低频缺失下跨孔雷达包络波形反演
|
摘要
全波形反演方法作为一种高分辨率成像手段在跨孔雷达反演中得到有效应用,但其仍受局部最小问题影响。一个有效的解决方法是为反演提供一个准确的初始模型。但在应用真实雷达数据时,由于地下介质未知且存在低频数据缺失的情况,全波形反演往往难以获得理想结果。为此,使用对包络目标函数求导的方法,详细推导了包络波形反演的梯度公式。该方法与传统全波形反演方法在原始数据低频成分缺失情况下的反演结果对比表明,该方法能够有效还原缺失的低频信息并且对低频缺失数据有更好的反演能力,可以直接为地下介质提供定量解释。
The full waveform inversion(FWI)has been used as a high resolution imaging method for cross-hole radar inversion;however,it is still trapped by local minimum.An effective way is to provide an accurate initial model for FWI.The fact is that the underground media is unknown,and the lowfrequency information are usually not available in the GPR field data,which lead to difficult to achieve accurate result in FWI.The gradient formula of envelope waveform inversion(EWI)is deduced in detail by using the method of derivation of the envelope objective function.In comparison with the inversionresult of the traditional FWI,the EWI has a better inversion ability for low-frequency missing data,and can effectively restore the missing low-frequency information.It can provide quantitative interpretation for subsurface media.
The full waveform inversion(FWI)has been used as a high resolution imaging method for cross-hole radar inversion;however,it is still trapped by local minimum.An effective way is to provide an accurate initial model for FWI.The fact is that the underground media is unknown,and the lowfrequency information are usually not available in the GPR field data,which lead to difficult to achieve accurate result in FWI.The gradient formula of envelope waveform inversion(EWI)is deduced in detail by using the method of derivation of the envelope objective function.In comparison with the inversionresult of the traditional FWI,the EWI has a better inversion ability for low-frequency missing data,and can effectively restore the missing low-frequency information.It can provide quantitative interpretation for subsurface media.
引文
[1]Tarantola A.Inversion of Seismic-Reflection Data in the Acoustic Approximation[J].Geophysics,1984,49:1259-1266.
[2]Pratt R G,Shin C,Hicks G J.Gauss-Newton and Full Newton Methods in Frequency Domain Seismic Waveform Inversion[J].Geophysical Journal International,1998,133:341-362.
[3]Pratt R G.Seismic Waveform Inversion in the Frequency Domai:Part 1:Theory and Verification in a Physical Scale Model[J].Geophysics,1999,64:888-901.
[4]Pratt R G,Shipp R M.Seismic Waveform Inversion in the Frequency Domain:Part 2:Fault Delineation in Sediments Using Crosshole Data[J].Geophysics,1999,64:902-914.
[5]冯晅,鲁晓满,刘财,等.基于逐减随机震源采样法的频率域二维黏滞声波方程全波形反演[J].吉林大学学报(地球科学版),2016,46(6):1865-1873.Feng Xuan,Lu Xiaoman,Liu Cai,et al.FrequencyDomain Full Waveform Inversion of 2D Viscous Acoustic Wave Equation Using Decreasing Random Shot Subsampling Method[J].Journal of Jilin University(Earth Science Edition),2016,46(6):1865-1873.
[6]Kuroda S,Takeuchi M,Kim H J.Full Waveform Inversion Algorithm for Interpreting Cross-Borehole GPR Data[J].Seg Technical Program Expanded Abstracts,1949,24(1):2668.
[7]Ernst J R,Maurer H,Green A G,et al.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,2007,45(9):2807-2828.
[8]Meles G A,Kruk J V D,Greenhalgh S A,et al.A New Vector Waveform Inversion Algorithm for Simultaneous Updating of Conductivity and Permittivity Parameters from Combination Crosshole/Borehole-to-Surface GPR Data[J].IEEE Transactions on Geoscience and Remote Sensing,2010,48(9):3391-3407.
[9]吴俊军,刘四新,李彦鹏,等.跨孔雷达全波形反演成像方法的研究[J].地球物理学报,2014,57(5):1623-1635.Wu Junjun,Liu Sixin,Li Yanpeng,et al.Study of Cross-Hole Radar Tomography Using FullWaveform Inversion[J].Chinese Journal of Geophysics,2014,57(5):1623-1635.
[10]孟旭,刘四新,傅磊,等.基于对数目标函数的跨孔雷达频域波形反演[J].地球物理学报,2016,59(5):1875-1887.Meng Xu,Liu Sixin,Fu Lei,et al.Frequency Domain Waveform Inversion of Cross-Hole GPR Data Based on a Logarithmic Objective Function[J].Chinese Journal of Geophysics,2016,59(5):1875-1887.
[11]Ernst J R,Green A G,Maurer H,et al.Application of a New 2D Time-Domain Full-Waveform Inversion Scheme to Crosshole Radar Data[J].Geophysics,2007,72(5):J53-J64.
[12]Virieux J,Operto S.An Overview of FullWaveform Inversion in Exploration Geophysics[J].Geophysics,2009,74(6),WCC1-WCC26.
[13]Bozdaˇg E,Trampert J,Tromp J.Misfit Functions for Full Waveform Inversion Based on Instantaneous Phase and Envelope Measurements[J].Geophysical Journal International,2011,185(2):845-870.
[14]Chi B X,Dong L G,Liu Y Z.Full Waveform Inversion Based on Envelope Objective Function[C]//75th EAGE Conference&Exhibition Incorporating Spe Europec 2013.London:EAGE,2013.
[15]Chi B X,Dong L G,Liu Y Z.Full Waveform Inversion Method Using Envelope Objective Function Without Low Frequency Data[J].Journal of Applied Geophysics,2014,109:36-46.
[16]Wu R S,Luo J R,Wu B Y.Seismic Envelope Inversion and Modulation Signal Model[J].Geophysics,2014,79(3):WA13-WA21.
[2]Pratt R G,Shin C,Hicks G J.Gauss-Newton and Full Newton Methods in Frequency Domain Seismic Waveform Inversion[J].Geophysical Journal International,1998,133:341-362.
[3]Pratt R G.Seismic Waveform Inversion in the Frequency Domai:Part 1:Theory and Verification in a Physical Scale Model[J].Geophysics,1999,64:888-901.
[4]Pratt R G,Shipp R M.Seismic Waveform Inversion in the Frequency Domain:Part 2:Fault Delineation in Sediments Using Crosshole Data[J].Geophysics,1999,64:902-914.
[5]冯晅,鲁晓满,刘财,等.基于逐减随机震源采样法的频率域二维黏滞声波方程全波形反演[J].吉林大学学报(地球科学版),2016,46(6):1865-1873.Feng Xuan,Lu Xiaoman,Liu Cai,et al.FrequencyDomain Full Waveform Inversion of 2D Viscous Acoustic Wave Equation Using Decreasing Random Shot Subsampling Method[J].Journal of Jilin University(Earth Science Edition),2016,46(6):1865-1873.
[6]Kuroda S,Takeuchi M,Kim H J.Full Waveform Inversion Algorithm for Interpreting Cross-Borehole GPR Data[J].Seg Technical Program Expanded Abstracts,1949,24(1):2668.
[7]Ernst J R,Maurer H,Green A G,et al.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,2007,45(9):2807-2828.
[8]Meles G A,Kruk J V D,Greenhalgh S A,et al.A New Vector Waveform Inversion Algorithm for Simultaneous Updating of Conductivity and Permittivity Parameters from Combination Crosshole/Borehole-to-Surface GPR Data[J].IEEE Transactions on Geoscience and Remote Sensing,2010,48(9):3391-3407.
[9]吴俊军,刘四新,李彦鹏,等.跨孔雷达全波形反演成像方法的研究[J].地球物理学报,2014,57(5):1623-1635.Wu Junjun,Liu Sixin,Li Yanpeng,et al.Study of Cross-Hole Radar Tomography Using FullWaveform Inversion[J].Chinese Journal of Geophysics,2014,57(5):1623-1635.
[10]孟旭,刘四新,傅磊,等.基于对数目标函数的跨孔雷达频域波形反演[J].地球物理学报,2016,59(5):1875-1887.Meng Xu,Liu Sixin,Fu Lei,et al.Frequency Domain Waveform Inversion of Cross-Hole GPR Data Based on a Logarithmic Objective Function[J].Chinese Journal of Geophysics,2016,59(5):1875-1887.
[11]Ernst J R,Green A G,Maurer H,et al.Application of a New 2D Time-Domain Full-Waveform Inversion Scheme to Crosshole Radar Data[J].Geophysics,2007,72(5):J53-J64.
[12]Virieux J,Operto S.An Overview of FullWaveform Inversion in Exploration Geophysics[J].Geophysics,2009,74(6),WCC1-WCC26.
[13]Bozdaˇg E,Trampert J,Tromp J.Misfit Functions for Full Waveform Inversion Based on Instantaneous Phase and Envelope Measurements[J].Geophysical Journal International,2011,185(2):845-870.
[14]Chi B X,Dong L G,Liu Y Z.Full Waveform Inversion Based on Envelope Objective Function[C]//75th EAGE Conference&Exhibition Incorporating Spe Europec 2013.London:EAGE,2013.
[15]Chi B X,Dong L G,Liu Y Z.Full Waveform Inversion Method Using Envelope Objective Function Without Low Frequency Data[J].Journal of Applied Geophysics,2014,109:36-46.
[16]Wu R S,Luo J R,Wu B Y.Seismic Envelope Inversion and Modulation Signal Model[J].Geophysics,2014,79(3):WA13-WA21.