钻孔雷达层析成像软件系统的研究与开发
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摘要
跨孔雷达层析成像技术,即CT成像技术,它是一种80年代引入地学的一门新兴的地球物理探测技术,由于其与地面普通雷达相比,它的探测深度更大、范围更广、分辨率更高,而且得到的图像结果非常直观,因此这种技术便于地学工作者直接的分析地下地层的结构,目前该被日益广泛的应用于工程与环境物探领域以及煤炭、油气和金属矿产等资源勘探开发方面,因此研究该方法技术具有很强的理论与实际意义。
本文从钻孔雷达层析成像的基本原理出发,研究了层析成像的正反演理论与影响反演效果的几种因素。其中正演方面研究了利用GprMax软件基于时域有限差分(FDTD)的数值模拟技术、雷达剖面直达波初至时的提取和平直射线追踪前提下的系数矩阵生成问题;反演方面重点介绍了代数重建法(ART)、联合迭代重建法(SIRT)、最小二乘法(LSQR)、极小残量法(GMRES)、共轭梯度法(CG)和双稳定共轭梯度法(BIGSTAB)这六种用于反演的算法,并例举了一些反演的实例;在影响成像效果的部分主要讨论了射线覆盖角度、正则化因子和装置排布与异常体走向这三个要素对结果的影响,并得出一定的结论。
GPR(Ground Penetrating Radar) is a kind of efficiently and high resolution technique for shallow layer geophysical explore. It sends high-frequency electromagnetic waves and makes use of the difference of the electrical property of underground medium to analyze and deduce the structure and character of the medium, based on kinematics and dynamics character of the wave, such as swing, wave form and frequency. In spite of high resolution , the detection range of GPR is limited, which is confined to within 100 meters below the surface. So as to solve the problem that the detection range of GPR is small, the borehole radar places the transmitting and receiving devices in boreholes. This technique now is increasingly applied.
Cross-hole tomography is a major mode of borehole radar. It is a new geophysical detection technique which uses the travel time or amplitude data of the electromagnetic waves between the boreholes to inverse velocity distribution or attenuation coefficient distribution of the detection region. This technique is that transmitting antenna is placed in a borehole, receiving antenna in another to receive the direct wave .It gets a mount of data, according to electromagnetic waves in different media at different speeds or different attenuation coefficient .Then it is inversed by the computer, and gets the detection area profiles of velocity or attenuation distribution. It can be studied vividly and intuitively that the causes of complex geological phenomena and local structure. This technique has obvious advantage on the bedrock of the fault , the rupture course , underground karst cave and other underground objects of unknown.
Cross-hole radar tomography consists of velocity tomography and attenuation tomography .This paper focuses on the velocity tomography study. Firstly, the exploition demain between the holes is discretized in cells with constant physical properties. For each transmitter-receiver pair , the length of each segment of ray in every cell is calculated(that generate the coefficient matrix L). Secondly, the first travel time of the direct waves is extracted. At last ,the slowness field is obtained by“inversion”of the segment length matrix multiplied by the measured time vector.
1. In the aspect of the extraction of the first travel time of the direct waves, this paper studies manual extraction and two kinds of automatic extraction (the maximum SNR method and the maximum energy ratio method). Three methods have different features. Manual extraction method can accurately extract first break when signal-to-noise ratio is relatively small, but slowly. Automatic extraction is efficient, but precision is less than manual extraction. Therefore, these three methods can be used to complement each other through human-computer interaction.
2. In the aspect of tomography inversion algorithm, this paper mainly introduces LSQR(Least Square QR Method), GMRES(Generalized Minimal Residual Method), CG(Conjugate gradient method), BICGSTAB(Bi-stable conjugate gradient method), ART(Aigebraic Reconstruction Technique) and SIRT(Simultaneous Iterative Reconstruction Technique). Then the algorithms are verified by the actual models simulated by GprMax software. All algorithms fulfill Practical demand.
3. In the aspect of the fators influencing the tomography result, this paper consists of the angle of ray coverage , regularization factor and the coupling between devices arrangement and direction of abnormal. When the ray coverage in the 40 degrees to 70 degrees, that is ground penetrating radar antenna beam width half-power range, the image effect is the best .When less than 40 degrees, the longitudinal extent of abnormal usually large than the actual ,instead, the image distortion .when larger than 70 degrees, due to the serious interference the image cannot be distinguished .The fundamental equations of tomography are usually ill-posed equations, requiring regularization .Regularization factor is also of significance on the inverse image of the smoothness and flatness .The appropriate regularization factors have important effects on the inversion. Specific parameters depend on the actual circumstances. Arrangement of transmitting and receiving devices also have important implications on imaging results ,.Because of restrictions by the position of the boreholes, projection ray can not make a full range of abnormal body. When the anomalous body horizontal, the inversion of the image is consistent with the model, and the result is the best .When the anomalous body vertical, the inversion of the image in the horizontal direction is more width than the actual, owing to anomalous body homogenized in the horizontal direction.
Finally, we have developed borehole radar tomography software system, the software can easily and convenient process tomography data and the final results of the inversion are displayed in graph, which can be intuitive analysis of the regional geological structure.
本文从钻孔雷达层析成像的基本原理出发,研究了层析成像的正反演理论与影响反演效果的几种因素。其中正演方面研究了利用GprMax软件基于时域有限差分(FDTD)的数值模拟技术、雷达剖面直达波初至时的提取和平直射线追踪前提下的系数矩阵生成问题;反演方面重点介绍了代数重建法(ART)、联合迭代重建法(SIRT)、最小二乘法(LSQR)、极小残量法(GMRES)、共轭梯度法(CG)和双稳定共轭梯度法(BIGSTAB)这六种用于反演的算法,并例举了一些反演的实例;在影响成像效果的部分主要讨论了射线覆盖角度、正则化因子和装置排布与异常体走向这三个要素对结果的影响,并得出一定的结论。
GPR(Ground Penetrating Radar) is a kind of efficiently and high resolution technique for shallow layer geophysical explore. It sends high-frequency electromagnetic waves and makes use of the difference of the electrical property of underground medium to analyze and deduce the structure and character of the medium, based on kinematics and dynamics character of the wave, such as swing, wave form and frequency. In spite of high resolution , the detection range of GPR is limited, which is confined to within 100 meters below the surface. So as to solve the problem that the detection range of GPR is small, the borehole radar places the transmitting and receiving devices in boreholes. This technique now is increasingly applied.
Cross-hole tomography is a major mode of borehole radar. It is a new geophysical detection technique which uses the travel time or amplitude data of the electromagnetic waves between the boreholes to inverse velocity distribution or attenuation coefficient distribution of the detection region. This technique is that transmitting antenna is placed in a borehole, receiving antenna in another to receive the direct wave .It gets a mount of data, according to electromagnetic waves in different media at different speeds or different attenuation coefficient .Then it is inversed by the computer, and gets the detection area profiles of velocity or attenuation distribution. It can be studied vividly and intuitively that the causes of complex geological phenomena and local structure. This technique has obvious advantage on the bedrock of the fault , the rupture course , underground karst cave and other underground objects of unknown.
Cross-hole radar tomography consists of velocity tomography and attenuation tomography .This paper focuses on the velocity tomography study. Firstly, the exploition demain between the holes is discretized in cells with constant physical properties. For each transmitter-receiver pair , the length of each segment of ray in every cell is calculated(that generate the coefficient matrix L). Secondly, the first travel time of the direct waves is extracted. At last ,the slowness field is obtained by“inversion”of the segment length matrix multiplied by the measured time vector.
1. In the aspect of the extraction of the first travel time of the direct waves, this paper studies manual extraction and two kinds of automatic extraction (the maximum SNR method and the maximum energy ratio method). Three methods have different features. Manual extraction method can accurately extract first break when signal-to-noise ratio is relatively small, but slowly. Automatic extraction is efficient, but precision is less than manual extraction. Therefore, these three methods can be used to complement each other through human-computer interaction.
2. In the aspect of tomography inversion algorithm, this paper mainly introduces LSQR(Least Square QR Method), GMRES(Generalized Minimal Residual Method), CG(Conjugate gradient method), BICGSTAB(Bi-stable conjugate gradient method), ART(Aigebraic Reconstruction Technique) and SIRT(Simultaneous Iterative Reconstruction Technique). Then the algorithms are verified by the actual models simulated by GprMax software. All algorithms fulfill Practical demand.
3. In the aspect of the fators influencing the tomography result, this paper consists of the angle of ray coverage , regularization factor and the coupling between devices arrangement and direction of abnormal. When the ray coverage in the 40 degrees to 70 degrees, that is ground penetrating radar antenna beam width half-power range, the image effect is the best .When less than 40 degrees, the longitudinal extent of abnormal usually large than the actual ,instead, the image distortion .when larger than 70 degrees, due to the serious interference the image cannot be distinguished .The fundamental equations of tomography are usually ill-posed equations, requiring regularization .Regularization factor is also of significance on the inverse image of the smoothness and flatness .The appropriate regularization factors have important effects on the inversion. Specific parameters depend on the actual circumstances. Arrangement of transmitting and receiving devices also have important implications on imaging results ,.Because of restrictions by the position of the boreholes, projection ray can not make a full range of abnormal body. When the anomalous body horizontal, the inversion of the image is consistent with the model, and the result is the best .When the anomalous body vertical, the inversion of the image in the horizontal direction is more width than the actual, owing to anomalous body homogenized in the horizontal direction.
Finally, we have developed borehole radar tomography software system, the software can easily and convenient process tomography data and the final results of the inversion are displayed in graph, which can be intuitive analysis of the regional geological structure.
引文
(1)宋文荣、吴仪芳、刘建达、许汉刚等,电磁波层析成像技术(CT)在地基勘探中的应用[J],地震学刊,1994年第二期,62-64。
(2)华卫兵,基于代数重建算法的CT图像仿真[D],北京科技大学,2005。
(3)李才名,电磁波层析成像(EWCT)技术及其在混凝土桩基础质量检测中的应用[D],南京大学,2003。
(4)高文利、马兰等,JW-5型地下电磁波探测系统设计[J],物化探计算技术,第27卷,第3期,2005-8
(5) Bernard Giroux ,bh_tomo-A Matlab borehole georadar 2D tomography package,March 2006.
(6) Hansruedi Maurer, Alan G.Green, and Klaus Holliger Full-Waveform Inversion of Crosshole Radar Data Based on 2-D Finite-Difference Time-Domain Solutions of Maxwell’s Equations[J]. IEEE transactions on geoscience and remote sensing. VOL.45, NO.9.SEPTEMBER 2007.
(7)余德平、严建文、吴继敏,全波场地震勘探技术[J],地球物理学进展,第21卷,第2期
(8)张赛民,跨孔地震层析成像研究[D],中南大学硕士学位论文,2003。
(9)曾昭发,刘四新,王者江,薛建.,探地雷达方法原理及应用[M].北京:科学出版社,2006.
(10)钟声.钻孔雷达于数字摄像动态勘察技术若干关键问题研究[D].武汉:中科院武汉岩土力学研究所,2008。
(11) Olsson, L. Falk, O. Forslund, L. Lundmark, and E. Sandberg. Borehole radar applied to the characterization of hydraulically conductive fracture zones in crystalline rock[J]. Geophysical Prospecting, 1992, 40(2): 109-142
(12)袁志亮,井间声波电磁波层析成像技术应用研究与软件开发[D],中国地质大学博士学位论文,2007。
(13)杨文采,地球物理反演和地震层析成像[M],地质出版社,1989。
(14)赫尔曼,由投影重建图像—CT的理论基础[M],科学出版社,1985。
(15) S.Hanafy and S.A.al Hagrey,Ground-penetrating radar tomography for soil-moisture heterogeneity, Geophysics[J], VOL.71, No.1 (January-February 2006), P.K9-K18。
(16) Erwan Gloaguen*, Denis Marcotte, Michel Chouteau, Borehole radar velocity inversion using cokriging and cosimulation[J]. Journal of Applied Geophysics Janurary 2005.
(17) K.Holliger, M.Musil, H.R.Maurer Ray-based amplitude tomography for crosshole georadar data: a numerical assessment[J]. Journal of Applied Geophysics 47 (2001)285-298
(18)杨薇,基于弯曲射线的跨孔层析成像算法研究[D],吉林大学硕士学位论文,2008。
(19) William P.Clement and Michael D.Knoll, Traveltime inversion of vertical radar profiles[J]. Geophysics,Vol71,NO.3 (MAY-JUNE 2006).
(20)左国平,地震记录初至拾取方法对比与研究[D]。中国地质大学硕士学位论文,2006。
(21)刘志成,初至智能拾取技术[J]。石油物探,2007,第5期。
(22)杨薇,跨孔层析成像lsqr算法的研究[J]。物探与化探,第23卷第2期,2008.4。
(23) Christopher C.Paiger and Michael A.Saunders,LSQR: An Algorithm for Spare Linear Equations and Sparse Least Squares.
(24) Youcef Saad and Martin H.Schultz. GMRES: A Generalized Minimal Residual Algorithm For Solving Nonsymmetric Line System[J].SLAM J,SCI. STAT. COMPUT , Vol 7, No.3 JULY 1986.
(25) David Kincaid and Ward Cheney,Numerical Analysis.王国荣、俞耀明、徐兆亮译,数值分析[M]。机械工业出版社,2005。
(26) Magnus R.Hestenes and Eduard Stiefel. Method of Conjugate Gradients for Solving Linear Systems[J]. Journal of the National Bureau of Strandards . Vol.49,No.6, December 1952.
(27) Gerard L.G. slejpen and Diederik R. fokkema. Bicgstab(L) for linear equations involving unsymmetric matrices with complex spectrum[J].. Electronic Trasactions on Numerical Analysis.Vol.1.September 1993.
(28) R Gordon, R Bender, GT Herman. Aigebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography[J]. Theoretical Biology,1970,29:471-481.
(29)宿淑春、王守东、吴律,井间层析成像的平滑SIRT算法[J],石油大学学报(自然科学版),2001年12月,第25卷第6期,29-31。
(30)赵连锋,井间地震波速与衰减联合层析成像方法研究[D],成都理工大学博士论文2003年。
(31)徐树方。矩阵计算的方法和理论[M]。北京大学出版社,1991。
(32)葛德彪,阎玉波,电磁波时域有限差分方法[M],西安:电子科技大学出版社,2001.
(33) How-Wei Chen, Tai-Min Huang. Finite-difference time-domain simulation of GPR data[J],Journal of Applied Geophysics, 1998, 39: 139-163.
(34) Antonis Giannopoulos. Modelling ground penetrating radar by GprMax[J],Construction and Building Materials,2005,22:755-762.
(35) W.A.Schneider,Jr.*, Kurt A.Ranzinger, A.H.Balch, and Curtis Kruse. A dynamic programming approach to first arrival traveltime computation in media with arbitrarily distributed velocities[J]. GEOPHYSICS, Vol,57, NO.1(JANUARY 1992):P. 39-50.
(36) Niklas Linde , Ari Tryggvason , John E. Peterson , and Susan S. Hubbard. Joint inversion of crosshole radar and seismic traveltimes acqrired at the South Oyster Bacterial Transport Site[J]. GEOPHYSICS, Vol,73, NO.4(JULY-AUGEST 2008):P. G39-G50.
(37)张建中,丁兴号。一种2.5维井间投射波层析成像方法[J]。声学学报,第32卷第1期,2007年1月。
(38)陈德运,李乐天,胡海涛。基于迭代Tikhonov正则化的电容层析成像重建。哈尔滨理工大学学报[J],第14卷,第2期,2009年4月
(2)华卫兵,基于代数重建算法的CT图像仿真[D],北京科技大学,2005。
(3)李才名,电磁波层析成像(EWCT)技术及其在混凝土桩基础质量检测中的应用[D],南京大学,2003。
(4)高文利、马兰等,JW-5型地下电磁波探测系统设计[J],物化探计算技术,第27卷,第3期,2005-8
(5) Bernard Giroux ,bh_tomo-A Matlab borehole georadar 2D tomography package,March 2006.
(6) Hansruedi Maurer, Alan G.Green, and Klaus Holliger Full-Waveform Inversion of Crosshole Radar Data Based on 2-D Finite-Difference Time-Domain Solutions of Maxwell’s Equations[J]. IEEE transactions on geoscience and remote sensing. VOL.45, NO.9.SEPTEMBER 2007.
(7)余德平、严建文、吴继敏,全波场地震勘探技术[J],地球物理学进展,第21卷,第2期
(8)张赛民,跨孔地震层析成像研究[D],中南大学硕士学位论文,2003。
(9)曾昭发,刘四新,王者江,薛建.,探地雷达方法原理及应用[M].北京:科学出版社,2006.
(10)钟声.钻孔雷达于数字摄像动态勘察技术若干关键问题研究[D].武汉:中科院武汉岩土力学研究所,2008。
(11) Olsson, L. Falk, O. Forslund, L. Lundmark, and E. Sandberg. Borehole radar applied to the characterization of hydraulically conductive fracture zones in crystalline rock[J]. Geophysical Prospecting, 1992, 40(2): 109-142
(12)袁志亮,井间声波电磁波层析成像技术应用研究与软件开发[D],中国地质大学博士学位论文,2007。
(13)杨文采,地球物理反演和地震层析成像[M],地质出版社,1989。
(14)赫尔曼,由投影重建图像—CT的理论基础[M],科学出版社,1985。
(15) S.Hanafy and S.A.al Hagrey,Ground-penetrating radar tomography for soil-moisture heterogeneity, Geophysics[J], VOL.71, No.1 (January-February 2006), P.K9-K18。
(16) Erwan Gloaguen*, Denis Marcotte, Michel Chouteau, Borehole radar velocity inversion using cokriging and cosimulation[J]. Journal of Applied Geophysics Janurary 2005.
(17) K.Holliger, M.Musil, H.R.Maurer Ray-based amplitude tomography for crosshole georadar data: a numerical assessment[J]. Journal of Applied Geophysics 47 (2001)285-298
(18)杨薇,基于弯曲射线的跨孔层析成像算法研究[D],吉林大学硕士学位论文,2008。
(19) William P.Clement and Michael D.Knoll, Traveltime inversion of vertical radar profiles[J]. Geophysics,Vol71,NO.3 (MAY-JUNE 2006).
(20)左国平,地震记录初至拾取方法对比与研究[D]。中国地质大学硕士学位论文,2006。
(21)刘志成,初至智能拾取技术[J]。石油物探,2007,第5期。
(22)杨薇,跨孔层析成像lsqr算法的研究[J]。物探与化探,第23卷第2期,2008.4。
(23) Christopher C.Paiger and Michael A.Saunders,LSQR: An Algorithm for Spare Linear Equations and Sparse Least Squares.
(24) Youcef Saad and Martin H.Schultz. GMRES: A Generalized Minimal Residual Algorithm For Solving Nonsymmetric Line System[J].SLAM J,SCI. STAT. COMPUT , Vol 7, No.3 JULY 1986.
(25) David Kincaid and Ward Cheney,Numerical Analysis.王国荣、俞耀明、徐兆亮译,数值分析[M]。机械工业出版社,2005。
(26) Magnus R.Hestenes and Eduard Stiefel. Method of Conjugate Gradients for Solving Linear Systems[J]. Journal of the National Bureau of Strandards . Vol.49,No.6, December 1952.
(27) Gerard L.G. slejpen and Diederik R. fokkema. Bicgstab(L) for linear equations involving unsymmetric matrices with complex spectrum[J].. Electronic Trasactions on Numerical Analysis.Vol.1.September 1993.
(28) R Gordon, R Bender, GT Herman. Aigebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography[J]. Theoretical Biology,1970,29:471-481.
(29)宿淑春、王守东、吴律,井间层析成像的平滑SIRT算法[J],石油大学学报(自然科学版),2001年12月,第25卷第6期,29-31。
(30)赵连锋,井间地震波速与衰减联合层析成像方法研究[D],成都理工大学博士论文2003年。
(31)徐树方。矩阵计算的方法和理论[M]。北京大学出版社,1991。
(32)葛德彪,阎玉波,电磁波时域有限差分方法[M],西安:电子科技大学出版社,2001.
(33) How-Wei Chen, Tai-Min Huang. Finite-difference time-domain simulation of GPR data[J],Journal of Applied Geophysics, 1998, 39: 139-163.
(34) Antonis Giannopoulos. Modelling ground penetrating radar by GprMax[J],Construction and Building Materials,2005,22:755-762.
(35) W.A.Schneider,Jr.*, Kurt A.Ranzinger, A.H.Balch, and Curtis Kruse. A dynamic programming approach to first arrival traveltime computation in media with arbitrarily distributed velocities[J]. GEOPHYSICS, Vol,57, NO.1(JANUARY 1992):P. 39-50.
(36) Niklas Linde , Ari Tryggvason , John E. Peterson , and Susan S. Hubbard. Joint inversion of crosshole radar and seismic traveltimes acqrired at the South Oyster Bacterial Transport Site[J]. GEOPHYSICS, Vol,73, NO.4(JULY-AUGEST 2008):P. G39-G50.
(37)张建中,丁兴号。一种2.5维井间投射波层析成像方法[J]。声学学报,第32卷第1期,2007年1月。
(38)陈德运,李乐天,胡海涛。基于迭代Tikhonov正则化的电容层析成像重建。哈尔滨理工大学学报[J],第14卷,第2期,2009年4月