基于归一化互相关成像条件的GPR逆时偏移成像
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摘要
针对基于零时刻成像条件的探地雷达(GPR)逆时偏移精度低、难以对复杂结构进行高精度成像的缺点,将归一化互相关成像条件应用于GPR叠前逆时偏移成像。从二维GPR电磁波方程出发,采用基于完全匹配层(PML)边界条件的时域有限单元法(FETD)模拟电磁波正向和逆向传播,采用归一化互相关成像条件获取叠前逆时偏移的偏移结果,将空间高通滤波用于压制互相关过程中产生的低频噪声,然后编制相应的GPR叠前逆时偏移程序。在此基础上,建立2个复杂的GPR模型,利用基于归一化互相关成像条件的GPR逆时偏移程序进行计算,并与基于零时刻成像条件的GPR逆时偏移剖面进行对比。研究结果表明:与基于零时刻成像条件的GPR逆时偏移剖面相比,基于归一化互相关成像条件的GPR叠前逆时偏移剖面能更清晰地反映异常体空间形态和内部结构信息,其分辨率和成像精度更高。
On account of the low imaging precision of ground penetrating radar(GPR) reverse time migration(RTM) based on the zero time imaging condition and it is difficult to imaging complex structure with high resolution, normalized cross-correlation imaging conditions was applied in GPR pre-stack RTM imaging. Based on the two-dimensional GPR wave equation, the time domain finite element method based on perfectly matched layer(PML) boundary condition(FETD) was used to simulate the forward and reverse electromagnetic waves, normalized cross-correlation imaging condition was used to obtain the pre-stack RTM results, the spatial high-pass filtering was applied to suppress cross-correlation process of low frequency noise and the corresponding program of GPR pre-stack RTM based on normalized cross-correlation imaging condition was designed and implemented. After that, the two complex GPR models were established and calculated by GPR RTM program based on the normalized cross-correlation imaging condition and zero time imaging condition,respectively.The results show that,compared with imaging results with zero time imaging condition,the imaging results with those in the normalized cross-correlation imaging condition have higher image quality and can more clearly display the detailed spatial form and internal structure information of the abnormal body space.
On account of the low imaging precision of ground penetrating radar(GPR) reverse time migration(RTM) based on the zero time imaging condition and it is difficult to imaging complex structure with high resolution, normalized cross-correlation imaging conditions was applied in GPR pre-stack RTM imaging. Based on the two-dimensional GPR wave equation, the time domain finite element method based on perfectly matched layer(PML) boundary condition(FETD) was used to simulate the forward and reverse electromagnetic waves, normalized cross-correlation imaging condition was used to obtain the pre-stack RTM results, the spatial high-pass filtering was applied to suppress cross-correlation process of low frequency noise and the corresponding program of GPR pre-stack RTM based on normalized cross-correlation imaging condition was designed and implemented. After that, the two complex GPR models were established and calculated by GPR RTM program based on the normalized cross-correlation imaging condition and zero time imaging condition,respectively.The results show that,compared with imaging results with zero time imaging condition,the imaging results with those in the normalized cross-correlation imaging condition have higher image quality and can more clearly display the detailed spatial form and internal structure information of the abnormal body space.
引文
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[15]傅磊,刘四新,刘澜波,等.机载探地雷达数值模拟及逆时偏移成像[J].地球物理学报,2014,57(5):1636-1646.FU Lei,LIU Sixin,LIU Lanbo,et al.Airborne ground penetrating radar numerical simulation and reverse time migration[J].Chinese Journal Geophysics,2014,57(5):1636-1646.
[16]LIU Sixin,LEI Linlin,FU Lei,et al.Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data[J].Journal of Applied Geophysics,2014,107(4):1-7.
[17]CLAERBOUT J F,JOHNSON A G.Extrapolation of time-dependent waveforms along their Path of Propagation[J].Geophysical Journal International,1971,26(1/2/3/4):285-293.
[18]戴前伟,王洪华,冯德山,等.基于双二次插值的探地雷达有限元数值模拟[J].地球物理学进展,2012,27(2):736-743.DAI Qianwei,WANG Honghua,FENG Deshan,et al.Finite element numerical simulation for GPR based on quadratic interpolation[J].Progress in Geophysics,2012,27(2):736-743.
[19]DROSSAERT F H,GIANNOPOULOS A.A nonsplit complex frequency-shifted PML based on recursive integration for FDTD modeling of elastic waves[J].Geophysics,2007,72(2):T9-T17.
[20]刘红伟,刘洪,邹振,等.地震叠前逆时偏移中的去噪与存储[J].地球物理学报,2010,53(9):2171-2180.LIU Hongwei,LIU Hong,ZHOU Zhen,et al.The problems of denoise and storage in seismic reverse time migration[J].Chinese Journal Geophysics,2010,53(9):2171-2180.
[21]张智,刘有山,徐涛,等.弹性波逆时偏移中的稳定激发振幅成像条件[J].地球物理学报,2013,56(10):3523-3533.ZHANG Zhi,LIU Youshan,XU Tao,et al.A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation[J].Chinese Journal Geophysics,2013,56(10):3523-3533.
[22]SCHLEICHER J,COSTA J,NOVAIS A.A comparison of imaging conditions for wave-equation shot-profile migration[J].Geophysics,2008,73(6):S219-S227.
[23]CHATTOPADHYAY S,MCMECHAN G A.Imaging conditions for prestack reverse-time migration[J].Geophysics,2008,73(3):S81-S89.
[2]ALANI A M,ABOUTALEBI M,KILIC G.Applications of ground penetrating radar(GPR)in bridge deck monitoring and assessment[J].Journal of Applied Geophysics,2013,97(13):45-54.
[3]CHANG C W,LIN C H,LIEN H S.Measurement radius of reinforcing steel bar in concrete using digital image GPR[J].Construction and Building Materials,2009,23(2):1057-1063.
[4]SOLLA M,LORENZO H,RIAL F I,et al.GPR evaluation of the Roman masonry arch bridge of Lugo(Spain)[J].Nondestructive Testing and Evaluation International,2011,44(1):8-12.
[5]戴前伟,冯德山,何继善.Kirchhoff偏移法在探地雷达正演图像处理中的应用[J].地球物理学进展,2005,20(3):849-853.DAI Qianwei,FENG Deshan,HE Jishan.The application of Kirchhoff's migration method in the image processing of the ground penetrating radar forward simulation[J].Progress in Geophysics,2005,20(3):849-853.
[6]BITRI A,GRANDJEAN G.Frequency-wavenumber modelling and migration of 2D GPR data in moderately heterogeneous dispersive media[J].Geophysical Prospecting,1998,46(3):287-301.
[7]雷林林,刘四新,傅磊,等.基于全波形反演的探地雷达数据逆时偏移成像[J].地球物理学报,2015,58(9):3346-3355.LEI Linlin,LIU Sixin,FU Lei,et al.Reverse time migration applied to GPR data based on full wave inversion[J].Chinese Journal of Geophysics,2015,58(9):3346-3355.
[8]朱尉强,黄清华.探地雷达衰减补偿逆时偏移成像方法[J].地球物理学报,2016,59(10):3909-3916.ZHU Weiqiang,HUANG Qinghua.Attenuation compensated reverse time migration method of ground penetrating radar signals[J].Chinese Journal of Geophysics,2016,59(10):3909-3916.
[9]FISHER E,MCMECHAN G A,ANNAN A P,et al.Examples of reverse-time migration of single-channel,ground-penetrating radar profiles[J].Geophysics,1992,57(4):577-586.
[10]LEUSCHEN C,PLUMB R.A matched-filter approach to wave migration[J].Journal of Applied Geophysics,2000,43(2):271-280.
[11]ZHOU H,SATO M,LIU H.Migration velocity analysis and prestack migration of common-transmitter GPR data[J].IEEE Transactions on Geoscience and Remote Sensing,2005,43(1):86-91.
[12]冯德山,戴前伟.基于小波多分辨探地雷达三维正演模拟及偏移处理[J].中南大学学报(自然科学版),2007,38(4):758-763.FENG Deshan,DAI Qianwei.GPR three dimension forward simulation and migration processing with multi-resolution of wavelets[J].Journal of Central South University(Science and Technology),2007,38(4):758-763.
[13]BRADFORD J H.Reverse-time prestack depth migration of GPR data from topography for amplitude reconstruction in complex environments[J].Journal of Earth Science,2015,26(6):791-798.
[14]戴前伟,张彬,冯德山,等.探地雷达各向异性介质有限差分偏移线性变换[J].中南大学学报(自然科学版),2012,43(5):1814-1820.DAI Qianwei,ZHANG Bin,FENG Deshan,et al.Linear transformation of finite difference migration of GPR in anisotropic medium[J].Journal of Central South University(Science and Technology),2012,43(5):1814-1820.
[15]傅磊,刘四新,刘澜波,等.机载探地雷达数值模拟及逆时偏移成像[J].地球物理学报,2014,57(5):1636-1646.FU Lei,LIU Sixin,LIU Lanbo,et al.Airborne ground penetrating radar numerical simulation and reverse time migration[J].Chinese Journal Geophysics,2014,57(5):1636-1646.
[16]LIU Sixin,LEI Linlin,FU Lei,et al.Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data[J].Journal of Applied Geophysics,2014,107(4):1-7.
[17]CLAERBOUT J F,JOHNSON A G.Extrapolation of time-dependent waveforms along their Path of Propagation[J].Geophysical Journal International,1971,26(1/2/3/4):285-293.
[18]戴前伟,王洪华,冯德山,等.基于双二次插值的探地雷达有限元数值模拟[J].地球物理学进展,2012,27(2):736-743.DAI Qianwei,WANG Honghua,FENG Deshan,et al.Finite element numerical simulation for GPR based on quadratic interpolation[J].Progress in Geophysics,2012,27(2):736-743.
[19]DROSSAERT F H,GIANNOPOULOS A.A nonsplit complex frequency-shifted PML based on recursive integration for FDTD modeling of elastic waves[J].Geophysics,2007,72(2):T9-T17.
[20]刘红伟,刘洪,邹振,等.地震叠前逆时偏移中的去噪与存储[J].地球物理学报,2010,53(9):2171-2180.LIU Hongwei,LIU Hong,ZHOU Zhen,et al.The problems of denoise and storage in seismic reverse time migration[J].Chinese Journal Geophysics,2010,53(9):2171-2180.
[21]张智,刘有山,徐涛,等.弹性波逆时偏移中的稳定激发振幅成像条件[J].地球物理学报,2013,56(10):3523-3533.ZHANG Zhi,LIU Youshan,XU Tao,et al.A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation[J].Chinese Journal Geophysics,2013,56(10):3523-3533.
[22]SCHLEICHER J,COSTA J,NOVAIS A.A comparison of imaging conditions for wave-equation shot-profile migration[J].Geophysics,2008,73(6):S219-S227.
[23]CHATTOPADHYAY S,MCMECHAN G A.Imaging conditions for prestack reverse-time migration[J].Geophysics,2008,73(3):S81-S89.