全球地磁感应测深数据三维反演
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摘要
全球地磁感应测深能获得地幔转换带及下地幔上部的导电结构.但目前稀疏的地磁台站分布及部分台站的观测数据稳定性较差,影响了三维反演对地下电性结构的分辨力和反演可靠性.为此,区别于传统的L2-范数反演方法,本文提出并实现了基于L1-范数的地磁测深响应三维反演技术.在反演中,利用L1-范数度量数据预测误差,降低"飞点"数据的影响,将相关系数较小的C-响应估计也纳入反演数据中.三维正演模拟采用球坐标系下的交错网格有限差分法,反演采用有限内存拟牛顿法.文中利用指数概率密度分布函数构造非高斯噪声的合成数据,并采用棋盘模型对反演方法的可靠性进行了验证.之后,我们将本文提出的三维反演方法用于全球129个地磁观测台站的C-响应数据反演,结果表明在地幔转换带深部,中国东北地区为高导电异常,南欧和北非则均为高阻;夏威夷在900km以下为高导;菲律宾海及以东地区在转换带表现为明显的高阻,这些结果与前人研究结果一致.由于采用了更多的台站数据,我们的反演结果还发现一些新的异常:南美洲南端,转换带表现为明显的高导;澳大利亚东南部,地幔转换带深部,也存在一个明显的高导异常,这些异常分布和地震层析成像的低速区一致.因此,L1-范数三维反演能够充分利用全球C-响应数据信息,提高地磁测深对地球深部电性结构的分辨能力,更好的研究全球地幔电性结构.
Global geomagnetic depth sounding(GDS)permits to detect the electrical structure of mantle transition zone and the upper part of lower mantle.However,the resolution and reliability of 3-D GDS inversion are restricted by sparse distribution of observatories and rejection caused by records′poor stability.In this paper,a 3-D GDS inversion method based on L1-norm has been developed to solve the problem,which differs from the traditional L2-norm inversion.The algorithm uses L1-norm in the measure of data misfit when outliers occur in the data,soduring inversion process we could take C-responses with low coherency into account at a certain observatory.The L-BFGS inversion method is used and the forward solver is based on a staggered-grid finite difference method in frequency domain for spherical geometry.Non-Gaussian noise of synthetic data are generated by using an exponential probability density function,then a checkerboard model inversion test is performed to ensure the valid of our method.This 3-D inversion method is applied to C-responses of 129 selected observatories around the world.Results show high conductivity beneath Northeast of China and high resistivity in lower mantle transition beneath South Europe and North Africa,while high conductivity also exists below 900 km in Hawaii and high resistivity is registered beneath Philippine Sea and the East.These features are coincident with previous studies.Due to more observatories are used,our results present more anomalies,such as the high conductivity in the mantle transition zone beneath southern South America,and the high conductivity in the lower part of mantle transition zone of southeastern Australia.These anomalies coincide with the low velocity areas derived from seismic tomography.This work demonstrates that the L1-norm inversion method can make full use of observatories′records and improve exploratory resolution of deep electrical distribution of the Earth,contributing to further study of the global mantle structure.
Global geomagnetic depth sounding(GDS)permits to detect the electrical structure of mantle transition zone and the upper part of lower mantle.However,the resolution and reliability of 3-D GDS inversion are restricted by sparse distribution of observatories and rejection caused by records′poor stability.In this paper,a 3-D GDS inversion method based on L1-norm has been developed to solve the problem,which differs from the traditional L2-norm inversion.The algorithm uses L1-norm in the measure of data misfit when outliers occur in the data,soduring inversion process we could take C-responses with low coherency into account at a certain observatory.The L-BFGS inversion method is used and the forward solver is based on a staggered-grid finite difference method in frequency domain for spherical geometry.Non-Gaussian noise of synthetic data are generated by using an exponential probability density function,then a checkerboard model inversion test is performed to ensure the valid of our method.This 3-D inversion method is applied to C-responses of 129 selected observatories around the world.Results show high conductivity beneath Northeast of China and high resistivity in lower mantle transition beneath South Europe and North Africa,while high conductivity also exists below 900 km in Hawaii and high resistivity is registered beneath Philippine Sea and the East.These features are coincident with previous studies.Due to more observatories are used,our results present more anomalies,such as the high conductivity in the mantle transition zone beneath southern South America,and the high conductivity in the lower part of mantle transition zone of southeastern Australia.These anomalies coincide with the low velocity areas derived from seismic tomography.This work demonstrates that the L1-norm inversion method can make full use of observatories′records and improve exploratory resolution of deep electrical distribution of the Earth,contributing to further study of the global mantle structure.
引文
Avdeev D,Avdeeva A.2009.3D magnetotelluric inversion using a limited-memory quasi-newton optimization.Geophysics,74(3):F45-F57.
Banks R J.1969.Geomagnetic variations and the electrical conductivity of the upper mantle.Geophysical Journal International,17(5):457-487,doi:10.1111/j.1365-246X.1969.tb00252.x.
Booker J R,Favetto A,Pomposiello M C.2004.Low electrical resistivity associated with plunging of the Nazca flat slab beneath Argentina.Nature,429(6990):399-403.
Chave A D,Thomson D J.2004.Bounded influence magnetotelluric response function estimation.Geophysical Journal International,157(3):988-1006.
Egbert G D,Kelbert A.2012.Computational recipes for electromagnetic inverse problems.Geophysical Journal International,189(1):251-267.
Ekblom H.1988.A new algorithm for the Huber estimator in linear models.BIT Numerical Mathematics,28(1):123-132.
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.2008.Constructing piecewise-constant models in multidimensional minimum-structure inversions.Geophysics,73(1):K1-K9.
Fujii I,Schultz A.2002.The 3Delectromagnetic response of the earth to ring current and auroral oval excitation.Geophysical Journal International,151(3):689-709.
Fukao Y,Koyama T,Obayashi M,et al.2004.Trans-Pacific temperature field in the mantle transition region derived from seismic and electromagnetic tomography.Earth&Planetary Science Letters,217(3-4):425-434.
Huang X G,Xu Y S,Karato S.2005.Water content in the transition zone from electrical conductivity of wadsleyite and ringwoodite.Nature,434(7034):746-749.
Karato S.1990.The role of hydrogen in the electrical conductivity of the upper mantle.Nature,347(6290):272-273.
Kelbert A,Egbert G D,Schultz A.2008.Non-linear conjugate gradient inversion for global EM induction:Resolution studies.Geophysical Journal International,173(2):365-381,doi:10.1111/j.1365-246X.2008.03717.x.
Kelbert A,Schultz A,Egbert G.2009.Global electromagnetic induction constraints on transition-zone water content variations.Nature,460(7258):1003-1006,doi:10.1038/nature08257.
Khan A,Connolly J A D,Olsen N.2006.Constraining the composition and thermal state of the mantle beneath Europe from inversion of long-period electromagnetic sounding data.Journal of Geophysical Research:Solid Earth,111(B10):207-208,B10102,doi:10.1029/2006JB004270.
Khan A,Kuvshinov A,Semenov A.2011.On the heterogeneous electrical conductivity structure of the Earth′s mantle with implications for transition zone water content.Journal of Geophysical Research,116(B1):B01103,doi:10.1029/2010JB007458.
Koyama T,Khan A,Kuvshinov A.2014.Three-dimensional electrical conductivity structure beneath Australia from inversion of geomagnetic observatory data:evidence for lateral variations in transition-zone temperature,water content and melt.Geophysical Journal International,196(3):1330-1350.
Li J P,Weng A H,Li S W,et al.2018a.3-D forward method for geomagnetic depth sounding based on finite difference method in spherical coordinate.Journal of Jilin University(Earth Science Edition)(in Chinese),48(2):411-419.
Li J P,Weng A H,Li S W,et al.2018b.The influence of ocean effect on geomagnetic observations in coastal areas of China:Acase study of the Guangzhou observatory.Chinese Journal of Geophysics(in Chinese),61(2):649-658,doi:10.6038/cjg2018L0433.
Liu Y H,Yin C C.2013.3Dinversion for frequency-domain HEMdata.Chinese Journal of Geophysics(in Chinese),56(12):4278-4287,doi:10.6038/cjg20131230.
Manthilake G,Bolfan-Casanova N,Novella D,et al.2016.Dehydration of chlorite explains anomalously high electrical conductivity in the mantle wedges.Science Advances,2(5):e1501631.
Menke W.1984.Geophysical Data Analysis:Discrete Inverse Theory.New York:Academic Press.
Munch F D,Grayver A V,Kuvshinov A,et al.2018.Stochastic inversion of geomagnetic observatory data including rigorous treatment of the ocean induction effect with implications for transition zone water content and thermal structure.Journal of Geophysical Research:Solid Earth,123(1):31-51.
Nocedal J,Wright S J.1999.Numerical Optimization.New York:Springer.
Oldenburg D W.1984.An introduction to linear inverse theory.IEEE Transactions on Geoscience&Remote Sensing,GE-22(6):665-674.
Olsen N.1998.The electrical conductivity of the mantle beneath Europe derived from C-responses from 3to 720hr.Geophysical Journal International,133(2):298-308.
Peyronneau J,Poirier J P.1989.Electrical conductivity of the Earth′s lower mantle.Nature,342(6249):537-539.
Püthe C,Kuvshinov A,Khan A,et al.2015.A new model of Earth′s radial conductivity structure derived from over 10yr of satellite and observatory magnetic data.Geophysical Journal International,203(3):1864-1872,doi:10.1093/gji/ggv407.
Schmucker U.1987.Substitute conductors for electromagnetic response estimates.Pure&Applied Geophysics,125(2-3):341-367.
Semenov A,Kuvshinov A.2012.Global 3-D imaging of mantle conductivity based on inversion of observatory C-responses-II:Data analysis and results.Geophysical Journal International,191(3):965-992,doi:10.1111/j.1365-246X.2012.05665.x.
Semenov V Y,Jozwiak W.2006.Lateral variations of the midmantle conductance beneath Europe.Tectonophysics,416(1-4):279-288.
Sun J,Kelbert A,Egbert G D.2015.Ionospheric current source modeling and global geomagnetic induction using ground geomagnetic observatory data.Journal of Geophysical Research:Solid Earth,120(10):6771-6796.
Tang J,Zhao G Z,Wang J J,et al.2006.Study of the formation mechanism for volcanism in Northeast China based on deep electric structure.Acta Petrologica Sinica(in Chinese),22(6):1503-1510.
Uyeshima M,Schultz A.2000.Geoelectromagnetic induction in a heterogeneous sphere:a new three-dimensional forward solver using a conservative staggered-grid finite difference method.Geophysical Journal International,140(3):636-650.
Wang Q,Huang Q H.2016.The spatio-temporal characteristics of geomagnetic induction vectors in North China.Chinese Journal of Geophysics(in Chinese),59(1):215-228,doi:10.6038/cjg20160118.
Weng A H,Li D J,Li Y B,et al.2015.Selection of parameter types in controlled source electromagnetic method.Chinese Journal of Geophysics(in Chinese),58(2):697-708,doi:10.6038/cjg20150230.
Wu X P,Xu G M.1998.Improvement of Occam′s inversion for MTdata.Chinese Journal of Geophysics(Acta Geophysica Sinica)(in Chinese),41(4):547-554.
Xu G J,Tang J,Huang Q H,et al.2015.Study on the conductivity structure of the upper mantle and transition zone beneath North China.Chinese Journal of Geophysics(in Chinese),58(2):566-575,doi:10.6038/cjg20150219.
Xu Y S,Shankland T J,Poe B T.2000.Laboratory-based electrical conductivity in the Earth′s mantle.Journal of Geophysical Research:Solid Earth,105(B12):27865-27875.
Yoshino T,Manthilake G,Matsuzaki T,et al.2008.Dry mantle transition zone inferred from the conductivity of wadsleyite and ringwoodite.Nature,451(7176):326-329.
Zhang Y H,Weng A H,Li S W,et al.2019.Estimation of C-responses of geomagnetic depth sounding based on global smooth constraint.Chinese Journal of Geophysics(in Chinese),62(5):1898-1907,doi:10.6038/cjg2019M0199.
Zhao D P.2004.Global tomographic images of mantle plumes and subducting slabs:insight into deep Earth dynamics.Physics of the Earth&Planetary Interiors,146(1-2):3-34.
Zhao G Z,Tang J,Liang J G,et al.2001.Measurement of network-MTin two areas of NE China for study of upper mantle conductivity structure of the back-arc region.Seismology and Geology(in Chinese),23(2):143-152.
李建平,翁爱华,李世文等.2018a.基于球坐标系下有限差分的地磁测深三维正演.吉林大学学报(地球科学版),48(2):411-419.
李建平,翁爱华,李世文等.2018b.海洋效应对中国沿海地磁观测影响——以广州台站为例.地球物理学报,61(2):649-658,doi:10.6038/cjg2018L0433.
刘云鹤,殷长春.2013.三维频率域航空电磁反演研究.地球物理学报,56(12):4278-4287,doi:10.6038/cjg20131230.
汤吉,赵国泽,王继军等.2006.基于地下电性结构探讨中国东北活动火山形成机制.岩石学报,22(6):1503-1510.
王桥,黄清华.2016.华北地磁感应矢量时空特征分析.地球物理学报,59(1):215-228,doi:10.6038/cjg20160118.
翁爱华,李大俊,李亚彬等.2015.数据类型对三维地面可控源电磁勘探效果的影响.地球物理学报,58(2):697-708,doi:10.6038/cjg20150230.
吴小平,徐果明.1998.大地电磁数据的Occam反演改进.地球物理学报,41(4):547-554.
徐光晶,汤吉,黄清华等.2015.华北地区上地幔及过渡带电性结构研究.地球物理学报,58(2):566-575,doi:10.6038/cjg20150219.
张艳辉,翁爱华,李世文等.2019.基于全局光滑约束的地磁测深C-响应估计.地球物理学报,62(5):1898-1907,doi:10.6038/cjg2019M0199.
赵国泽,汤吉,梁竞阁等.2001.用大地电磁网法在长春等地探测上地幔电导率结构.地震地质,23(2):143-152.
Banks R J.1969.Geomagnetic variations and the electrical conductivity of the upper mantle.Geophysical Journal International,17(5):457-487,doi:10.1111/j.1365-246X.1969.tb00252.x.
Booker J R,Favetto A,Pomposiello M C.2004.Low electrical resistivity associated with plunging of the Nazca flat slab beneath Argentina.Nature,429(6990):399-403.
Chave A D,Thomson D J.2004.Bounded influence magnetotelluric response function estimation.Geophysical Journal International,157(3):988-1006.
Egbert G D,Kelbert A.2012.Computational recipes for electromagnetic inverse problems.Geophysical Journal International,189(1):251-267.
Ekblom H.1988.A new algorithm for the Huber estimator in linear models.BIT Numerical Mathematics,28(1):123-132.
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.2008.Constructing piecewise-constant models in multidimensional minimum-structure inversions.Geophysics,73(1):K1-K9.
Fujii I,Schultz A.2002.The 3Delectromagnetic response of the earth to ring current and auroral oval excitation.Geophysical Journal International,151(3):689-709.
Fukao Y,Koyama T,Obayashi M,et al.2004.Trans-Pacific temperature field in the mantle transition region derived from seismic and electromagnetic tomography.Earth&Planetary Science Letters,217(3-4):425-434.
Huang X G,Xu Y S,Karato S.2005.Water content in the transition zone from electrical conductivity of wadsleyite and ringwoodite.Nature,434(7034):746-749.
Karato S.1990.The role of hydrogen in the electrical conductivity of the upper mantle.Nature,347(6290):272-273.
Kelbert A,Egbert G D,Schultz A.2008.Non-linear conjugate gradient inversion for global EM induction:Resolution studies.Geophysical Journal International,173(2):365-381,doi:10.1111/j.1365-246X.2008.03717.x.
Kelbert A,Schultz A,Egbert G.2009.Global electromagnetic induction constraints on transition-zone water content variations.Nature,460(7258):1003-1006,doi:10.1038/nature08257.
Khan A,Connolly J A D,Olsen N.2006.Constraining the composition and thermal state of the mantle beneath Europe from inversion of long-period electromagnetic sounding data.Journal of Geophysical Research:Solid Earth,111(B10):207-208,B10102,doi:10.1029/2006JB004270.
Khan A,Kuvshinov A,Semenov A.2011.On the heterogeneous electrical conductivity structure of the Earth′s mantle with implications for transition zone water content.Journal of Geophysical Research,116(B1):B01103,doi:10.1029/2010JB007458.
Koyama T,Khan A,Kuvshinov A.2014.Three-dimensional electrical conductivity structure beneath Australia from inversion of geomagnetic observatory data:evidence for lateral variations in transition-zone temperature,water content and melt.Geophysical Journal International,196(3):1330-1350.
Li J P,Weng A H,Li S W,et al.2018a.3-D forward method for geomagnetic depth sounding based on finite difference method in spherical coordinate.Journal of Jilin University(Earth Science Edition)(in Chinese),48(2):411-419.
Li J P,Weng A H,Li S W,et al.2018b.The influence of ocean effect on geomagnetic observations in coastal areas of China:Acase study of the Guangzhou observatory.Chinese Journal of Geophysics(in Chinese),61(2):649-658,doi:10.6038/cjg2018L0433.
Liu Y H,Yin C C.2013.3Dinversion for frequency-domain HEMdata.Chinese Journal of Geophysics(in Chinese),56(12):4278-4287,doi:10.6038/cjg20131230.
Manthilake G,Bolfan-Casanova N,Novella D,et al.2016.Dehydration of chlorite explains anomalously high electrical conductivity in the mantle wedges.Science Advances,2(5):e1501631.
Menke W.1984.Geophysical Data Analysis:Discrete Inverse Theory.New York:Academic Press.
Munch F D,Grayver A V,Kuvshinov A,et al.2018.Stochastic inversion of geomagnetic observatory data including rigorous treatment of the ocean induction effect with implications for transition zone water content and thermal structure.Journal of Geophysical Research:Solid Earth,123(1):31-51.
Nocedal J,Wright S J.1999.Numerical Optimization.New York:Springer.
Oldenburg D W.1984.An introduction to linear inverse theory.IEEE Transactions on Geoscience&Remote Sensing,GE-22(6):665-674.
Olsen N.1998.The electrical conductivity of the mantle beneath Europe derived from C-responses from 3to 720hr.Geophysical Journal International,133(2):298-308.
Peyronneau J,Poirier J P.1989.Electrical conductivity of the Earth′s lower mantle.Nature,342(6249):537-539.
Püthe C,Kuvshinov A,Khan A,et al.2015.A new model of Earth′s radial conductivity structure derived from over 10yr of satellite and observatory magnetic data.Geophysical Journal International,203(3):1864-1872,doi:10.1093/gji/ggv407.
Schmucker U.1987.Substitute conductors for electromagnetic response estimates.Pure&Applied Geophysics,125(2-3):341-367.
Semenov A,Kuvshinov A.2012.Global 3-D imaging of mantle conductivity based on inversion of observatory C-responses-II:Data analysis and results.Geophysical Journal International,191(3):965-992,doi:10.1111/j.1365-246X.2012.05665.x.
Semenov V Y,Jozwiak W.2006.Lateral variations of the midmantle conductance beneath Europe.Tectonophysics,416(1-4):279-288.
Sun J,Kelbert A,Egbert G D.2015.Ionospheric current source modeling and global geomagnetic induction using ground geomagnetic observatory data.Journal of Geophysical Research:Solid Earth,120(10):6771-6796.
Tang J,Zhao G Z,Wang J J,et al.2006.Study of the formation mechanism for volcanism in Northeast China based on deep electric structure.Acta Petrologica Sinica(in Chinese),22(6):1503-1510.
Uyeshima M,Schultz A.2000.Geoelectromagnetic induction in a heterogeneous sphere:a new three-dimensional forward solver using a conservative staggered-grid finite difference method.Geophysical Journal International,140(3):636-650.
Wang Q,Huang Q H.2016.The spatio-temporal characteristics of geomagnetic induction vectors in North China.Chinese Journal of Geophysics(in Chinese),59(1):215-228,doi:10.6038/cjg20160118.
Weng A H,Li D J,Li Y B,et al.2015.Selection of parameter types in controlled source electromagnetic method.Chinese Journal of Geophysics(in Chinese),58(2):697-708,doi:10.6038/cjg20150230.
Wu X P,Xu G M.1998.Improvement of Occam′s inversion for MTdata.Chinese Journal of Geophysics(Acta Geophysica Sinica)(in Chinese),41(4):547-554.
Xu G J,Tang J,Huang Q H,et al.2015.Study on the conductivity structure of the upper mantle and transition zone beneath North China.Chinese Journal of Geophysics(in Chinese),58(2):566-575,doi:10.6038/cjg20150219.
Xu Y S,Shankland T J,Poe B T.2000.Laboratory-based electrical conductivity in the Earth′s mantle.Journal of Geophysical Research:Solid Earth,105(B12):27865-27875.
Yoshino T,Manthilake G,Matsuzaki T,et al.2008.Dry mantle transition zone inferred from the conductivity of wadsleyite and ringwoodite.Nature,451(7176):326-329.
Zhang Y H,Weng A H,Li S W,et al.2019.Estimation of C-responses of geomagnetic depth sounding based on global smooth constraint.Chinese Journal of Geophysics(in Chinese),62(5):1898-1907,doi:10.6038/cjg2019M0199.
Zhao D P.2004.Global tomographic images of mantle plumes and subducting slabs:insight into deep Earth dynamics.Physics of the Earth&Planetary Interiors,146(1-2):3-34.
Zhao G Z,Tang J,Liang J G,et al.2001.Measurement of network-MTin two areas of NE China for study of upper mantle conductivity structure of the back-arc region.Seismology and Geology(in Chinese),23(2):143-152.
李建平,翁爱华,李世文等.2018a.基于球坐标系下有限差分的地磁测深三维正演.吉林大学学报(地球科学版),48(2):411-419.
李建平,翁爱华,李世文等.2018b.海洋效应对中国沿海地磁观测影响——以广州台站为例.地球物理学报,61(2):649-658,doi:10.6038/cjg2018L0433.
刘云鹤,殷长春.2013.三维频率域航空电磁反演研究.地球物理学报,56(12):4278-4287,doi:10.6038/cjg20131230.
汤吉,赵国泽,王继军等.2006.基于地下电性结构探讨中国东北活动火山形成机制.岩石学报,22(6):1503-1510.
王桥,黄清华.2016.华北地磁感应矢量时空特征分析.地球物理学报,59(1):215-228,doi:10.6038/cjg20160118.
翁爱华,李大俊,李亚彬等.2015.数据类型对三维地面可控源电磁勘探效果的影响.地球物理学报,58(2):697-708,doi:10.6038/cjg20150230.
吴小平,徐果明.1998.大地电磁数据的Occam反演改进.地球物理学报,41(4):547-554.
徐光晶,汤吉,黄清华等.2015.华北地区上地幔及过渡带电性结构研究.地球物理学报,58(2):566-575,doi:10.6038/cjg20150219.
张艳辉,翁爱华,李世文等.2019.基于全局光滑约束的地磁测深C-响应估计.地球物理学报,62(5):1898-1907,doi:10.6038/cjg2019M0199.
赵国泽,汤吉,梁竞阁等.2001.用大地电磁网法在长春等地探测上地幔电导率结构.地震地质,23(2):143-152.