随机介质中的探地雷达叠前逆时偏移成像
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摘要
为了更好地分析探地雷达(GPR)叠前逆时偏移算法对实际地下随机分布介质的成像效果,采用随机过程的谱分解和混合型自相关函数理论构建了不同自相关长度的GPR随机介质模型。基于时域有限差分法(FDTD)构建了GPR叠前逆时偏移成像算法,其中FDTD用于计算正传和反传电磁波场,归一化互相关成像条件用于获取逆时偏移成像剖面。在此基础上,利用该算法对两个随机介质模型的多偏移距正演数据进行计算,并与相应背景介质为均匀介质的逆时偏移结果进行对比。结果表明:电磁波在随机介质中散射强烈,反射波扭曲变形、不连续,形成了明显的随机扰动,致使逆时偏移成像剖面的空间分辨率更低,低频噪声更强;自相关长度是影响随机介质中异常体成像效果的主要因素,自相关长度越小,异常体的成像越清晰,自相关长度越大,异常体的成像效果越差,且不易被识别。
In order to better analyze the imaging effect of ground penetrating radar(GPR) prestack reverse time migration algorithm on actual underground random distribution media, we build two GPR random media models with different auto-correlation length based on spectral decomposition of stochastic process and hybrid auto-correlation function theory in this paper, respectively. The GPR reverse time migration based on finite different time domain(FDTD) method is proposed, in which FDTD used to calculate the forward and reverse propagation process of electromagnetic wave and the normalized cross-correlation imaging condition is applied to obtain the migration result. After that, the GPR prestack reverse time migration imaging algorithm is applied to the simulated multi-offset GPR datasets of two typical random media models, separately, which are compared with imaging results of the simulated multi-offset GPR dataset of GPR model with homogeneous media. The compared results demonstrate that the electromagnetic wave is strongly scattered in random media, and the reflected wave is distorted and discontinuous, forming a distinct random disturbance. This results in the reverse time migration profile with lower spatial resolution and stronger low frequency noise. The parameters of auto-correlation length is the main factor for affecting the imaging effect of GPR prestack reverse time migration of random media. The smaller the auto-correlation length is, the clearer the imaging of the anomalous body is. On the contary, the imaging effect of the anomalous body is worse and it is not easy to be identified.
In order to better analyze the imaging effect of ground penetrating radar(GPR) prestack reverse time migration algorithm on actual underground random distribution media, we build two GPR random media models with different auto-correlation length based on spectral decomposition of stochastic process and hybrid auto-correlation function theory in this paper, respectively. The GPR reverse time migration based on finite different time domain(FDTD) method is proposed, in which FDTD used to calculate the forward and reverse propagation process of electromagnetic wave and the normalized cross-correlation imaging condition is applied to obtain the migration result. After that, the GPR prestack reverse time migration imaging algorithm is applied to the simulated multi-offset GPR datasets of two typical random media models, separately, which are compared with imaging results of the simulated multi-offset GPR dataset of GPR model with homogeneous media. The compared results demonstrate that the electromagnetic wave is strongly scattered in random media, and the reflected wave is distorted and discontinuous, forming a distinct random disturbance. This results in the reverse time migration profile with lower spatial resolution and stronger low frequency noise. The parameters of auto-correlation length is the main factor for affecting the imaging effect of GPR prestack reverse time migration of random media. The smaller the auto-correlation length is, the clearer the imaging of the anomalous body is. On the contary, the imaging effect of the anomalous body is worse and it is not easy to be identified.
引文
[1] 刘澜波,钱荣毅.探地雷达:浅表地球物理科学技术中的重要工具[J].地球物理学报,2015,58(8):2606-2617.LIU L B,QIAN R Y.Ground penetrating radar:A critical tool in near-surface geophysics [J].Chinese Journal of Geophysics,2015,58(8):2606-2617.(In Chinese)
[2] 葛双成,邵长云.岩溶勘察中的探地雷达技术及应用[J].地球物理进展,2005,20(2):476-481.GE S C,SHAO C Y,Technique and application of GPR in karst prospecting[J].Progress in Geophysics,2005,20(2):476-481.(In Chinese)
[3] 杨剑,李华,焦彦杰.探地雷达在城市地下管线探测中的应用[J].物探化探计算技术,2010,32(6):669-673.YANG J,LI H,JIAO Y J.Application of detection underground pipes by ground penetrating radar in urban[J].Computing Techniques for Geophysical and Geochemical Exploration,2010,32(6):669-673.(In Chinese)
[4] 刘敦文,徐国元,黄仁东.浅谈探地雷达技术在环境工程中的应用[J].环境保护,2001(8):14-16.LIU D W,XU G Y,HUANG R D.Discussion on the application of GPR in environmental engineering [J].Environmental Protection,2001(8):14-16.(In Chinese)
[5] 李孟娟,李川.探地雷达检测隧道衬砌厚度的研究[J].物探化探计算技术,2008,30(3):231-234+170.LI M J,LI C.A study on the thickness detection of tunnel lining-walls by GPR[J].Computing Techniques for Geophysical and Geochemical Exploration,2008,30(3):231-234+170.(In Chinese)
[6] 魏超,肖国强,王法刚.地质雷达在混凝土质量检测中的应用研究[J].工程地球物理学报,2004,1(5):447-451.WEI C,XIAO G Q,WANG F G.The application of geo radar in concrete quality detection [J].Chinese Journal of Engineering Geophysics,2004,1(5):447-451.(In Chinese)
[7] 薛桂霞,邓世坤,刘秀娟.逆时偏移在探地雷达信号处理中的应用[J].煤田地质与勘探,2004,32(1):55-57.XUE G X,DENG S K,LIU X J.An application of reverse time migration in the ground penetrating radar data processing[J].Coal Geology & Exploration,2004,32(1):55-57.(In Chinese)
[8] 邓世坤.克希霍夫积分偏移法在探地雷达图象处理中的应用[J].地球科学,1993,18(3):303-309.DENG S K.Application of Kirchhoff integral migration method to processing GPR image[J].Earth Science,1993,18(3):303-309.(In Chinese)
[9] 底青云,许琨,王妙月.衰减雷达波有限元偏移[J].地球物理学报,2000,43(2):257-263.DI Q Y,XU K,WANG M Y.The attenuated radar wave migration with finite element method [J].Chinese Journal of Geophysics,2000,43(2):257-263.(In Chinese)
[10] 鲁兴林,钱荣毅.地质雷达有限差分逆时偏移方法研究[J].地球物理学进展,2017,32(2):885-890.LU X L,QIAN R Y.Ground-penetrating radar finite-difference reverse time migration [J].Progress in Geophysics,2017,32(2):885-890.(In Chinese)
[11] FU L,LIU C,LIU S,et al.Migration deconvolution of ground penetrating radar (GPR) data [C].2018 17th International Conference on Ground Penetrating Radar (GPR).IEEE,2018:1-4.
[12] LIU H,XING B,HAN F,et al.Frequency domain reverse time migration of GPR with attenenuation compensation [C].2018 17th International Conference on Ground Penetrating Radar (GPR).IEEE,2018:1-4.
[13] 王敏玲,王洪华,张智,等.基于激发振幅成像条件的探地雷达逆时偏移成像[J].地球物理学报,2018,61(8):3435-3445.WANG M L,WANG H H,ZHANG Z,et al.Reverse time migration in ground penetrating radar based on the excitation amplitude imaging condition [J].Chinese Journal of Geophysics,2018,61(8):3435-3445.(In Chinese)
[14] BRADFORD J H,PRIVETTE J,WILKINS D,et al.Reverse-time migration from rugged topography to Image Ground-Penetrating Radar Data in Complex Environments [J].Engineering,2018,4(5):661-666.
[15] 陈可洋.三维随机建模方法及其波场模拟分析[J].勘探地球物理进展,2009,32(5):315-320.CHEN K Y.3-D random modeling scheme and wavefield simulation analysis [J].Progress in Exploration Geophysics,2009,32(5):315-320.(In Chinese)
[16] 奚先,姚姚.二维随机介质及波动方程正演模拟[J].石油地球物理勘探,2001,36(5):546-552.XI XIAN,YAO Y.2-D random media and wave equation forward modeling [J].Oil Geophysics Prospecting,2001,36(5):546-552.(In Chinese)
[17] 戴前伟,王洪华.基于随机介质模型的 GPR 无单元法正演模拟[J].中国有色金属学报,2013,23(9):2436-2443.DAI Q W,WANG H H.Element free method forward modeling of GPR based on random medium model [J].The Chinese Journal of Nonferrous Metals,2013,23(9):2436-2443.(In Chinese)
[18] 宋二乔,刘四新,何荣钦,等.探地雷达探测季节性冻土的正演模拟[J].物探与化探,2018,42(5):962-969.SONG E Q,LIU S X,HE R Q,et al.Forward modeling on the seasonal frozen soil region detection by ground penetrating radar [J].Geophysical and Geochemical Exploration,2018,42(5):962-969.(In Chinese)
[19] 郭士礼,冀孟恩,朱培民,等.多相离散随机介质模型及其探地雷达波场特征研究[J].地球物理学报,2015,58(8):2779-2791.GUO S L,JI M E,ZHU P M,et al.Study on multiphase discrete random medium model and its GPR wave field characteristics [J].Chinese Journal of Geophysics,2018,58(8):2779-2791.(In Chinese)
[20] 殷学鑫,刘洋.二维随机介质模型正演模拟及其波场分析[J].石油地球物理勘探,2011,46(6):862-872.YIN X X,LIU Y.Random medium 2-D modeling and its wavefield analysis [J].Oil Geophysics Prospecting,2011,46(6):862-872.(In Chinese)
[21] 陈德鹏,戴前伟,冯德山,等.基于归一化互相关成像条件的GPR 逆时偏移成像[J].中南大学学报 (自然科学版),2018,49(5):1221-1227.CHEN D P,DAI Q W,FENG D S,et al.Reverse time migration of ground penetrating radar based on normalized cross correlation imaging condition [J].Journal of Central South University (Science and Technology),2018,49(5):1221-1227.(In Chinese)
[22] 冯德山.地质雷达二维时域有限差分正演[D].长沙:中南大学,2004.FENG D S.Two-dimension finite-difference time-domain (fdtd) forward simulation for Ground Penetrating Radar (GPR) [D].Changsha:Central South University ,2004.(In Chinese)
[23] 王洪华,戴前伟.频散介质中探地雷达有限元法正演模拟[J].中南大学学报 (自然科学版),2014,45(3):790-797.WANG H H,DAI Q W.Finite element method GPR forward simulation in dispersive medium [J].Journal of Central South University:science and technology,2014,45(3):790-797.(In Chinese)
[24] 李展辉,黄清华,王彦宾.三维错格时域伪谱法在频散介质井中雷达模拟中的应用[J].地球物理学报,2009,52(7):1915-1922.LI Z H,HUANG Q H,WANG Y B.A 3-D staggered grid PSTD method for borehole radar simulations in dispersive media [J].Chinese Journal of Geophysics,2009,52(7):1915-1922.(In Chinese)
[25] CHATTOPADHYAY S,MCMECHAN G A.Imaging conditions for prestack reverse-time migration [J].Geophysics,2008,73(3):S81-S89.
[26] KAELIN B,GUITTON A.Imaging condition for reverse time migration [J].Expanded Abstracts of 76th Annual Internat SEG Mtg,2006,25(1):2594-2598.
[27] 侯爵,刘有山,兰海强,等.基于起伏地形平化策略的弹性波逆时偏移成像方法[J].地球物理学报,2018,61(4):1434-1446.HOU J,LIU Y S,LAN H Q,et al.Elastic reverse time migration using a topography flattening scheme [J].Chinese Journal of Geophysics,2018,61(4):1434-1446.(In Chinese)
[28] 何兵寿,张会星,魏修成,等.双程声波方程叠前逆时深度偏移的成像条件[J].石油地球物理勘探,2010,45(2):237-243.HE B S,ZHANG H X,WEI X C,et al.Imaging conditions for two-way acoustic wave equation pre-stack reverse-time depth migration [J].Oil Geophysics Prospecting,2010,45(2):237-243.(In Chinese)
[2] 葛双成,邵长云.岩溶勘察中的探地雷达技术及应用[J].地球物理进展,2005,20(2):476-481.GE S C,SHAO C Y,Technique and application of GPR in karst prospecting[J].Progress in Geophysics,2005,20(2):476-481.(In Chinese)
[3] 杨剑,李华,焦彦杰.探地雷达在城市地下管线探测中的应用[J].物探化探计算技术,2010,32(6):669-673.YANG J,LI H,JIAO Y J.Application of detection underground pipes by ground penetrating radar in urban[J].Computing Techniques for Geophysical and Geochemical Exploration,2010,32(6):669-673.(In Chinese)
[4] 刘敦文,徐国元,黄仁东.浅谈探地雷达技术在环境工程中的应用[J].环境保护,2001(8):14-16.LIU D W,XU G Y,HUANG R D.Discussion on the application of GPR in environmental engineering [J].Environmental Protection,2001(8):14-16.(In Chinese)
[5] 李孟娟,李川.探地雷达检测隧道衬砌厚度的研究[J].物探化探计算技术,2008,30(3):231-234+170.LI M J,LI C.A study on the thickness detection of tunnel lining-walls by GPR[J].Computing Techniques for Geophysical and Geochemical Exploration,2008,30(3):231-234+170.(In Chinese)
[6] 魏超,肖国强,王法刚.地质雷达在混凝土质量检测中的应用研究[J].工程地球物理学报,2004,1(5):447-451.WEI C,XIAO G Q,WANG F G.The application of geo radar in concrete quality detection [J].Chinese Journal of Engineering Geophysics,2004,1(5):447-451.(In Chinese)
[7] 薛桂霞,邓世坤,刘秀娟.逆时偏移在探地雷达信号处理中的应用[J].煤田地质与勘探,2004,32(1):55-57.XUE G X,DENG S K,LIU X J.An application of reverse time migration in the ground penetrating radar data processing[J].Coal Geology & Exploration,2004,32(1):55-57.(In Chinese)
[8] 邓世坤.克希霍夫积分偏移法在探地雷达图象处理中的应用[J].地球科学,1993,18(3):303-309.DENG S K.Application of Kirchhoff integral migration method to processing GPR image[J].Earth Science,1993,18(3):303-309.(In Chinese)
[9] 底青云,许琨,王妙月.衰减雷达波有限元偏移[J].地球物理学报,2000,43(2):257-263.DI Q Y,XU K,WANG M Y.The attenuated radar wave migration with finite element method [J].Chinese Journal of Geophysics,2000,43(2):257-263.(In Chinese)
[10] 鲁兴林,钱荣毅.地质雷达有限差分逆时偏移方法研究[J].地球物理学进展,2017,32(2):885-890.LU X L,QIAN R Y.Ground-penetrating radar finite-difference reverse time migration [J].Progress in Geophysics,2017,32(2):885-890.(In Chinese)
[11] FU L,LIU C,LIU S,et al.Migration deconvolution of ground penetrating radar (GPR) data [C].2018 17th International Conference on Ground Penetrating Radar (GPR).IEEE,2018:1-4.
[12] LIU H,XING B,HAN F,et al.Frequency domain reverse time migration of GPR with attenenuation compensation [C].2018 17th International Conference on Ground Penetrating Radar (GPR).IEEE,2018:1-4.
[13] 王敏玲,王洪华,张智,等.基于激发振幅成像条件的探地雷达逆时偏移成像[J].地球物理学报,2018,61(8):3435-3445.WANG M L,WANG H H,ZHANG Z,et al.Reverse time migration in ground penetrating radar based on the excitation amplitude imaging condition [J].Chinese Journal of Geophysics,2018,61(8):3435-3445.(In Chinese)
[14] BRADFORD J H,PRIVETTE J,WILKINS D,et al.Reverse-time migration from rugged topography to Image Ground-Penetrating Radar Data in Complex Environments [J].Engineering,2018,4(5):661-666.
[15] 陈可洋.三维随机建模方法及其波场模拟分析[J].勘探地球物理进展,2009,32(5):315-320.CHEN K Y.3-D random modeling scheme and wavefield simulation analysis [J].Progress in Exploration Geophysics,2009,32(5):315-320.(In Chinese)
[16] 奚先,姚姚.二维随机介质及波动方程正演模拟[J].石油地球物理勘探,2001,36(5):546-552.XI XIAN,YAO Y.2-D random media and wave equation forward modeling [J].Oil Geophysics Prospecting,2001,36(5):546-552.(In Chinese)
[17] 戴前伟,王洪华.基于随机介质模型的 GPR 无单元法正演模拟[J].中国有色金属学报,2013,23(9):2436-2443.DAI Q W,WANG H H.Element free method forward modeling of GPR based on random medium model [J].The Chinese Journal of Nonferrous Metals,2013,23(9):2436-2443.(In Chinese)
[18] 宋二乔,刘四新,何荣钦,等.探地雷达探测季节性冻土的正演模拟[J].物探与化探,2018,42(5):962-969.SONG E Q,LIU S X,HE R Q,et al.Forward modeling on the seasonal frozen soil region detection by ground penetrating radar [J].Geophysical and Geochemical Exploration,2018,42(5):962-969.(In Chinese)
[19] 郭士礼,冀孟恩,朱培民,等.多相离散随机介质模型及其探地雷达波场特征研究[J].地球物理学报,2015,58(8):2779-2791.GUO S L,JI M E,ZHU P M,et al.Study on multiphase discrete random medium model and its GPR wave field characteristics [J].Chinese Journal of Geophysics,2018,58(8):2779-2791.(In Chinese)
[20] 殷学鑫,刘洋.二维随机介质模型正演模拟及其波场分析[J].石油地球物理勘探,2011,46(6):862-872.YIN X X,LIU Y.Random medium 2-D modeling and its wavefield analysis [J].Oil Geophysics Prospecting,2011,46(6):862-872.(In Chinese)
[21] 陈德鹏,戴前伟,冯德山,等.基于归一化互相关成像条件的GPR 逆时偏移成像[J].中南大学学报 (自然科学版),2018,49(5):1221-1227.CHEN D P,DAI Q W,FENG D S,et al.Reverse time migration of ground penetrating radar based on normalized cross correlation imaging condition [J].Journal of Central South University (Science and Technology),2018,49(5):1221-1227.(In Chinese)
[22] 冯德山.地质雷达二维时域有限差分正演[D].长沙:中南大学,2004.FENG D S.Two-dimension finite-difference time-domain (fdtd) forward simulation for Ground Penetrating Radar (GPR) [D].Changsha:Central South University ,2004.(In Chinese)
[23] 王洪华,戴前伟.频散介质中探地雷达有限元法正演模拟[J].中南大学学报 (自然科学版),2014,45(3):790-797.WANG H H,DAI Q W.Finite element method GPR forward simulation in dispersive medium [J].Journal of Central South University:science and technology,2014,45(3):790-797.(In Chinese)
[24] 李展辉,黄清华,王彦宾.三维错格时域伪谱法在频散介质井中雷达模拟中的应用[J].地球物理学报,2009,52(7):1915-1922.LI Z H,HUANG Q H,WANG Y B.A 3-D staggered grid PSTD method for borehole radar simulations in dispersive media [J].Chinese Journal of Geophysics,2009,52(7):1915-1922.(In Chinese)
[25] CHATTOPADHYAY S,MCMECHAN G A.Imaging conditions for prestack reverse-time migration [J].Geophysics,2008,73(3):S81-S89.
[26] KAELIN B,GUITTON A.Imaging condition for reverse time migration [J].Expanded Abstracts of 76th Annual Internat SEG Mtg,2006,25(1):2594-2598.
[27] 侯爵,刘有山,兰海强,等.基于起伏地形平化策略的弹性波逆时偏移成像方法[J].地球物理学报,2018,61(4):1434-1446.HOU J,LIU Y S,LAN H Q,et al.Elastic reverse time migration using a topography flattening scheme [J].Chinese Journal of Geophysics,2018,61(4):1434-1446.(In Chinese)
[28] 何兵寿,张会星,魏修成,等.双程声波方程叠前逆时深度偏移的成像条件[J].石油地球物理勘探,2010,45(2):237-243.HE B S,ZHANG H X,WEI X C,et al.Imaging conditions for two-way acoustic wave equation pre-stack reverse-time depth migration [J].Oil Geophysics Prospecting,2010,45(2):237-243.(In Chinese)