基于全局光滑约束的地磁测深C-响应估计
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摘要
地磁测深C-响应,包含着地球内部结构的导电信息,因此获得高质量的C-响应估计对于揭示地球内部准确的电性结构至关重要,为此本文提出一种计算地磁测深C-响应的新思路.不同于以往单个频点估计办法,新方法基于相邻频率C-响应连续光滑的特性同时估计所有频率的C-响应.首先,根据求取C-响应的Z/H方法,由观测的Hr和Hθ构造估计C-响应的线性方程组;为了增强方程组求解的稳定性,克服噪声影响,要求估计的C-响应满足光滑性条件,从而将无约束的C-响应估计转化为阻尼最小二乘理论的C-响应估计优化问题.合成数据和实际台站数据的测试结果表明,光滑约束优化技术能比传统的逐频求取方法得到更加合理和连续的响应曲线;虽然正则化参数的选择对C-响应估计的结果有明显影响,但通过L-曲线和V-曲线确定的最优正则化参数可以在保证数据真实性的前提下获得最佳的C-响应估计.基于全局光滑约束获得的C-响应为提高反演结果的可靠性奠定基础,为利用更多台站的C-响应获得高分辨力的地球深部电性结构提供了技术支持.
C-responses of geomagnetic depth sounding(GDS)contain effective information on the internal structure of the earth,so the accurate C-responses estimation is very important for revealing the accurate electrical structure in the earth.To this end,a new method to estimate the C-responses of GDS is proposed in this paper.Different from the previous single frequency estimation methods,this approach simultaneously estimates the C-responses of all frequencies based on the continuous smoothing characteristic of the adjacent frequency.First,the linear equations are constructed from the observed Hrand Hθbased on the Z/H method.In order to enhance the stability of the equations and overcome the influence of noise,the estimated C-responses are required to satisfy the smoothness condition,and the unconstrained C-responses estimation is transformed into an optimization problem of the damped least squares theory.The tests of synthetic data and real observational data indicate that the smooth constrained technology can obtain more reasonable and continuous curves than the traditional methods.Although the regularizationparameter has an important influence on the estimation,the optimal regularization parameter determined by L-curve and V-curve methods can obtain the best C-responses while ensuring the authenticity of the data.The C-responses obtained by this method lay the foundation for improving the reliability of the inversion results,and provide technical support for the high-resolution electrical structure of the earth′s interior by using C-responses of more observatories.
C-responses of geomagnetic depth sounding(GDS)contain effective information on the internal structure of the earth,so the accurate C-responses estimation is very important for revealing the accurate electrical structure in the earth.To this end,a new method to estimate the C-responses of GDS is proposed in this paper.Different from the previous single frequency estimation methods,this approach simultaneously estimates the C-responses of all frequencies based on the continuous smoothing characteristic of the adjacent frequency.First,the linear equations are constructed from the observed Hrand Hθbased on the Z/H method.In order to enhance the stability of the equations and overcome the influence of noise,the estimated C-responses are required to satisfy the smoothness condition,and the unconstrained C-responses estimation is transformed into an optimization problem of the damped least squares theory.The tests of synthetic data and real observational data indicate that the smooth constrained technology can obtain more reasonable and continuous curves than the traditional methods.Although the regularizationparameter has an important influence on the estimation,the optimal regularization parameter determined by L-curve and V-curve methods can obtain the best C-responses while ensuring the authenticity of the data.The C-responses obtained by this method lay the foundation for improving the reliability of the inversion results,and provide technical support for the high-resolution electrical structure of the earth′s interior by using C-responses of more observatories.
引文
Armadillo E,Bozzo E,Cerv V,et al.2001.Geomagnetic depth sounding in the northern Apennines(Italy).Earth,Planets&Space,53(5):385-396.
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.
Chave A D,Jones A G.2012.The Magnetotelluric Method:Theory and Practice.Cambridge University Press.
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.
Frasso G,Eilers P.2015.L-and V-curves for optimal smoothing.Statistical Modelling,15(1):91-111.
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.
Hansen P C.1992.Analysis of discrete ill-posed problems by means of the L-curve.SIAM Review,34(4):561-580.
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.JournalofGeophysicalResearch,116(B1):B01103,doi:10.1029/2010JB007458.
Li S W,Weng A H,Li J P,et al.2017.1-D inversion of C-response data from geomagnetic depth sounding with shallow resistivity constraint.Chinese Journal of Geophysics(in Chinese),60(3):1201-1210,doi:10.6038/cjg20170330.
Nabighian M N.1987.Electromagnetic Methods in Applied Geophysics:Volume 1,Theory.Tulsa:Society of Exploration Geophysics,doi:10.1190/1.9781560802631.
Olsen N.1992.Day-to-Day C-Response estimation for Sqfrom 1cpd to 6cpd using the Z:Y-method.Journal of Geomagnetism&Geoelectricity,44(6):433-447.
Olsen N.1998.The electrical conductivity of the mantle beneath Europe derived fromC-responses from 3to 720hr.Geophysical Journal International,133(2):298-308.
Olsen N.1999.Long-period(30days-1year)electromagnetic sounding and the electrical conductivity of the lower mantle beneath Europe.Geophysical Journal International,138(1):179-187.
Pardo D,Torres-Verdín C.2015.Fast 1Dinversion of loggingwhile-drilling resistivity measurements for improved estimation of formation resistivity in high-angle and horizontal wells.Geophysics,80(2):E111-E124.
Püthe C,Kuvshinov A.2014.Mapping 3-D mantle electrical conductivity from space:a new 3-D inversion scheme based on analysis of matrix q-responses.Geophysical Journal International,197(2):768-784.
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.1970.Anomalies of geomagnetic variations in the southwest United States.Bull.Scripps Inst.Ocean.,Univ.Calif.,13:1-165.
Schmucker U.1979.Erdmagnetische Variationen und die elektrische Leitfhigkeit in tieferen Schichten der Erde.∥Sitzungsbericht und Mitteilungen Braunschweigische Wiss.Gesellschaft,Sonderheft,4:45-102.
Schmucker U.1985.Magnetic and electric fields due to electromagnetic induction by external sources,electrical properties of the earth′s interior.∥Landolt-B9rnstein,New-Series,5/2b.Berlin:SpringerVerlag.
Schmucker U.1990.Die eindringtiefen tagesperiodischer variationen.∥Haak V,Homilius J eds.Protokoll Koll.Elektromagnetische Tiefenforschung,Hornburg.Niederschsisches Landesamt,Hannover,31-66.
Schultz A,Larsen J C.1987.On the electrical conductivity of the mid-mantle:I.Calculation of equivalent scalar MT response functions.Geophysical Journal International,88(3):733-761.
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.
Tikhonov A N.1963.Regularization of incorrectly posed problems.Soviet Mathematics Doklady,4(1):1624-1627.
Tikhonov A N,Arsenin V Y.1977.Solutions of Ill-Posed Problems.New York:John Wiley&Sons.
Wang J Y.2002.Inverse Theory in Geophysics(in Chinese).Beijing:Higher Education Press.
Zhdanov M S.1993.Tutorial:Regularization in Inversion Theory.Colorado:Colorado School of Mines.
李世文,翁爱华,李建平等.2017.浅部约束的地磁测深C-响应一维反演.地球物理学报,60(3):1201-1210,doi:10.6038/cjg20170330.
王家映.2002.地球物理反演理论.北京:高等教育出版社.
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.
Chave A D,Jones A G.2012.The Magnetotelluric Method:Theory and Practice.Cambridge University Press.
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.
Frasso G,Eilers P.2015.L-and V-curves for optimal smoothing.Statistical Modelling,15(1):91-111.
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.
Hansen P C.1992.Analysis of discrete ill-posed problems by means of the L-curve.SIAM Review,34(4):561-580.
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.JournalofGeophysicalResearch,116(B1):B01103,doi:10.1029/2010JB007458.
Li S W,Weng A H,Li J P,et al.2017.1-D inversion of C-response data from geomagnetic depth sounding with shallow resistivity constraint.Chinese Journal of Geophysics(in Chinese),60(3):1201-1210,doi:10.6038/cjg20170330.
Nabighian M N.1987.Electromagnetic Methods in Applied Geophysics:Volume 1,Theory.Tulsa:Society of Exploration Geophysics,doi:10.1190/1.9781560802631.
Olsen N.1992.Day-to-Day C-Response estimation for Sqfrom 1cpd to 6cpd using the Z:Y-method.Journal of Geomagnetism&Geoelectricity,44(6):433-447.
Olsen N.1998.The electrical conductivity of the mantle beneath Europe derived fromC-responses from 3to 720hr.Geophysical Journal International,133(2):298-308.
Olsen N.1999.Long-period(30days-1year)electromagnetic sounding and the electrical conductivity of the lower mantle beneath Europe.Geophysical Journal International,138(1):179-187.
Pardo D,Torres-Verdín C.2015.Fast 1Dinversion of loggingwhile-drilling resistivity measurements for improved estimation of formation resistivity in high-angle and horizontal wells.Geophysics,80(2):E111-E124.
Püthe C,Kuvshinov A.2014.Mapping 3-D mantle electrical conductivity from space:a new 3-D inversion scheme based on analysis of matrix q-responses.Geophysical Journal International,197(2):768-784.
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.1970.Anomalies of geomagnetic variations in the southwest United States.Bull.Scripps Inst.Ocean.,Univ.Calif.,13:1-165.
Schmucker U.1979.Erdmagnetische Variationen und die elektrische Leitfhigkeit in tieferen Schichten der Erde.∥Sitzungsbericht und Mitteilungen Braunschweigische Wiss.Gesellschaft,Sonderheft,4:45-102.
Schmucker U.1985.Magnetic and electric fields due to electromagnetic induction by external sources,electrical properties of the earth′s interior.∥Landolt-B9rnstein,New-Series,5/2b.Berlin:SpringerVerlag.
Schmucker U.1990.Die eindringtiefen tagesperiodischer variationen.∥Haak V,Homilius J eds.Protokoll Koll.Elektromagnetische Tiefenforschung,Hornburg.Niederschsisches Landesamt,Hannover,31-66.
Schultz A,Larsen J C.1987.On the electrical conductivity of the mid-mantle:I.Calculation of equivalent scalar MT response functions.Geophysical Journal International,88(3):733-761.
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.
Tikhonov A N.1963.Regularization of incorrectly posed problems.Soviet Mathematics Doklady,4(1):1624-1627.
Tikhonov A N,Arsenin V Y.1977.Solutions of Ill-Posed Problems.New York:John Wiley&Sons.
Wang J Y.2002.Inverse Theory in Geophysics(in Chinese).Beijing:Higher Education Press.
Zhdanov M S.1993.Tutorial:Regularization in Inversion Theory.Colorado:Colorado School of Mines.
李世文,翁爱华,李建平等.2017.浅部约束的地磁测深C-响应一维反演.地球物理学报,60(3):1201-1210,doi:10.6038/cjg20170330.
王家映.2002.地球物理反演理论.北京:高等教育出版社.
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