二维MT电阻率与磁导率同时反演研究
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摘要
开展了同时考虑介质电阻率与磁导率变化的大地电磁二维正则化反演问题研究。不考虑位移电流影响的大地电磁勘探,电阻率与磁导率是影响观测电磁场的主要物理参数;考虑岩石的电阻率变化范围相比磁导率大的多,所以大地电磁反演解释常常只考虑电阻率;然而,二维正演模拟表明,当地下介质含有较多铁磁性矿物时,磁导率的局部异常体对大地电磁观测的影响不能忽略。因此,开展了同时反演电阻率与磁导率的正则化反演,建立了同时反演两个参数的正则化反演目标函数,并通过高斯-牛顿法对正则化目标函数进行最优化求解;采用模型空间到反演空间的函数映射技术,将电阻率与磁导率限定在具有实际物理意义的变化区间,并通过双共轭梯度稳定算法求解高斯-牛顿系统,以确保反演稳定性。对合成数据与实测数据进行了反演,表明从大地电磁数据可以恢复地下介质磁导率,开展磁导率与电阻率的同时反演提高了反演效果,丰富了数据解释依据。
The two-dimensional magnetotelluric regularization inversion considering the resistivity and magnetic permeability of underground medium is studied. It is generally believed that magnetotelluric method is not affected by the displacement current in the low frequency. So resistivity and magnetic permeability are the mainly physical parameters that affect observed electromagnetic fields of magnetotelluric method. But magnetotelluric inversion is based on resistivity, because the resistivity variation range of rock is much larger than that of magnetic permeability. However, the magnetic permeability value increases with the increase of ferromagnetic mineral content, and the influence of the local anomalous bodies of permeability on magnetotelluric observation cannot be ignored, which is also proved by the two dimensional numerical simulation. Therefore, the regularization inversion method considering both resistivity and permeability is studied. The regularized inversion cost function with resistivity and magnetic permeability of earth is established, and the cost function is optimized by Gauss-Newton method. There are two technologies which are used in the inversion, one is the function mapping form model space to inversion space in order to limit the range of resistivity and magnetic permeability keep them with actual physical meaning. The other is bi-conjugate gradient stabilization algorithm is adopted to solve Gauss-Newton equation, in order to ensure the inversion stability. Through the inversion of synthetic data and field data, it is proved that inversion magnetic permeability form magnetotelluric data is feasible, and the simultaneously inversion of resistivity and permeability improve the inversion effect, the magnetic permeability parameter can help to improve interpretations.
The two-dimensional magnetotelluric regularization inversion considering the resistivity and magnetic permeability of underground medium is studied. It is generally believed that magnetotelluric method is not affected by the displacement current in the low frequency. So resistivity and magnetic permeability are the mainly physical parameters that affect observed electromagnetic fields of magnetotelluric method. But magnetotelluric inversion is based on resistivity, because the resistivity variation range of rock is much larger than that of magnetic permeability. However, the magnetic permeability value increases with the increase of ferromagnetic mineral content, and the influence of the local anomalous bodies of permeability on magnetotelluric observation cannot be ignored, which is also proved by the two dimensional numerical simulation. Therefore, the regularization inversion method considering both resistivity and permeability is studied. The regularized inversion cost function with resistivity and magnetic permeability of earth is established, and the cost function is optimized by Gauss-Newton method. There are two technologies which are used in the inversion, one is the function mapping form model space to inversion space in order to limit the range of resistivity and magnetic permeability keep them with actual physical meaning. The other is bi-conjugate gradient stabilization algorithm is adopted to solve Gauss-Newton equation, in order to ensure the inversion stability. Through the inversion of synthetic data and field data, it is proved that inversion magnetic permeability form magnetotelluric data is feasible, and the simultaneously inversion of resistivity and permeability improve the inversion effect, the magnetic permeability parameter can help to improve interpretations.
引文
李曼, 林文东.2014.基于最小支持的2.5维直流电阻率正则化反演研究[J]. 东华理工大学学报:自然科学版, 37(3):292-298.
刘云, 王绪本.2010.大地电磁二维自适应地形有限元正演模拟[J]. 地震地质, 32(3):382-391.
张志勇, 李曼, 邓居智,等.2015.基于二次场算法的大地电磁二维有限单元法正演[J]. 同济大学学报:自然科学版, 43(8):1259-1265.
张志勇, 刘庆成.2013.基于收缩二叉树结构网格剖分的大地电磁二维有限单元法正演研究[J].石油地球物理勘探, 48(3):482-487.
Abedi M, Gholami A, Norouzi G H, et al.2013.Fast inversion of magnetic data using Lanczos bidiagonalization method[J]. Journal of Applied Geophysics, 90(90):126-137.
Cao J. 2005. An approach for simultaneously inverting MT data for resistivity and susceptibility[J]. Seg Technical Program Expanded Abstracts, 24(1): 613-616.
Clark D A, Emerson D W, Clark D A, et al. 1991. Notes on rock magnetization characteristics in applied geophysical studies[J]. Exploration Geophysics, 22(3):547-555.
Commer M, Newman G A. 2008. New advances in three-dimensional controlled-source electromagnetic inversion[J]. Geophysical Journal International, 172(2): 513-535.
Constable S, Parker R L, Constable C G, et al. 1987. Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data[J]. Geophysics, 52(3): 289-300.
De Lug?o P P, Portaniaguine O, Zhdanov M S. 1997. Fast and Stable Two-Dimensional Inversion of Magnetotelluric Data[J]. Geomagnetics, 49(11):1469-1497.
De Lug?o P P, Wannamaker P E. 1996. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity[J]. Geophysical Journal International, 127(3): 806-810.
Degroot-Hedlin C, Constable S. 1990. Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data[J]. Geophysics, 55(12): 1613-1624.
Farquharson C G, Oldenburg D W, Routh P S, et al. 2003. Simultaneous 1D inversion of loop-loop electromagnetic data for magnetic susceptibility and electrical conductivity[J]. Geophysics, 68(6): 1857-1869.
Farquharson C G, Oldenburg D W. 1996. Approximate sensitivities for the electromagnetic inverse problem[J]. Geophysical Journal International, 126(1): 235-252.
Grayver A V, Streich R, Ritter O. 2013. Three-dimensional parallel distributed inversion of CSEM data using a direct forward solver[J]. Geophysical Journal International, 193(3):1432-1446.
Habashy T M, Abubakar A. 2004. A General Framework for Constraint Minimization for the Inversion of Electromagnetic Measurements[J]. Progress In Electromagnetics Research, 46(1):265-312.
Haber E, Oldenburg D. 2000. A GCV based method for nonlinear ill-posed problems[J]. Computational Geosciences, 4(1):41-63.
Hansen P C. 1992. Analysis of Discrete Ill-Posed Problems by Means of the L-Curve[J]. Siam Review, 34(4):561-580.
Jahandari H, Farquharson C G. 2017. 3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids[J]. Geophysical Journal International, 211(2):1211-1227.
Jupp D L B, Vozoff K. 1975. Stable Iterative Methods for the Inversion of Geophysical Data[J]. Geophysical Journal of the Royal Astronomical Society, 42(3):957-976.
Jupp D L B, Vozoff K. 1977. Two-dimensional magnetotelluric inversion[J]. Geophysical Journal of the Royal Astronomical Society, 50(2):333-352.
Key K, Weiss C J. 2006. Adaptive finite-element modeling using unstructured grids: The 2D magnetotelluric example[J]. Geophysics, 71(6):G291-G299.
Key K. 2009. 1D inversion of multicomponent, multifrequency marine CSEM data: Methodology and synthetic studies for resolving thin resistive layers[J]. Geophysics, 74(2):F9-F20.
Key K. 2016. MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data[J]. Geophysical Journal International, 207(1):571-588.
Kordy M, Wannamaker P, Maris V, et al. 2016. 3-dimensional magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on symmetric multiprocessor computers-PartII: direct data-space inverse solution[J]. Geophysical Journal International, 204(1):94-110.
Li Y, Oldenburg D W. 1996. 3-D Inversion of Magnetic Data[J]. Geophysics, 61(2):394-408.
Li Y, Oldenburg D W. 2000. 3-D inversion of induced polarization data[J]. Geophysics, 65(6): 1931-1945.
Loke M H, Chambers J E, Ogilvy R D. 2006. Inversion of 2D spectral induced polarization imaging data[J]. Geophysical Prospecting, 54(3):287-301.
Mackie R L, Madden T R. 1993. Three-dimensional magnetotelluric inversion using conjugate gradients[J]. Geophysical Journal of the Royal Astronomical Society, 115(1):215-229.
McGillivray P R, Oldenburg D W, Ellis R G, et al. 1994. Calculation of sensitivities for the frequency-domain electromagnetic problem[J]. Geophysical Journal of the Royal Astronomical Society, 116(1):1-4.
Müller H, Von Dobeneck T, Hilgenfeldt C, et al. 2012. Mapping the magnetic susceptibility and electric conductivity of marine surficial sediments by benthic EM profiling[J]. Geophysics, 77(1):E43-E56.
Newman G A, Alumbaugh D L. 2000. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients[J]. Geophysical Journal International, 140(2): 410-424.
Newman G A, Recher S, Tezkan B, et al. 2003. 3D inversion of a scalar radio magnetotelluric field data set[J]. Geophysics, 68(3): 791-802.
Pilkington M. 1997. 3-D magnetic imaging using conjugate gradients[J].Geophysics, 64(4):1432-1142.
Portniaguine O, Zhdanov M S. 2000. 3-D magnetic inversion with data compression and image focusing[J]. Geophysics, 67(5):1532-1541.
Rodi W L. 1976. A Technique for Improving the Accuracy of Finite Element Solutions for Magnetotelluric Data[J]. Geophysical Journal of the Royal Astronomical Society, 44(2):483-506.
Rodi W, Mackie R L. 2001. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion[J]. Geophysics, 66(1):174-187.
Routh P S, Oldenburg D W, Li Y. 1998. Regularized in version of spectral IP parameters from complex resistivity data[C]. In SEG Technical Parogram Expanded Abstracts, Society of Exploration Geophsicists.
Saad Y. 1996. Iterative Methods for Sparse Linear Systems[M]. PWS Pub:625-635.
Sasaki Y, Kim J, Cho S J, et al. 2010. Multidimensional inversion of loop-loop frequency-domain EM data for resistivity and magnetic susceptibility[J]. Geophysics, 75(6): 213-223.
Sasaki Y. 1989. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data[J]. Geophysics, 54(2): 254-262.
Sasaki Y. 2001. Full 3-D inversion of electromagnetic data on PC[J]. Journal of Applied Geophysics, 46(1): 45-54.
Sheen D H, Kim H J, Baag C E. 2000. A technique for improving the efficiency of finite element solutions in magnetotelluric modeling[J]. Seg Technical Program Expanded Abstracts, 19(1):2484.
Siripunvaraporn W, Egbert G D. 2000. An efficient data-subspace inversion method for 2-D magnetotelluric data[J]. Geophysics, 65(3): 791-803.
Siripunvaraporn W, Egbert G D. 2009. WSINV3DMT: Vertical magnetic field transfer function inversion and parallel implementation[J]. Physics of the Earth and Planetary Interiors, 173(3-4):317-329.
Smith J T, Booker J R. 1991. Rapid inversion of two-and three-dimensional magnetotelluric data[J]. Journal of Geophysical Research, 96(4):3905-3922.
Usui Y. 2015. 3-D inversion of magnetotelluric data using unstructured tetrahedral elements: applicability to data affected by topography[J]. Geophysical Journal International, 202(2):828-849.
Van D R L, Hendrickx J M H, Cassidy N J, et al. 2013. Effects of magnetite on high-frequency ground-penetrating radar[J]. Geophysics, 78(5):H1-H11.
Wannamaker P E, Stodt J A, Rijo L. 1986. Two-dimensional topographic responses in magnetotellurics modeled using finite elements[J]. Geophysics, 51(11):384-384.
Zhdanov M S, Tolstaya E. 2004 Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem[J]. Inverse Problems, 20(3): 937-952.
Zhdanov M S. 2002. Geophysical inverse theory and regularization problems[M]. Elsevier, 36:467-529.
刘云, 王绪本.2010.大地电磁二维自适应地形有限元正演模拟[J]. 地震地质, 32(3):382-391.
张志勇, 李曼, 邓居智,等.2015.基于二次场算法的大地电磁二维有限单元法正演[J]. 同济大学学报:自然科学版, 43(8):1259-1265.
张志勇, 刘庆成.2013.基于收缩二叉树结构网格剖分的大地电磁二维有限单元法正演研究[J].石油地球物理勘探, 48(3):482-487.
Abedi M, Gholami A, Norouzi G H, et al.2013.Fast inversion of magnetic data using Lanczos bidiagonalization method[J]. Journal of Applied Geophysics, 90(90):126-137.
Cao J. 2005. An approach for simultaneously inverting MT data for resistivity and susceptibility[J]. Seg Technical Program Expanded Abstracts, 24(1): 613-616.
Clark D A, Emerson D W, Clark D A, et al. 1991. Notes on rock magnetization characteristics in applied geophysical studies[J]. Exploration Geophysics, 22(3):547-555.
Commer M, Newman G A. 2008. New advances in three-dimensional controlled-source electromagnetic inversion[J]. Geophysical Journal International, 172(2): 513-535.
Constable S, Parker R L, Constable C G, et al. 1987. Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data[J]. Geophysics, 52(3): 289-300.
De Lug?o P P, Portaniaguine O, Zhdanov M S. 1997. Fast and Stable Two-Dimensional Inversion of Magnetotelluric Data[J]. Geomagnetics, 49(11):1469-1497.
De Lug?o P P, Wannamaker P E. 1996. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity[J]. Geophysical Journal International, 127(3): 806-810.
Degroot-Hedlin C, Constable S. 1990. Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data[J]. Geophysics, 55(12): 1613-1624.
Farquharson C G, Oldenburg D W, Routh P S, et al. 2003. Simultaneous 1D inversion of loop-loop electromagnetic data for magnetic susceptibility and electrical conductivity[J]. Geophysics, 68(6): 1857-1869.
Farquharson C G, Oldenburg D W. 1996. Approximate sensitivities for the electromagnetic inverse problem[J]. Geophysical Journal International, 126(1): 235-252.
Grayver A V, Streich R, Ritter O. 2013. Three-dimensional parallel distributed inversion of CSEM data using a direct forward solver[J]. Geophysical Journal International, 193(3):1432-1446.
Habashy T M, Abubakar A. 2004. A General Framework for Constraint Minimization for the Inversion of Electromagnetic Measurements[J]. Progress In Electromagnetics Research, 46(1):265-312.
Haber E, Oldenburg D. 2000. A GCV based method for nonlinear ill-posed problems[J]. Computational Geosciences, 4(1):41-63.
Hansen P C. 1992. Analysis of Discrete Ill-Posed Problems by Means of the L-Curve[J]. Siam Review, 34(4):561-580.
Jahandari H, Farquharson C G. 2017. 3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids[J]. Geophysical Journal International, 211(2):1211-1227.
Jupp D L B, Vozoff K. 1975. Stable Iterative Methods for the Inversion of Geophysical Data[J]. Geophysical Journal of the Royal Astronomical Society, 42(3):957-976.
Jupp D L B, Vozoff K. 1977. Two-dimensional magnetotelluric inversion[J]. Geophysical Journal of the Royal Astronomical Society, 50(2):333-352.
Key K, Weiss C J. 2006. Adaptive finite-element modeling using unstructured grids: The 2D magnetotelluric example[J]. Geophysics, 71(6):G291-G299.
Key K. 2009. 1D inversion of multicomponent, multifrequency marine CSEM data: Methodology and synthetic studies for resolving thin resistive layers[J]. Geophysics, 74(2):F9-F20.
Key K. 2016. MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data[J]. Geophysical Journal International, 207(1):571-588.
Kordy M, Wannamaker P, Maris V, et al. 2016. 3-dimensional magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on symmetric multiprocessor computers-PartII: direct data-space inverse solution[J]. Geophysical Journal International, 204(1):94-110.
Li Y, Oldenburg D W. 1996. 3-D Inversion of Magnetic Data[J]. Geophysics, 61(2):394-408.
Li Y, Oldenburg D W. 2000. 3-D inversion of induced polarization data[J]. Geophysics, 65(6): 1931-1945.
Loke M H, Chambers J E, Ogilvy R D. 2006. Inversion of 2D spectral induced polarization imaging data[J]. Geophysical Prospecting, 54(3):287-301.
Mackie R L, Madden T R. 1993. Three-dimensional magnetotelluric inversion using conjugate gradients[J]. Geophysical Journal of the Royal Astronomical Society, 115(1):215-229.
McGillivray P R, Oldenburg D W, Ellis R G, et al. 1994. Calculation of sensitivities for the frequency-domain electromagnetic problem[J]. Geophysical Journal of the Royal Astronomical Society, 116(1):1-4.
Müller H, Von Dobeneck T, Hilgenfeldt C, et al. 2012. Mapping the magnetic susceptibility and electric conductivity of marine surficial sediments by benthic EM profiling[J]. Geophysics, 77(1):E43-E56.
Newman G A, Alumbaugh D L. 2000. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients[J]. Geophysical Journal International, 140(2): 410-424.
Newman G A, Recher S, Tezkan B, et al. 2003. 3D inversion of a scalar radio magnetotelluric field data set[J]. Geophysics, 68(3): 791-802.
Pilkington M. 1997. 3-D magnetic imaging using conjugate gradients[J].Geophysics, 64(4):1432-1142.
Portniaguine O, Zhdanov M S. 2000. 3-D magnetic inversion with data compression and image focusing[J]. Geophysics, 67(5):1532-1541.
Rodi W L. 1976. A Technique for Improving the Accuracy of Finite Element Solutions for Magnetotelluric Data[J]. Geophysical Journal of the Royal Astronomical Society, 44(2):483-506.
Rodi W, Mackie R L. 2001. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion[J]. Geophysics, 66(1):174-187.
Routh P S, Oldenburg D W, Li Y. 1998. Regularized in version of spectral IP parameters from complex resistivity data[C]. In SEG Technical Parogram Expanded Abstracts, Society of Exploration Geophsicists.
Saad Y. 1996. Iterative Methods for Sparse Linear Systems[M]. PWS Pub:625-635.
Sasaki Y, Kim J, Cho S J, et al. 2010. Multidimensional inversion of loop-loop frequency-domain EM data for resistivity and magnetic susceptibility[J]. Geophysics, 75(6): 213-223.
Sasaki Y. 1989. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data[J]. Geophysics, 54(2): 254-262.
Sasaki Y. 2001. Full 3-D inversion of electromagnetic data on PC[J]. Journal of Applied Geophysics, 46(1): 45-54.
Sheen D H, Kim H J, Baag C E. 2000. A technique for improving the efficiency of finite element solutions in magnetotelluric modeling[J]. Seg Technical Program Expanded Abstracts, 19(1):2484.
Siripunvaraporn W, Egbert G D. 2000. An efficient data-subspace inversion method for 2-D magnetotelluric data[J]. Geophysics, 65(3): 791-803.
Siripunvaraporn W, Egbert G D. 2009. WSINV3DMT: Vertical magnetic field transfer function inversion and parallel implementation[J]. Physics of the Earth and Planetary Interiors, 173(3-4):317-329.
Smith J T, Booker J R. 1991. Rapid inversion of two-and three-dimensional magnetotelluric data[J]. Journal of Geophysical Research, 96(4):3905-3922.
Usui Y. 2015. 3-D inversion of magnetotelluric data using unstructured tetrahedral elements: applicability to data affected by topography[J]. Geophysical Journal International, 202(2):828-849.
Van D R L, Hendrickx J M H, Cassidy N J, et al. 2013. Effects of magnetite on high-frequency ground-penetrating radar[J]. Geophysics, 78(5):H1-H11.
Wannamaker P E, Stodt J A, Rijo L. 1986. Two-dimensional topographic responses in magnetotellurics modeled using finite elements[J]. Geophysics, 51(11):384-384.
Zhdanov M S, Tolstaya E. 2004 Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem[J]. Inverse Problems, 20(3): 937-952.
Zhdanov M S. 2002. Geophysical inverse theory and regularization problems[M]. Elsevier, 36:467-529.
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