探地雷达各向异性介质有限差分偏移线性变换
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摘要
将地震偏移技术中的线性变换差分偏移应用于探地雷达的数据偏移,在讨论各向同性介质线性变换差分偏移算法的基础上,研究各向异性介质偏移归位情况来解决该算法对速度的高敏感性问题,编写探地雷达线性变换差分偏移算法的Matlat程序;通过对线性变换差分方程推导,得到一系列三对角线性方程组;在求解这些特殊方程组过程中,通过调用Matlat程序中定义的Pursue函数来循环求解这一系列大型的三对角线性方程组,并将计算结果进行储存供后续迭代使用,最后将满足终止条件的偏移成像矩阵输出并可视化,运用该算法分别对各向异性的正演雷达数据和实测雷达数据进行处理。研究结果表明:该算法在对各向异性介质中存在多次反射质点和主要反射层的地质问题进行偏移归位时具有明显优势。
The linear transformation of finite difference migration method in reflection seismology was applied to improve the GPR(ground penetrating radar) migration technology.Based on the fact that the migration effect is highly sensitive to the medium velocity in isotropic condition,the anisotropic case was extended when the theory of the traditional finite difference migration was established.In order to solve the velocity restrictions of the traditional algorithm,the detailed migration process was presented as well as a part of numerical calculation process using Matlab.Through solving circular tri-diagonal equation systems,the entire solve process was implemented by the functions of Pursue,which is defined in the Matlat program,and then this results were compared to those of the traditional migration.The results indicate that the improved migration algorithm of GPR data migration processing technology is more flexible to solve multiple reflection particles and a main reflector layers when dealing with anisotropic geological medium.
The linear transformation of finite difference migration method in reflection seismology was applied to improve the GPR(ground penetrating radar) migration technology.Based on the fact that the migration effect is highly sensitive to the medium velocity in isotropic condition,the anisotropic case was extended when the theory of the traditional finite difference migration was established.In order to solve the velocity restrictions of the traditional algorithm,the detailed migration process was presented as well as a part of numerical calculation process using Matlab.Through solving circular tri-diagonal equation systems,the entire solve process was implemented by the functions of Pursue,which is defined in the Matlat program,and then this results were compared to those of the traditional migration.The results indicate that the improved migration algorithm of GPR data migration processing technology is more flexible to solve multiple reflection particles and a main reflector layers when dealing with anisotropic geological medium.
引文
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[3]Claerbout J F.Coarse grid calculations of waves in inhomogeneous media with application to delineation of complicated seismic structure[J].Geophysics,1970,35(3):407-418.
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[11]张志涌,杨祖樱.掌握和精通MATLAB[M].北京:北京航空航天大学出版社,2000:162-183.ZHANG Zhi-yong,YANG Zu-yin.Master and master in MATLAB[M].Beijing:Beijing University of Aeronautics and Astronautics Press,2000:162-183.
[12]熊彬,阮百尧.MATLAB在有限差分法中的应用[J].桂林工学院学报,2001,21(2):104-109.XIONG Bing,RUAN Bai-yao.The application of MATLAB to finite difference method[J].Journal of Guilin Institute of Technology,2001,21(2):104-109.
[13]Chapman S J.MATLAB programming for engineers[M].2卷.北京:科学出版社,2002:81-179.Chapman S J.MATLAB programming for engineers[M].2nd ed.Beijing:Science Press,2002:81-179.
[14]王飞,裴永祥.有限差分方法的MATLAB编程[J].新疆师范大学学报:自然科学版,2003,22(4):22-27.WANG Fei,PEI Yong-xiang.The edit program by MATLAB for finite difference method[J].Journal of Xiangjiang Normal University:Natural Science Edition,2003,22(4):22-27.
[15]Irving J,Knight R.Numerical modeling of ground-penetrating radar in 2-D using MATLAB[J].Computers Geosciences,2006(32):1246-1258.
[16]刘晓,李文强.追赶法在求解循环和拟循环三对角方程组中的一种推广[J].河南师范大学学报:自然科学版,2009,37(1):13-16.LIU Xiao,LI Wen-qiang.An extension of chasing method for solving circular and quasi-circular tri-diagonal systems[J].Journal of Henan Normal University:Natural Science,2009,37(1):13-16.
[17]迟利华,刘杰,李晓梅.三对角线性方程组的一种有效并行算法[J].计算机学报,1999,22(2):218-221.CHI Li-hua,LIU Jie,LI Xiao-mei.An effective parallel algorithm for tri-diagonal linear equation[J].Chinese Journal of Computers,1999,22(2):218-221.
[18]李青,王能超.解循环三对角线性方程组的追赶法[J].小型微型计算机系统,2002,23(11):1393-1395.LI Qing,WANG Neng-chao.An algorithm for solving circular tri-diagonal systems[J].Mini-micro Systems,2002,23(11):1393-1395.
[2]周彬忠,包吉山.复杂地区地震波场的正演模拟与反时偏移[J].石油地球物理勘探,1988,23(3):257-262.ZHOU Bing-zhong,BAO Ji-shan.The forward modeling and reverse time migration of seismic wave field in complex medium[J].Oil Geophysical Prospecting,1988,23(3):257-262.
[3]Claerbout J F.Coarse grid calculations of waves in inhomogeneous media with application to delineation of complicated seismic structure[J].Geophysics,1970,35(3):407-418.
[4]Stolt R H.Migration by Fourier transforms[J].Geophysics,1978,43(1):23-48.
[5]马在田.高阶方程偏移的分裂算法[J].地球物理学报,1983,26(4):377-388.MA Zai-tian.High order equation migration of splitting algorithm[J].Chinese Journal of Geophysics,1983,26(4):377-388.
[6]张关泉.利用低阶偏微分方程组的大倾角差分偏移[J].地球物理学报,1986,29(3):273-282.ZHANG Guan-quan.Steep dip finite-difference migration using the system of lower-order partial differential equations[J].Chinese Journal of Geophysics,1986,29(3):273-282.
[7]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.DONG Liang-guo,MA Zai-tian,CAO Jin-zhong,et al.A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese Journal of Geophysics,2000,43(3):411-419.
[8]LI Zhi-ming.Wave field extrapolation by the linearly transformed wave equation operator[J].Geophysics,1986,51(8):38-41.
[9]LI Zhi-ming.Imaging steep-dip reflection by the linearly transformed wave equation method[C]//Proceeding of SEG 56th Annual Meeting.Tulsa,1986:47-49.
[10]李广场.有限差分法探地雷达波动方程偏移[D].天津:河海大学土木学院,2004:33-36.LI Guan-chang.The wave equation migration of ground penetrating radar by the method of finite difference[D].Hohai University.College of Civil Engineering,2004:33-36.
[11]张志涌,杨祖樱.掌握和精通MATLAB[M].北京:北京航空航天大学出版社,2000:162-183.ZHANG Zhi-yong,YANG Zu-yin.Master and master in MATLAB[M].Beijing:Beijing University of Aeronautics and Astronautics Press,2000:162-183.
[12]熊彬,阮百尧.MATLAB在有限差分法中的应用[J].桂林工学院学报,2001,21(2):104-109.XIONG Bing,RUAN Bai-yao.The application of MATLAB to finite difference method[J].Journal of Guilin Institute of Technology,2001,21(2):104-109.
[13]Chapman S J.MATLAB programming for engineers[M].2卷.北京:科学出版社,2002:81-179.Chapman S J.MATLAB programming for engineers[M].2nd ed.Beijing:Science Press,2002:81-179.
[14]王飞,裴永祥.有限差分方法的MATLAB编程[J].新疆师范大学学报:自然科学版,2003,22(4):22-27.WANG Fei,PEI Yong-xiang.The edit program by MATLAB for finite difference method[J].Journal of Xiangjiang Normal University:Natural Science Edition,2003,22(4):22-27.
[15]Irving J,Knight R.Numerical modeling of ground-penetrating radar in 2-D using MATLAB[J].Computers Geosciences,2006(32):1246-1258.
[16]刘晓,李文强.追赶法在求解循环和拟循环三对角方程组中的一种推广[J].河南师范大学学报:自然科学版,2009,37(1):13-16.LIU Xiao,LI Wen-qiang.An extension of chasing method for solving circular and quasi-circular tri-diagonal systems[J].Journal of Henan Normal University:Natural Science,2009,37(1):13-16.
[17]迟利华,刘杰,李晓梅.三对角线性方程组的一种有效并行算法[J].计算机学报,1999,22(2):218-221.CHI Li-hua,LIU Jie,LI Xiao-mei.An effective parallel algorithm for tri-diagonal linear equation[J].Chinese Journal of Computers,1999,22(2):218-221.
[18]李青,王能超.解循环三对角线性方程组的追赶法[J].小型微型计算机系统,2002,23(11):1393-1395.LI Qing,WANG Neng-chao.An algorithm for solving circular tri-diagonal systems[J].Mini-micro Systems,2002,23(11):1393-1395.
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