基于广义模型约束的时间域航空电磁反演研究
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摘要
由于航空电磁具有海量数据,因此快速有效的成像和反演手段至关重要.本文针对层状介质模型推导与实现了广义模型约束条件下时间域航空电磁一维反演.从正则化反演的目标函数出发,通过改变模型约束项构造Lp范数反演和聚焦反演,进而通过改变模型求解域构造出基于小波变换的稀疏约束反演.针对不同反演方法目标函数的构建方式,本文进一步从数学原理上分析不同反演方法的预期效果,并通过理论模型和实测数据进行验证.结果表明L0.8范数反演、聚焦反演和基于小波变换的稀疏约束反演可以得到更符合地下层状介质陡变界面的反演结果.
Since Airborne Electromagnetic(AEM)survey produces massive data,an effective imaging and inversion tool is very important.In this work,we take a layered earth model as an example to derive the one-dimensional(1D)time-domain AEM inversion under generalized model constraints.Starting from the objective functional for the regularized inversion,we establish the Lp-norm inversion and focusing inversion by changing the model constraints,and the sparse constraint inversion based on wavelet transform by changing the model solution domain.Further we mathematically analyze the effectiveness of different inversion methods taking into account the structures of their objective functions and verify our conclusions via both a synthetic model and survey data.Results show that for a layered earth model with distinct layer interfaces,the L0.8-norm inversion,focusing inversion,and sparse constraint inversion based on wavelet transform can obtain the subsurface structures such as steep interfaces that are more close to real ones.
Since Airborne Electromagnetic(AEM)survey produces massive data,an effective imaging and inversion tool is very important.In this work,we take a layered earth model as an example to derive the one-dimensional(1D)time-domain AEM inversion under generalized model constraints.Starting from the objective functional for the regularized inversion,we establish the Lp-norm inversion and focusing inversion by changing the model constraints,and the sparse constraint inversion based on wavelet transform by changing the model solution domain.Further we mathematically analyze the effectiveness of different inversion methods taking into account the structures of their objective functions and verify our conclusions via both a synthetic model and survey data.Results show that for a layered earth model with distinct layer interfaces,the L0.8-norm inversion,focusing inversion,and sparse constraint inversion based on wavelet transform can obtain the subsurface structures such as steep interfaces that are more close to real ones.
引文
Auken E,Christiansen A V.2004.Layered and laterally constrained 2D inversion of resistivity data.Geophysics,69(3):752-761.
Auken E,Christiansen A V,Jacobsen L H,et al.2008.A resolution study of buried valleys using laterally constrained inversion of TEMdata.Journal of Applied Geophysics,65(1):10-20.
Cai J,Qi Y F,Yin C C.2014.Weighted Laterally-constrained inversion of frequency-domain airborne EM data.Chinese J.Geophys.(in Chinese),57(3):953-960,doi:10.6038/cjg20140324.
Chen T Y,Hodges G,Miles P.2015.MULTIPULSE-high resolution and high power in one TDEM system.Exploration Geophysics,46(1):49-57.
Chiao L Y,Kuo B Y.2001.Multiscale seismic tomography.Geophysical Journal International,145(2):517-527.
Constable S C,Parker R L,Constable C G.1987.Occam′s inversion:A practical algorithm for generating smooth models from electromagnetic sounding data.Geophysics,52(3):289-300.
Donoho D L.2006.For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution.Communications on Pure and Applied Mathematics,59(6):797-829.
Ekblom H.1987.The L1-estimate as limiting case of an Lp-or Huber-estimate.∥Doge Y.Statistical Data Analysis based on the L1-Norm and Related Methods.Amsterdam:Elsevier,109-116.
Farquharson C G.2008.Constructing piecewise-constant models in multidimensional minimum-structure inversion.Geophysics,73(1):K1-K9.
Farquharson C G,Oldenburg D W.1998.Non-linear inversion using general measures of data misfit and model structure.Geophysical Journal International,134(1):213-227.
Farquharson C G,Oldenburg D W.2003.Constructing piece-wise-constant models using general measures in non-linear,minimumstructure inversion algorithms.∥6th International Symposium,Society of Exploration Geophysicists of Japan,Expanded Abstracts,240-243.
Last B J,Kubik K.1983.Compact gravity inversion.Geophysics,48(6):713-721.
Loke M H,Acworth I,Dahlin T.2003.A comparison of smooth and blocky inversion methods in 2Delectrical imaging surveys.Exploration Geophysics,34(3):182-187.
Portniaguine O,Zhdanov M S.1999.Focusing geophysical inversion images.Geophysics,64(3):874-887.
Portniaguine O,Zhdanov M S.2002.3-D magnetic inversion with data compression and image focusing.Geophysics,67(5):1532-1541.
Press W H,Teukolsky S A,Vetterling W T,et al.1996.Numerical Recipes in Fortran 90:The Art of Parallel Scientific Computing.Cambridge:Cambridge University Press.
Xu Y X,Wang J Y.1998.A multiresolution inversion of onedimensional magnetotelluric data.Acta Geophysica Sinica(in Chinese),41(5):704-711.
Yin C C,Hodges G.2007.Simulated annealing for airborne EMinversion.Geophysics,72(4):F189-F195.
Yin C C,Qi Y F,Liu Y H,et al.2014.Trans-dimensional Bayesian inversion of frequency-domain airborne EM data.Chinese J.Geophys.(in Chinese),57(9):2971-2980,doi:10.6038/cjg20140922.
Yin C C,Zhang B,Liu Y H,et al.2015.Review on airborne EMtechnology and developments.Chinese J.Geophys.(in Chinese),58(8):2637-2653,doi:10.6038/cjg20150804.
Zhdanov M S.2009.New advances in regularized inversion of gravity and electromagnetic data.Geophysical Prospecting,57(4):463-478.
蔡晶,齐彦福,殷长春.2014.频率域航空电磁数据的加权横向约束反演.地球物理学报,57(3):953-960,doi:10.6038/cjg20140324.
徐义贤,王家映.1998.大地电磁的多尺度反演.地球物理学报,41(5):704-711.
殷长春,齐彦福,刘云鹤等.2014.频率域航空电磁数据变维数贝叶斯反演研究.地球物理学报,57(9):2971-2980,doi:10.6038/cjg20140922.
殷长春,张博,刘云鹤等.2015.航空电磁勘查技术发展现状及展望.地球物理学报,58(8):2637-2653,doi:10.6038/cjg20150804.
Auken E,Christiansen A V,Jacobsen L H,et al.2008.A resolution study of buried valleys using laterally constrained inversion of TEMdata.Journal of Applied Geophysics,65(1):10-20.
Cai J,Qi Y F,Yin C C.2014.Weighted Laterally-constrained inversion of frequency-domain airborne EM data.Chinese J.Geophys.(in Chinese),57(3):953-960,doi:10.6038/cjg20140324.
Chen T Y,Hodges G,Miles P.2015.MULTIPULSE-high resolution and high power in one TDEM system.Exploration Geophysics,46(1):49-57.
Chiao L Y,Kuo B Y.2001.Multiscale seismic tomography.Geophysical Journal International,145(2):517-527.
Constable S C,Parker R L,Constable C G.1987.Occam′s inversion:A practical algorithm for generating smooth models from electromagnetic sounding data.Geophysics,52(3):289-300.
Donoho D L.2006.For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution.Communications on Pure and Applied Mathematics,59(6):797-829.
Ekblom H.1987.The L1-estimate as limiting case of an Lp-or Huber-estimate.∥Doge Y.Statistical Data Analysis based on the L1-Norm and Related Methods.Amsterdam:Elsevier,109-116.
Farquharson C G.2008.Constructing piecewise-constant models in multidimensional minimum-structure inversion.Geophysics,73(1):K1-K9.
Farquharson C G,Oldenburg D W.1998.Non-linear inversion using general measures of data misfit and model structure.Geophysical Journal International,134(1):213-227.
Farquharson C G,Oldenburg D W.2003.Constructing piece-wise-constant models using general measures in non-linear,minimumstructure inversion algorithms.∥6th International Symposium,Society of Exploration Geophysicists of Japan,Expanded Abstracts,240-243.
Last B J,Kubik K.1983.Compact gravity inversion.Geophysics,48(6):713-721.
Loke M H,Acworth I,Dahlin T.2003.A comparison of smooth and blocky inversion methods in 2Delectrical imaging surveys.Exploration Geophysics,34(3):182-187.
Portniaguine O,Zhdanov M S.1999.Focusing geophysical inversion images.Geophysics,64(3):874-887.
Portniaguine O,Zhdanov M S.2002.3-D magnetic inversion with data compression and image focusing.Geophysics,67(5):1532-1541.
Press W H,Teukolsky S A,Vetterling W T,et al.1996.Numerical Recipes in Fortran 90:The Art of Parallel Scientific Computing.Cambridge:Cambridge University Press.
Xu Y X,Wang J Y.1998.A multiresolution inversion of onedimensional magnetotelluric data.Acta Geophysica Sinica(in Chinese),41(5):704-711.
Yin C C,Hodges G.2007.Simulated annealing for airborne EMinversion.Geophysics,72(4):F189-F195.
Yin C C,Qi Y F,Liu Y H,et al.2014.Trans-dimensional Bayesian inversion of frequency-domain airborne EM data.Chinese J.Geophys.(in Chinese),57(9):2971-2980,doi:10.6038/cjg20140922.
Yin C C,Zhang B,Liu Y H,et al.2015.Review on airborne EMtechnology and developments.Chinese J.Geophys.(in Chinese),58(8):2637-2653,doi:10.6038/cjg20150804.
Zhdanov M S.2009.New advances in regularized inversion of gravity and electromagnetic data.Geophysical Prospecting,57(4):463-478.
蔡晶,齐彦福,殷长春.2014.频率域航空电磁数据的加权横向约束反演.地球物理学报,57(3):953-960,doi:10.6038/cjg20140324.
徐义贤,王家映.1998.大地电磁的多尺度反演.地球物理学报,41(5):704-711.
殷长春,齐彦福,刘云鹤等.2014.频率域航空电磁数据变维数贝叶斯反演研究.地球物理学报,57(9):2971-2980,doi:10.6038/cjg20140922.
殷长春,张博,刘云鹤等.2015.航空电磁勘查技术发展现状及展望.地球物理学报,58(8):2637-2653,doi:10.6038/cjg20150804.