边值问题的弯曲法)的不足,对三维介质模型下的地震波旅行时进行了研究。在线性插值计算二维地震波旅行时射线追踪方法(LTI)的基础上,探索出了一种基于双线性插值计算三维地震波旅行时的方法原理,并推导了相应的计算公式。通过数值模拟计算、与解析解的对比,不仅证明了该方法原理的正确性,而且还证明了该方法原理具有较高的计算精度。
The computation of seismic traveltime is important content of ray tracing method,how to calculate the seismic traveltime effectively and increase the computation accuracy are widely concerned.In order to overcome the shortcomings of the traditional ray tracing algorithm(Shooting method of initial value and Bending method of boundary value),A variety of new methods and new technologies have been improved in the past 10 years.With the development of seismic exploration technology,it is necessary to study the computation of seismic traveltime and the methods of ray tracing in three-dimensional medium model.Based on the linear traveltime interpolation (LTI) method to calculate two-dimensional seismic traveltime,in this article,a method to calculate the three-dimensional seismic traveltime is proposed by using bilinear interpolation,and its calculation formula deduced.Through numerical simulation calculation and the contrast with the analytic solution,the correctness of the principle of the method is proved,but also the method proved with a higher computation accuracy.
The computation of seismic traveltime is important content of ray tracing method,how to calculate the seismic traveltime effectively and increase the computation accuracy are widely concerned.In order to overcome the shortcomings of the traditional ray tracing algorithm(Shooting method of initial value and Bending method of boundary value),A variety of new methods and new technologies have been improved in the past 10 years.With the development of seismic exploration technology,it is necessary to study the computation of seismic traveltime and the methods of ray tracing in three-dimensional medium model.Based on the linear traveltime interpolation (LTI) method to calculate two-dimensional seismic traveltime,in this article,a method to calculate the three-dimensional seismic traveltime is proposed by using bilinear interpolation,and its calculation formula deduced.Through numerical simulation calculation and the contrast with the analytic solution,the correctness of the principle of the method is proved,but also the method proved with a higher computation accuracy.
引文
[1]佘德平.波场数值模拟技术[J].勘探地球物理进展,2004,27(1):16-21.
[2]张永刚.地震波场数值模拟方法[J].石油物探,2003,42(2):143-148.
[3]王华忠,方正茂,徐兆涛,等.地震波旅行时计算[J].石油地球物理勘探,1999,34(2):155-163.
[4]张钋,刘洪,李幼铭.射线追踪方法的发展现状[J].地球物理学进展,2000,15(1):36-44.
[5]邵卫红.射线追踪法的现状和展望[J].土工基础,2007,21(4):74-76.
[6]赵改善,郝守玲,杨尔皓,等.基于旅行时线性插值的地震射线追踪算法[J].石油物探,1998,37(2):14-24.
[7]赵成斌,许云,乌达巴拉.地震波走时和射线的有限差分计算[J].华北地震科学,1995,13(4):41-46.
[8]刘清林.地震初至波射线路径的追踪[J].石油物探,1993,32(2):14-20.
[9]涂齐催,刘怀山.利用线性旅行时插值射线追踪计算近地表模型初至波走时[J].物探与化探,2006,30(2):148-153.
[10]张赛民,周竹生,陈灵君,等.对旅行时进行抛物型插值的地震射线追踪方法[J].地球物理学进展,2007,22(1):43-48.
[11]Reshef M,Kosloff D.Migration of common shot gathers[J].Geophysics,1986,52(2):324-331.
[12]Vidale J E.Finite-difference calculation of traveltimes[J].Bull.Seic.Soc.Am.,1988,78(6):2062-2076.
[13]Vidale J E.Finite-difference calculation of traveltimes inthree dimensions[J].Geophysics,1990,55(5):521-526.
[14]刘清林.求解三维程函方程的波前扩展法[J].石油物探,1992,31(4):36-43.
[15]Asawaka E,Kawanaka T.Seismic ray tracing using lineartraveltime interpolation[J].Geophysics,1993,57(2):326-333.
[17]赵谊,高尔根,赵振东,等.三维场地波动传播的快速射线追踪法[J].地震工程与工程振动,2001,21(2):24-29.
[18]赵爱华,张中杰.三维复杂介质中转换波走时快速计算[J].地球物理学报,2004,47(4):702-707.
[19]梁春涛,朱介寿,曹家敏,等.球坐标系下三维射线追踪的方法和应用[J].物探化探计算技术,2001,23(3):199-205.
[2]张永刚.地震波场数值模拟方法[J].石油物探,2003,42(2):143-148.
[3]王华忠,方正茂,徐兆涛,等.地震波旅行时计算[J].石油地球物理勘探,1999,34(2):155-163.
[4]张钋,刘洪,李幼铭.射线追踪方法的发展现状[J].地球物理学进展,2000,15(1):36-44.
[5]邵卫红.射线追踪法的现状和展望[J].土工基础,2007,21(4):74-76.
[6]赵改善,郝守玲,杨尔皓,等.基于旅行时线性插值的地震射线追踪算法[J].石油物探,1998,37(2):14-24.
[7]赵成斌,许云,乌达巴拉.地震波走时和射线的有限差分计算[J].华北地震科学,1995,13(4):41-46.
[8]刘清林.地震初至波射线路径的追踪[J].石油物探,1993,32(2):14-20.
[9]涂齐催,刘怀山.利用线性旅行时插值射线追踪计算近地表模型初至波走时[J].物探与化探,2006,30(2):148-153.
[10]张赛民,周竹生,陈灵君,等.对旅行时进行抛物型插值的地震射线追踪方法[J].地球物理学进展,2007,22(1):43-48.
[11]Reshef M,Kosloff D.Migration of common shot gathers[J].Geophysics,1986,52(2):324-331.
[12]Vidale J E.Finite-difference calculation of traveltimes[J].Bull.Seic.Soc.Am.,1988,78(6):2062-2076.
[13]Vidale J E.Finite-difference calculation of traveltimes inthree dimensions[J].Geophysics,1990,55(5):521-526.
[14]刘清林.求解三维程函方程的波前扩展法[J].石油物探,1992,31(4):36-43.
[15]Asawaka E,Kawanaka T.Seismic ray tracing using lineartraveltime interpolation[J].Geophysics,1993,57(2):326-333.
[17]赵谊,高尔根,赵振东,等.三维场地波动传播的快速射线追踪法[J].地震工程与工程振动,2001,21(2):24-29.
[18]赵爱华,张中杰.三维复杂介质中转换波走时快速计算[J].地球物理学报,2004,47(4):702-707.
[19]梁春涛,朱介寿,曹家敏,等.球坐标系下三维射线追踪的方法和应用[J].物探化探计算技术,2001,23(3):199-205.
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