地质雷达有限差分逆时偏移方法研究
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摘要
地质雷达技术是用于研究水文、环境与气候变化等重大科学问题最有效的地球物理技术之一,并广泛应用于检测道路和建筑内部结构,探测冻土层、沙漠沙丘演化特征,进行地质灾害和考古探测等.具有探测速度快、分辨率高和探测结果直观成像的优势.但由于受到介质横向速度变化,孤立块体的绕射波和倾斜界面复杂反射波的影响等,在雷达探测剖面上经常难以真实地反映地下目标体的空间位置和形态.偏移处理技术可以提高成像的真实性.逆时偏移能有效地利用回转波、多次波成像,使反射波准确归位,绕射波完全收敛,是一种受横向变化影响小,倾斜界面成像精度高的偏移方法.本文推导出基于麦克斯韦方程组TM波方程的有限差分格式、稳定性条件和PML边界条件,并编程实现有限差分零偏移距逆时偏移算法.两层模型和空洞模型的逆时偏移剖面与对应的原速度模型完全相同,有效地验证了有限差分零偏移距逆时偏移算法的准确性.相比于两层模型和空洞模型的Kirchhoff偏移剖面,逆时偏移剖面能更有效地提高垂直界面和空洞底界面的成像分辨率,更真实地反映两层模型和空洞模型的空间形态和内部结构信息.
Ground-penetrating radar( GPR) is one most effectively technology of researching some unify scientific problem,such as hydrology,environment,climate change,disaster and archaeology etc. It can detect engineering construction,road,building internal structure,permafrost layer and internal structure of desert. It has some advantages,including rapid detection,higher resolution and directly-vision imaging. However,Due to have influence on the change of lateral radar velocity,the diffraction of isolated block,it's difficult to effectively reflect the inner fine structure at subsurface from GPR section. The process of migration can improve the resolution. Combined with traditional Kirchhoff migration,reverse time migration( RTM) can effectively use reverse branch wave and multiple-wave to image subsurface,make the underground reflection point information back to properly position reflections,and the reflection wave simultaneously,the diffraction wave automatic convergence,which can adapt to medium of lateral velocity changes and high resolution for imaging to dip interface. In this paper,we deduced the finite-difference scheme of TM wave equation from Maxwell's equations,stability and PML boundary condition. The result of RTM imaging of two layers model and cavitas model are same with the original their velocity model,respectively,which can demonstrate the accurate of the finite-difference zero-offset RTM algorithm. Combined with Kirchhoff migration section of two layers model and cavitas model, RTM sections can more effectively improve the resolution of the vertical interface and bottom boundary of cavitas,and can more really reflect the space position and inner structure of two layers model and cavitas model.
Ground-penetrating radar( GPR) is one most effectively technology of researching some unify scientific problem,such as hydrology,environment,climate change,disaster and archaeology etc. It can detect engineering construction,road,building internal structure,permafrost layer and internal structure of desert. It has some advantages,including rapid detection,higher resolution and directly-vision imaging. However,Due to have influence on the change of lateral radar velocity,the diffraction of isolated block,it's difficult to effectively reflect the inner fine structure at subsurface from GPR section. The process of migration can improve the resolution. Combined with traditional Kirchhoff migration,reverse time migration( RTM) can effectively use reverse branch wave and multiple-wave to image subsurface,make the underground reflection point information back to properly position reflections,and the reflection wave simultaneously,the diffraction wave automatic convergence,which can adapt to medium of lateral velocity changes and high resolution for imaging to dip interface. In this paper,we deduced the finite-difference scheme of TM wave equation from Maxwell's equations,stability and PML boundary condition. The result of RTM imaging of two layers model and cavitas model are same with the original their velocity model,respectively,which can demonstrate the accurate of the finite-difference zero-offset RTM algorithm. Combined with Kirchhoff migration section of two layers model and cavitas model, RTM sections can more effectively improve the resolution of the vertical interface and bottom boundary of cavitas,and can more really reflect the space position and inner structure of two layers model and cavitas model.
引文
Arcone S A,Lawson D E,Delaney A J,et al.1998.Groundpenetratinng radar reflection profiling of groundwater and bedrock in an area of discontinuous permafrost[J].Geophysics,63(5):1573-1584.
Arcone S A,Prentice M L,Delaney A J.2002.Stratigraphic profiling with ground-penetrating radar in permafrost:A review of possible analogs for Mars[J].Journal of Geophysical Research,107(E11):5108.
Bradford J.2015.Reverse-time prestack depth migration of GPR data from topography for amplitude reconstruction in complex environments[J].Journal of Earth Science,26(6):791-798.
Bristow C,Pugh J,Goodall T.1996.Internal structure of aeolian dunes in Abu Dhabi determined using ground-penetrating radar[J].Sedimentology,43(6):995-1003.
Bristow C S,Bailey S D,Lancaster N.2000.The sedimentary structure of linear sand dunes[J].Nature,406(6791):56-59.
Brown J,Nichols J,Steinbronn L,et al.2009.Improved GPRinterpretation through resolution of lateral velocity heterogeneity:Example from an archaeological site investigation[J].Journal of Applied Geophysics,68(1):3-8.
Cai H.2014.Application of ground penetrating radar in detection of tunnel karst[J].Subgrade Engineering(in Chinese),(1):175-178.
Doolittle J A,Jenkinson B,Hopkins D,et al.2006.Hydropedological investigations with ground-penetrating radar(GPR):Estimating water-table depths and local ground-water flow pattern in areas of coarse-textured soils[J].Geoderma,131(3-4):317-329.
Feng X,Sato M.2004.Pre-stack migration applied to GPR for landmine detection[J].Inverse Problems,20(6):S99-S115.
Fisher E,Mc Mechan G A,Annan A P,et al.1992.Examples of reverse-time migration of single-channel,ground-penetrating radar profiles[J].Geophysics,57(4):577-586.
Ge D B,Yan Y B.2002.Finite-difference Time-domain Method for Electromagnetic Waves(in Chinese)[M].Xi’an:Xi’an University of Electronic Science and Technology Press.
Guitton A,Kaelin B,Biondi B.2007.Least-squares attenuation of reverse-time-migration artifacts[J].Geophysics,72(1):S19-S23.
Leuschen C J,Plumb R G.2001.A matched-filter-based reverse-time migration algorithm for ground-penetrating radar data[J].IEEETransactions on Geoscience and Remote Sensing,39(5):929-936.
Li S W,Fomel S.2013.Kirchhoff migration using eikonal-based computation of traveltime source derivatives[J].Geophysics,78(4):S211-S219.
Liao H J,Zhu Q N,Zan Y W,et al.2016.Detection of ballastless track diseases in high-speed railway based on ground penetrating radar[J].Journal of Southwest Jiaotong University(in Chinese),51(1):8-13.
Liu L B,Qian R Y.2015.Ground penetrating radar:A critical tool in near-surface geophysics[J].Chinese Journal of Geophysics(in Chinese),58(8):2606-2617,doi:10.6038/cjg20150802.
Liu S X,Lei L L,Fu L,et al.2014.Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data[J].Journal of Applied Geophysics,107:1-7.
Liu Y,Li C C,Mou Y G.1998.Finite-difference numerical modeling of any even-order accuracy[J].Oil Geophysical Prospecting,33(1):1-10.
Livingstone I,Wiggs G F S,Weaver C M.2007.Geomorphology of desert sand dunes:A review of recent progress[J].Earth Science Reviews,80(3-4):239-257.
Merz K,Maurer H,Buchli T,et al.2015.Evaluation of ground-based and helicopter ground-penetrating radar data acquired across an alpine rock glacier[J].Permafrost and Periglacial Processes,26(1):13-27.
Moran M L,Greenfield R J,Arcone S A,et al.2000.Multidimensional GPR array processing using Kirchhoff migration[J].Journal of Applied Geophysics,43(2-4):281-295.
Sakamoto T,Sato T,Aubry P J,et al.2015.Ultra-wideband radar imaging using a hybrid of Kirchhoff migration and Stolt F-K migration with an inverse boundary scattering transform[J].IEEETransactions on Antennas and Propagation,63(8):3502-3512.
Sanada Y,Ashida Y.1999.An imaging algorithm for GPR data[C].//Symposium on the Application of Geophysics to Engineering and Environmental Problems 1999.Tulsa,OK:Environment and Engineering Geophysical Society,565-573.
Sun R,Mc Mechan G A.2011.Prestack 2D parsimonious Kirchhoff depth migration of elastic seismic data[J].Geophysics,76(4):S157-S164.
Sun R,Mc Mechan G A,Lee C S,et al.2006.Prestack scalar reversetime depth migration of 3D elastic seismic data[J].Geophysics,71(5):S199-S207.
Wainstein P,Moorman B,Whitehead K.2014.Glacial conditions that contribute to the regeneration of Fountain Glacier proglacial icing,Bylot Island,Canada[J].Hydrological Processes,28(5):2749-2760.
Yan H Y,Liu Y.2013.Acoustic prestack reverse time migration using the adaptive high-order finite-difference method in the time-space domain[J].Chinese Journal of Geophysics,56(3):181-195.
Zhang Y,Sun J.2009.Practical issues in reverse time migration:True amplitude gathers,noise removal and harmonic source encoding[J].First Break,26:29-35.
Zhou H,Sato M,Liu H J.2005.Migration velocity analysis and prestack migration of common-transmitter GPR data[J].IEEETransactions on Geoscience and Remote Sensing,43(1):86-91.
蔡晖.2014.探地雷达在隧道岩溶探测中的应用[J].路基工程,(1):175-178.
葛德彪,闫玉波.2002.电磁波时域有限差分方法[M].西安:西安电子科技大学出版社.
廖红建,朱庆女,昝月稳,等.2016.基于探地雷达的高铁无砟轨道结构层病害检测[J].西南交通大学学报,51(1):8-13.
刘澜波,钱荣毅.2015.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,58(5):2606-2617,doi:10.6038/cjg20150802.
Arcone S A,Prentice M L,Delaney A J.2002.Stratigraphic profiling with ground-penetrating radar in permafrost:A review of possible analogs for Mars[J].Journal of Geophysical Research,107(E11):5108.
Bradford J.2015.Reverse-time prestack depth migration of GPR data from topography for amplitude reconstruction in complex environments[J].Journal of Earth Science,26(6):791-798.
Bristow C,Pugh J,Goodall T.1996.Internal structure of aeolian dunes in Abu Dhabi determined using ground-penetrating radar[J].Sedimentology,43(6):995-1003.
Bristow C S,Bailey S D,Lancaster N.2000.The sedimentary structure of linear sand dunes[J].Nature,406(6791):56-59.
Brown J,Nichols J,Steinbronn L,et al.2009.Improved GPRinterpretation through resolution of lateral velocity heterogeneity:Example from an archaeological site investigation[J].Journal of Applied Geophysics,68(1):3-8.
Cai H.2014.Application of ground penetrating radar in detection of tunnel karst[J].Subgrade Engineering(in Chinese),(1):175-178.
Doolittle J A,Jenkinson B,Hopkins D,et al.2006.Hydropedological investigations with ground-penetrating radar(GPR):Estimating water-table depths and local ground-water flow pattern in areas of coarse-textured soils[J].Geoderma,131(3-4):317-329.
Feng X,Sato M.2004.Pre-stack migration applied to GPR for landmine detection[J].Inverse Problems,20(6):S99-S115.
Fisher E,Mc Mechan G A,Annan A P,et al.1992.Examples of reverse-time migration of single-channel,ground-penetrating radar profiles[J].Geophysics,57(4):577-586.
Ge D B,Yan Y B.2002.Finite-difference Time-domain Method for Electromagnetic Waves(in Chinese)[M].Xi’an:Xi’an University of Electronic Science and Technology Press.
Guitton A,Kaelin B,Biondi B.2007.Least-squares attenuation of reverse-time-migration artifacts[J].Geophysics,72(1):S19-S23.
Leuschen C J,Plumb R G.2001.A matched-filter-based reverse-time migration algorithm for ground-penetrating radar data[J].IEEETransactions on Geoscience and Remote Sensing,39(5):929-936.
Li S W,Fomel S.2013.Kirchhoff migration using eikonal-based computation of traveltime source derivatives[J].Geophysics,78(4):S211-S219.
Liao H J,Zhu Q N,Zan Y W,et al.2016.Detection of ballastless track diseases in high-speed railway based on ground penetrating radar[J].Journal of Southwest Jiaotong University(in Chinese),51(1):8-13.
Liu L B,Qian R Y.2015.Ground penetrating radar:A critical tool in near-surface geophysics[J].Chinese Journal of Geophysics(in Chinese),58(8):2606-2617,doi:10.6038/cjg20150802.
Liu S X,Lei L L,Fu L,et al.2014.Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data[J].Journal of Applied Geophysics,107:1-7.
Liu Y,Li C C,Mou Y G.1998.Finite-difference numerical modeling of any even-order accuracy[J].Oil Geophysical Prospecting,33(1):1-10.
Livingstone I,Wiggs G F S,Weaver C M.2007.Geomorphology of desert sand dunes:A review of recent progress[J].Earth Science Reviews,80(3-4):239-257.
Merz K,Maurer H,Buchli T,et al.2015.Evaluation of ground-based and helicopter ground-penetrating radar data acquired across an alpine rock glacier[J].Permafrost and Periglacial Processes,26(1):13-27.
Moran M L,Greenfield R J,Arcone S A,et al.2000.Multidimensional GPR array processing using Kirchhoff migration[J].Journal of Applied Geophysics,43(2-4):281-295.
Sakamoto T,Sato T,Aubry P J,et al.2015.Ultra-wideband radar imaging using a hybrid of Kirchhoff migration and Stolt F-K migration with an inverse boundary scattering transform[J].IEEETransactions on Antennas and Propagation,63(8):3502-3512.
Sanada Y,Ashida Y.1999.An imaging algorithm for GPR data[C].//Symposium on the Application of Geophysics to Engineering and Environmental Problems 1999.Tulsa,OK:Environment and Engineering Geophysical Society,565-573.
Sun R,Mc Mechan G A.2011.Prestack 2D parsimonious Kirchhoff depth migration of elastic seismic data[J].Geophysics,76(4):S157-S164.
Sun R,Mc Mechan G A,Lee C S,et al.2006.Prestack scalar reversetime depth migration of 3D elastic seismic data[J].Geophysics,71(5):S199-S207.
Wainstein P,Moorman B,Whitehead K.2014.Glacial conditions that contribute to the regeneration of Fountain Glacier proglacial icing,Bylot Island,Canada[J].Hydrological Processes,28(5):2749-2760.
Yan H Y,Liu Y.2013.Acoustic prestack reverse time migration using the adaptive high-order finite-difference method in the time-space domain[J].Chinese Journal of Geophysics,56(3):181-195.
Zhang Y,Sun J.2009.Practical issues in reverse time migration:True amplitude gathers,noise removal and harmonic source encoding[J].First Break,26:29-35.
Zhou H,Sato M,Liu H J.2005.Migration velocity analysis and prestack migration of common-transmitter GPR data[J].IEEETransactions on Geoscience and Remote Sensing,43(1):86-91.
蔡晖.2014.探地雷达在隧道岩溶探测中的应用[J].路基工程,(1):175-178.
葛德彪,闫玉波.2002.电磁波时域有限差分方法[M].西安:西安电子科技大学出版社.
廖红建,朱庆女,昝月稳,等.2016.基于探地雷达的高铁无砟轨道结构层病害检测[J].西南交通大学学报,51(1):8-13.
刘澜波,钱荣毅.2015.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,58(5):2606-2617,doi:10.6038/cjg20150802.