大地电磁主轴各向异性二维理论模型反演分析
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摘要
地下介质普遍存在各向异性,为反应地下真实地质情况,需建立各向异性模型进行研究。主要进行主轴各向异性大地电磁二维反演研究,采用有限单元法作为正演模拟方法,将正演响应结果与前人计算结果进行对比分析,验证了算法的正确性,并对不同方向上电阻率响应灵敏度进行分析。采用非线性共轭梯度法进行反演研究,该方法不需要直接计算雅克比矩阵,相对于其他反演方法节省了计算时间,计算效率高;目标函数的建立对于不同方向上的电阻率采用不同的正则化参数来进行约束。通过复杂的各向异性体模型进行反演,结果显示对于不同方向上电阻率的恢复以及异常体位置的圈定都取得了较好的效果,说明了反演算法的有效性。
Anisotropy is common in underground media,there is a need to establish anisotropic models to perform more accurate and realistic geological modelling. As such,a two-dimensional magnetotelluric inversion study of principal axis anisotropy was presented. By comparing the calculated results with predecessor's,the correctness of forward algorithm using finite element method was proved. The resistivity response sensitivity in different directions was also analyzed. The nonlinear conjugate gradients inversion algorithm was also used in this paper. This method does not need to directly calculate the Jacobian matrix,which saves computation time and has high computational efficiency compared to other inversion methods. The objective function was established to restrain the resistivity in different directions by using different regularization parameters. The inversion results of complex principal axis anisotropic models show that good effects have been achieved including the resistivity recovery and the delineation of abnormal body position in different directions,which illustrates the effectiveness of the inversion algorithm.
Anisotropy is common in underground media,there is a need to establish anisotropic models to perform more accurate and realistic geological modelling. As such,a two-dimensional magnetotelluric inversion study of principal axis anisotropy was presented. By comparing the calculated results with predecessor's,the correctness of forward algorithm using finite element method was proved. The resistivity response sensitivity in different directions was also analyzed. The nonlinear conjugate gradients inversion algorithm was also used in this paper. This method does not need to directly calculate the Jacobian matrix,which saves computation time and has high computational efficiency compared to other inversion methods. The objective function was established to restrain the resistivity in different directions by using different regularization parameters. The inversion results of complex principal axis anisotropic models show that good effects have been achieved including the resistivity recovery and the delineation of abnormal body position in different directions,which illustrates the effectiveness of the inversion algorithm.
引文
1 Pek J,Santos F A M. Magnetotelluric inversion for anisotropic conductivities in layered media[J]. Physics of the Earth and Planetary Interiors,2006,158:139-158
2 Pek J,Santos F A M. Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media[J]. Computer&Geosciences,2002,28:939-950
3 Reddy I K,Rankin D. Magnetotelluric effect of dipping anisotropies[J]. Geophysical Prospecting,1971,19(1):84-97
4 霍光谱,胡祥云,方慧,等.层状各向异性介质大地电磁联合反演研究[J].物理学报,2012,61(12):129101Huo Guangpu,Hu Xiangyun,Fang Hui,et al. Magnetotelluric joint inversion for anisotropic conductivities in layered media[J]. Acta Physica Sinica,2012,61(12):129101
5 林长佑,武玉霞,杨长福,等.水平层状对称各向异性介质的大地电磁资料反演[J].地球物理学报,1996,39(增刊1):342-348Lin Changyou,Wu Yuxia,Yang Changfu,et al. Magnetotelluric inversion for symmetrically anisotropic layered medium[J]. Chinese Journal of Geophysics,1996,39(S1):342-348
6 秦林江,杨长福.大地电磁全张量响应的一维各向异性反演[J].地球物理学报,2012,55(2):693-701Qin Linjiang,Yang Changfu. A magnetotelluric inversion method of the whole tensor impedance response to one-dimensional anisotropic structure[J]. Chinese Journal of Geophysics, 2012, 55(2):693-701
7 Reddy I K,Rankin D. Magnetotelluric response of laterally inhomogeneous and anisotropic structure[J]. Geophysics, 1975, 40:1035-1045
8 徐世浙,赵生凯.二维各向异性地电剖面的大地电磁场的有限元解法[J].地震学报,1985,7(1):80-90Xu Shizhe,Zhao Shengkai. Solution of magnetotelluric field equations for a two-dimensional,anisotropic geoelectric section by the finite element method[J]. Acta Seismologica Sinica,1985,7(1):80-90
9 Pek J,Verner T. Finite-difference modeling of magnetotelluric fields in two-dimensional anisotropic media[J]. Geophysical Journal International,1997,128(1):505-521
10 Li Y. A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures[J]. Geophysical Journal International,2002,148:389-401
11 Li Y,Josef P. Adaptive finite element modeling of two-dimensional magnetotelluric fields in general anisotropic media[J]. Geophysical Journal International,2008,175:942-954
12 胡祥云,霍光谱,高锐,等.大地电磁各向异性二维模拟及实例分析[J].地球物理学报,2013,56(12):4268-4277Hu Xiangyun,Huo Guangpu,Gao Rui,et al. The magnetotelluric anisotropic two-dimensional simulation and case analysis[J]. Chinese Journal of Geophysics,2013,56(12):4268-4277
13 秦林江.各向异性介质的MT正反演研究[D].杭州:浙江大学,2013Qin Linjiang. The forward and inversion of MT field in anisotropic conductivity structures[D]. Hangzhou:Zhejiang University,2013
14 Pain C C,Herwanger J R V,Saunders J H,et al. Anisotropic resistivity inversion[J]. Inverse Problems,2003,19(5):1081-1111
15 杨长福,林长佑,孙崇赤,等.二维对称各向异性介质大地电磁反演[J].地震学报,2005,27(3):339-345Yang Changfu,Lin Changyou,Sun Chongchi,et al. Inversions for MT data in 2-D symmetrical anisotropic media[J]. Acta Seismologica Sinica,2005,27(3):339-345
16 Newman G A,Commer M,Carazzone J J. Imaging CSEM data in the presence of electrical anisotropy[J]. Geophysics,2010,75(2):F51-F61
17 Rodi W,Mackie R L. Nonlinear conjugate gradients algorithm for2 -D magnetotelluric inversion[J]. Geophysics,2001,66:174-187
18 林昌洪.大地电磁张量阻抗三维共轭梯度反演研究[D].北京:中国地质大学(北京),2009.Lin Changhong. Three-dimensional conjugate gradients inversion of magnetotelluric impedance tensor[D]. Beijing:China University of Geosciences(Beijing),2009
19 徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994Xu Shizhe. The finite element method in geophysics[M]. Beijing:Science Press,1994
2 Pek J,Santos F A M. Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media[J]. Computer&Geosciences,2002,28:939-950
3 Reddy I K,Rankin D. Magnetotelluric effect of dipping anisotropies[J]. Geophysical Prospecting,1971,19(1):84-97
4 霍光谱,胡祥云,方慧,等.层状各向异性介质大地电磁联合反演研究[J].物理学报,2012,61(12):129101Huo Guangpu,Hu Xiangyun,Fang Hui,et al. Magnetotelluric joint inversion for anisotropic conductivities in layered media[J]. Acta Physica Sinica,2012,61(12):129101
5 林长佑,武玉霞,杨长福,等.水平层状对称各向异性介质的大地电磁资料反演[J].地球物理学报,1996,39(增刊1):342-348Lin Changyou,Wu Yuxia,Yang Changfu,et al. Magnetotelluric inversion for symmetrically anisotropic layered medium[J]. Chinese Journal of Geophysics,1996,39(S1):342-348
6 秦林江,杨长福.大地电磁全张量响应的一维各向异性反演[J].地球物理学报,2012,55(2):693-701Qin Linjiang,Yang Changfu. A magnetotelluric inversion method of the whole tensor impedance response to one-dimensional anisotropic structure[J]. Chinese Journal of Geophysics, 2012, 55(2):693-701
7 Reddy I K,Rankin D. Magnetotelluric response of laterally inhomogeneous and anisotropic structure[J]. Geophysics, 1975, 40:1035-1045
8 徐世浙,赵生凯.二维各向异性地电剖面的大地电磁场的有限元解法[J].地震学报,1985,7(1):80-90Xu Shizhe,Zhao Shengkai. Solution of magnetotelluric field equations for a two-dimensional,anisotropic geoelectric section by the finite element method[J]. Acta Seismologica Sinica,1985,7(1):80-90
9 Pek J,Verner T. Finite-difference modeling of magnetotelluric fields in two-dimensional anisotropic media[J]. Geophysical Journal International,1997,128(1):505-521
10 Li Y. A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures[J]. Geophysical Journal International,2002,148:389-401
11 Li Y,Josef P. Adaptive finite element modeling of two-dimensional magnetotelluric fields in general anisotropic media[J]. Geophysical Journal International,2008,175:942-954
12 胡祥云,霍光谱,高锐,等.大地电磁各向异性二维模拟及实例分析[J].地球物理学报,2013,56(12):4268-4277Hu Xiangyun,Huo Guangpu,Gao Rui,et al. The magnetotelluric anisotropic two-dimensional simulation and case analysis[J]. Chinese Journal of Geophysics,2013,56(12):4268-4277
13 秦林江.各向异性介质的MT正反演研究[D].杭州:浙江大学,2013Qin Linjiang. The forward and inversion of MT field in anisotropic conductivity structures[D]. Hangzhou:Zhejiang University,2013
14 Pain C C,Herwanger J R V,Saunders J H,et al. Anisotropic resistivity inversion[J]. Inverse Problems,2003,19(5):1081-1111
15 杨长福,林长佑,孙崇赤,等.二维对称各向异性介质大地电磁反演[J].地震学报,2005,27(3):339-345Yang Changfu,Lin Changyou,Sun Chongchi,et al. Inversions for MT data in 2-D symmetrical anisotropic media[J]. Acta Seismologica Sinica,2005,27(3):339-345
16 Newman G A,Commer M,Carazzone J J. Imaging CSEM data in the presence of electrical anisotropy[J]. Geophysics,2010,75(2):F51-F61
17 Rodi W,Mackie R L. Nonlinear conjugate gradients algorithm for2 -D magnetotelluric inversion[J]. Geophysics,2001,66:174-187
18 林昌洪.大地电磁张量阻抗三维共轭梯度反演研究[D].北京:中国地质大学(北京),2009.Lin Changhong. Three-dimensional conjugate gradients inversion of magnetotelluric impedance tensor[D]. Beijing:China University of Geosciences(Beijing),2009
19 徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994Xu Shizhe. The finite element method in geophysics[M]. Beijing:Science Press,1994