频率域航空电磁三维矢量有限元正演模拟

黄威; 殷长春; 贲放; 刘云鹤; 陈辉; 蔡晶

doi:10.3799/dqkx.2016.025

Volume 41 Issue 2

Feb. 2016

Turn off MathJax

Article Contents

Article Navigation > Earth Science > 2016 > 41(2): 331-342

Huang Wei, Yin Changchun, Ben Fang, Liu Yunhe, Chen Hui, Cai Jing, 2016. 3D Forward Modeling for Frequency AEM by Vector Finite Element. Earth Science, 41(2): 331-342. doi: 10.3799/dqkx.2016.025

Citation:

Huang Wei, Yin Changchun, Ben Fang, Liu Yunhe, Chen Hui, Cai Jing, 2016. 3D Forward Modeling for Frequency AEM by Vector Finite Element. Earth Science, 41(2): 331-342. doi: 10.3799/dqkx.2016.025

Huang Wei, Yin Changchun, Ben Fang, Liu Yunhe, Chen Hui, Cai Jing, 2016. 3D Forward Modeling for Frequency AEM by Vector Finite Element. Earth Science, 41(2): 331-342. doi: 10.3799/dqkx.2016.025

Citation:

Huang Wei, Yin Changchun, Ben Fang, Liu Yunhe, Chen Hui, Cai Jing, 2016. 3D Forward Modeling for Frequency AEM by Vector Finite Element. Earth Science, 41(2): 331-342. doi: 10.3799/dqkx.2016.025

PDF( 2101 KB)

3D Forward Modeling for Frequency AEM by Vector Finite Element

doi: 10.3799/dqkx.2016.025

College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China

Received Date: 2015-09-25
Publish Date: 2016-02-15

Abstract

Abstract

The finite-element method and application in EM exploration are well-developed. However, applications of the technology are focused mostly on ground and marine EM. Little attention has been put on airborne EM. Based on the previous research, we work on three-dimensional (3D) modeling for airborne systems by vector finite-element. We apply double-curl inhomogeneous vector Helmholtz equation for the second field and obtain the variational equations by using the generalized variational principle. By dividing the model domain into hexahedral elements and putting the field on the edge, we use linear interpolation for each element and put them together to set up the linear equations. For the multiple-source problem of AEM, we use the MUMPS solver that could achieve satisfying results both on speed and accuracy. We test the stability of our algorithm on a single abnormal body model first and check the practicability of the algorithm by simulating on typical geoelectrical models. The model results show that the overburden and the vertical contacting zone have great influence on the AEM responses.
- airborne EM,
- vector finite element,
- vertical magnetic dipole,
- fast solver,
- electric prospecting

FullText(HTML)

References(72)

References

Andersen, L.S., Volakis, J.L., 1998.Hierarchical Tangential Vector Finite Elements for Tetrahedra.IEEE Microwave and Guided Wave Letters, 8(3):127-129.doi: 10.1109/75.661137

Agullo, E., 2008.Méthodes Directes Hors-Mémoire (Out-of-Core) Pour la Résolution de Systèmes Linéaires Creux de Grande Taille(Dissertation).Université Sciences et Technologies-Bordeaux I, Bordeaux.

Amestoy, P.R., Duff, I.S., L'Excellent, J.Y., et al., 2012.On Computing Inverse Entries of a Sparse Matrix in an Out-Of-Core Environment.SIAM Journal on Scientific Computing, 34(4):A1975-A1999.doi: 10.1137/100799411

Amestoy, P.R., Duff, I.S., L'Excellent, J.Y., et al., 2001.A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling.SIAM Journal on Matrix Analysis and Applications, 23(1):15-41.doi: 10.1137/s0895479899358194

Avdeev, D.B., Kuvshinov, A.V., Pankratov, O.V., et al., 1998.Three-Dimensional Frequency-Domain Modeling of Airborne Electromagnetic Responses.Exploration Geophysics, 29(2):111.doi: 10.1071/eg998111

Cai, J., Qi, Y.F., Yin, C.C., 2014.Weighted Laterally-Constrained Inversion of Frequency-Domain Airborne EM Data.Chinese Journal of Geophysics, 57(3):953-960 (in Chinese with English abstract). http://manu39.magtech.com.cn/Geophy/EN/abstract/abstract10223.shtml

Coggon, J.H., 1971.Electromagnetic and Electrical Modeling by the Finite Element Method.Geophysics, 36(1):132-155.doi: 10.1190/1.1440151

Fan, C.S., 2013.Research on Complex Resistivity Forward and Inversion with Finite Element Method and Its Application(Dissertation).Jilin University, Changchun, 51-58 (in Chinese with English abstract).

Farquharson, C.G., Miensopust, M.P., 2011.Three-Dimensional Finite-Element Modelling of Magnetotelluric Data with a Divergence Correction.Journal of Applied Geophysics, 75(4):699-710.doi: 10.1016/j.jappgeo.2011.09.025

Fèvre, A., L'Excellent, J.Y., Pralet, S., 2006.Scilab and MATLAB Interfaces to MUMPS.Institut National de Recherche en Informatique et en Automatique, Paris.

Fountain, D., 1998.Airborne Electromagnetic Systems-50 Years of Development.Exploration Geophysics, 29(2):1.doi: 10.1071/eg998001

Fraser, D.C., 1981.Magnetite Mapping with a Multicoil Airborne Electromagnetic System.Geophysics, 46(11):1579-1593.doi: 10.1190/1.1441165

Gu, G.W., Wu, W.P., Li, T.L., 2014.Modeling for the Effect of Magnetotelluric 3D Topography Based on the Vector Finite-Element Method.Journal of Jilin University (Earth Science Edition), 44(5):1678-1686 (in Chinese with English abstract). https://www.researchgate.net/publication/286941298_Modeling_for_the_effect_of_magnetotelluric_3D_topography_based_on_the_vector_finite-element_method

Haber, E., Ascher, U.M., Oldenburg, D.W., 2004.Inversion of 3D Electromagnetic Data in Frequency and Time Domain Using an Inexact All-at-Once Approach.Geophysics, 69(5):1216-1228.doi: 10.1190/1.1801938

Hauser, J., Gunning, J., Annetts, D., 2015.Probabilistic Inversion of Airborne Electromagnetic Data under Spatial Constraints.Geophysics, 80(2):E135-E146.doi: 10.1190/geo2014-0389.1

Hohmann, G.W., 1975.Three-Dimensional Induced Polarization and Electromagnetic Modeling.Geophysics, 40(2):309-324.doi: 10.1190/1.1440527

Hu, Y.C., 2015.Three Dimensional Tensor Controlled Source Electromagnetic Modeling Based the Vector Finite Element(Dissertation).Jilin University, Changchun, 58-59 (in Chinese with English abstract).

Huang, H., Palacky, G.J., 1991.Damped Least-Squares Inversion of Time-Domain Airborne EM Data Based on Singular Value Decomposition1.Geophysical Prospecting, 39(6):827-844. doi: 10.1111/gpr.1991.39.issue-6

Huang, H.P., Wang, W.Z., 1990.Inversion of Time-Domain Airborne Electromagnetic Data.Chinese Journal of Geophysics, 33(1):87-97 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWX199001012.htm

Huang, J.G., Ruan, B.Y., Bao, G.S., 2002.Fem under Quantic-Boundary Condition for Modeling Resistivity on 3-D Geoelectric Section.Journal of Guilin Institute of Technology, (1):11-14 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-GLGX200201002.htm

Jahandari, H., Farquharson, C.G., 2014.A Finite-Volume Solution to the Geophysical Electromagnetic Forward Problem Using Unstructured Grids.Geophysics, 79(6):E287-E302.doi: 10.1190/GEO2013-0312.1.

Jin, J.M., 1998.Electromagnetic FEM.Translated by Wang J.G., Xi'an University of Electronic Science and Technology Press, Xi'an, 96 (in Chinese).

Key, K., Weiss, C., 2006.Adaptive Finite-Element Modeling Using Unstructured Grids: The 2D Magnetotelluric Example.Geophysics, 71(6):G291-G299.doi: 10.1190/1.2348091

Li, Y., Wu, X.P., Lin, P.R., 2015.Three-Dimensional Controlled Source Electromagnetic Finite Element Simulation Using the Secondary Field for Continuous Variation of Electrical Conductivity within Each Block.Chinese Journal of Geophysics, 58(3):1072-1087 (in Chinese with English abstract). http://manu39.magtech.com.cn/Geophy/EN/abstract/abstract11374.shtml

Liu, Y.H., Yin, C.C., 2013.3D Inversion for Frequency-Domain HEM Data.Chinese Journal of Geophysics, 56(12):4278-4287 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWX201312030.htm

Livelybrooks, D., 1993.Program 3Dfeem: A Multidimensional Electromagnetic Finite Element Model.Geophysical Journal International, 114(3):443-458.doi: 10.1111/j.1365-246x.1993.tb06978.x

Macnae, J.C., Smith, R., Polzer, B.D., et al., 1991.Conductivity-Depth Imaging of Airborne Electromagnetic Step-Response Data.Geophysics, 56(1):102-114.doi: 10.1190/1.1442945

Mitsuhata, Y., Uchida, T., 2004.3D Magnetotelluric Modeling Using the T-Ω Finite-Element Method.Geophysics, 69(1):108-119.doi: 10.1190/1.1649380

Nabighian, M.N., 1992.Electromagnetic Methods in Applied Geophysics Volume 1, Theory Society of Exploration Geophysicists.Translated by Zhao, J.X., et al., Geology Press, Beijing, 306 (in Chinese).

Newman, G.A., Alumbaugh, D.L., 1995.Frequency-Domain Modelling of Airborne Electromagnetic Responses Using Staggered Finite Differences1.Geophysical Prospecting, 43(8):1021-1042.doi: 10.1111/j.1365-2478.1995.tb00294.x

Oldenburg, D.W., Haber, E., Shekhtman, R., 2013.Three Dimensional Inversion of Multisource Time Domain Electromagnetic Data.Geophysics, 78(1):E47-E57.doi: 10.1190/geo2012-0131.1

Pemberton, R.H., 1962.Airborne Electromagnetics in Review.Geophysics, 27(5):691-713.doi: 10.1190/1.1439081

Puzyrev, V., Koldan, J., de la Puente, J., et al., 2013.A Parallel Finite-Element Method for Three-Dimensional Controlled-Source Electromagnetic Forward Modelling.Geophysical Journal International, 193(2):678-693.doi: 10.1093/gji/ggt027

Rachowicz, W., Zdunek, A., 2011.Application of the FEM with Adaptivity for Electromagnetic Inverse Medium Scattering Problems.Computer Methods in Applied Mechanics and Engineering, 200(29-32):2337-2347.doi: 10.1016/j.cma.2011.04.005

Raiche, A., 1998.Modelling the Time-Domain Response of AEM Systems.Exploration Geophysics, 29(2):103-106.doi: 10.1071/eg998103

Ruan, B.Y., Xiong, B., Xu, S.Z., 2001.Finite Element Method for Modeling Resistivity Sounding on 3-D Geoelectric Section.Earth Science, 26 (1):73-77 (in Chinese with English abstract). http://downloads.hindawi.com/journals/mpe/2017/8027616.pdf

Schwarzbach, C., Haber, E., 2013.Finite Element Based Inversion for Time-Harmonic Electromagnetic Problems.Geophysical Journal International, 193(2):615-634.doi: 10.1093/gji/ggt006

Tang, J.T., Zhang, L.C., Gong, J.Z., et al., 2014.3D Frequency Domain Controlled Source Electromagnetic Numerical Modeling with Coupled Finite-Infinite Element Method.Journal of Central South University (Science and Technology), 45(4):1251-12603 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZNGD201404033.htm

Tang, J.T., Wang, F.Y., Ren, Z.Y., 2010.2.5D DC Resistivity Modeling by Adaptive Finite-Element Method with Unstructured Triangulation.Chinese Journal of Geophysics, 53(3):708-716.doi: 10.3969/j.issn.0001-5733.2010.03.026

Tong, X.Z., Liu, J.X., Xie, W., et al., 2009.Three-Dimensional Forward Modeling for Magnetotelluric Sounding by Finite Element Method.Journal of Central South University of Technology, 16(1):136-142.doi: 10.1007/s11771-009-0023-5

Wang, W.P., Zeng, Z.F., Wu, C.P., 2015.Coil Attitude Influence and Attitude Correction Method for Frequency Domain Airborne Electromagnetic System.Earth Science, 7(7):1266-1275 (in Chinese with English abstract). https://www.researchgate.net/publication/290024870_Vehicle-borne_array_radar_attitude_correction_method

Wannamaker, P.E., Hohmann, G.W., SanFilipo, W.A., 1984.Electromagnetic Modeling of Three-Dimensional Bodies in Layered Earths Using Integral Equations.Geophysics, 49(1):60-74.doi: 10.1190/1.1441562

Xu, S.Z., 1994.The Finite Element Method in Geophysics.Science Press, Beijing, 247 (in Chinese).

Yang, B., Xu, Y.X., He, Z.X., 2012.3D Frequency-Domain Modeling of Marine Controlled Source Electromagnetic Responses with Topography Using Finite Volume Method.Chinese Journal of Geophysics, 55(4):1390-1399 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWX201204036.htm

Yang, H.J., Pan, H.P., Luo, M., et al., 2015.Numerical Modeling for Transient Anomalous Secondary Electromagnetic of Tabular Orebodyin Borehole.Earth Science, 40(10):1689-1700 (in Chinese with English abstract). https://www.researchgate.net/publication/249864657_The_borehole_transient_electromagnetic_response_of_a_three-dimensional_fracture_zone_in_a_conductive_half-space

Yin, C.C., Hodges, G., 2007.Simulated Annealing for Airborne EM Inversion.Geophysics, 72(4):F189-F195.doi: 10.1190/1.2736195

Yin, C.C., Huang, W., Ben, F., 2013.The Full-Time Electromagnetic Modeling for Time-Domain Airborne Electromagnetic Systems.Chinese Journal of Geophysics, 56(9):3153-3162.(in Chinese with English abstract) http://manu39.magtech.com.cn/Geophy_en/EN/abstract/abstract9765.shtml

Yin, C.C., Huang, X., Liu, Y.H., et al., 2014.Footprint for Frequency-Domain Airborne Electromagnetic Systems.Geophysics, 79(6):E243-E254.doi: 10.1190/geo2014-0007.1

Yin, C.C., Qi, Y.F., Liu, Y.H., et al., 2014.Trans-Dimensional Bayesian Inversion of Frequency-Domain Airborne EM Data.Chinese Journal of Geophysics, 57(9):2971-2980 (in Chinese with English abstract). http://manu39.magtech.com.cn/Geophy/EN/abstract/abstract10735.shtml

Yin, C.C., Zhang, B., Liu, Y.H., et al., 2015.2.5-D Forward Modeling of the Time-Domain Airborne EM System in Areas with Topographic Relief.Chinese Journal of Geophysics, 58(4):1411-1424.(in Chinese with English abstract) http://manu39.magtech.com.cn/Geophy/EN/abstract/abstract11402.shtml

Zhang, J.F., Tang, J.T., Yu, Y., et al., 2009.Three Dimensional Controlled Source Electromagnetic Numerical Simulation Based on Electric Field Vector Wave Equation Using Finite Element Method.Chinese Journal of Geophysics, 52(12):3132-3141 (in Chinese with English abstract). https://www.researchgate.net/publication/282794995_Three-dimensional_CSAMT_numerical_modeling_using_finite_difference_method_based_on_the_SQMR_method

Zyserman, F.I., Santos, J.E., 2000.Parallel Finite Element Algorithm with Domain Decomposition for Three-Dimensional Magnetotelluric Modelling.Journal of Applied Geophysics, 44(4):337-351.doi: 10.1016/S0926-9851(00)00012-4

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(1):953-960. http://www.cnki.com.cn/Article/CJFDTOTAL-DQWX201403024.htm

范翠松, 2013. 基于有限元法的复电阻率正反演研究及应用(博士学位论文). 吉林大学, 长春, 51-58. http://cdmd.cnki.com.cn/Article/CDMD-10183-1013193112.htm

顾观文, 吴文鹏, 李桐林, 2014.大地电磁场三维地形影响的矢量有限元数值模拟.吉林大学学报(地球科学版), 44(5):1678-1686. http://www.cnki.com.cn/Article/CJFDTOTAL-CCDZ201405028.htm

胡英才, 2015. 矢量有限元三维CSAMT正演模拟(博士学位论文). 长春: 吉林大学, 58-59.

黄皓平, 王维中, 1990.时间域航空电磁数据的反演.地球物理学报, 33(1):87-97. http://cdmd.cnki.com.cn/Article/CDMD-10183-1015590947.htm

黄俊革, 阮百尧, 鲍光淑, 2002.齐次边界条件下三维地电断面电阻率有限元数值模拟法.桂林工学学院学报, 22(1):11-14. http://www.cnki.com.cn/Article/CJFDTOTAL-GLGX200201002.htm

金建铭, 1998. 电磁场有限元方法. 王建国译, 西安: 西安电子科技大学出版社, 96.

李勇, 吴小平, 林平荣, 2015.基于二次场电导率分块连续变化的三维可控源电磁有限元数值模拟.地球物理学报, 58(3):1072-1087. doi: 10.6038/cjg20150331

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

Nabighian, M. N. , 1992. 勘察地球物理电磁法第一卷理论. 赵经祥等译, 北京: 地质出版社, 306.

阮百尧, 熊彬, 徐世浙, 2001.三维地电断面电阻率测深有限元数值模拟.地球科学, 26(1):73-77. http://www.earth-science.net/WebPage/Article.aspx?id=812

汤井田, 张林成, 公劲喆, 等, 2014.三维频率域可控源电磁法有限元-无限远结合数值模拟, 中南大学学报(自然科学版), 45(4):1251-1260. http://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201404033.htm

王卫平, 曾昭发, 吴成平, 2015.频率域航空电磁系统线圈姿态变化影响及校正方法.地球科学, 7(7):1266-1275. http://www.earth-science.net/WebPage/Article.aspx?id=3121

徐世浙, 1994.地球物理中的有限单元法.北京:科学出版社, 247.

杨波, 徐义贤, 何展翔, 2012.考虑海底地形的三维频率域可控源电磁响应有限体积法的模拟.地球物理学报, 55(4):1390-1399. http://www.cnki.com.cn/Article/CJFDTOTAL-DQWX201204036.htm

杨怀杰, 潘和平, 骆淼, 等, 2015.井中板状矿体瞬态异常二次场数值模拟.地球科学, 40(10):1689-1700. http://www.earth-science.net/WebPage/Article.aspx?id=3171

殷长春, 黄威, 贲放, 2013.时间域航空电磁系统瞬变全时响应正演模拟.地球物理学报, 56(9):3153-3162. doi: 10.6038/cjg20130928

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, 2015.2.5维起伏地表条件下时间域航空电磁正演模拟.地球物理学报, 58(4):1411-1424. doi: 10.6038/cjg20150427

张继峰, 汤井田, 喻言, 等.2009.基于电场矢量波动方程的三维可控源电磁法有限元法数值模拟.地球物理学报, 52(12):3132-3141. doi: 10.3969/j.issn.0001-5733.2009.12.023

Relative Articles

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(12)

Get Citation

PDF

XML

Article views (4847) PDF downloads(26)

3D Forward Modeling for Frequency AEM by Vector Finite Element

doi: 10.3799/dqkx.2016.025

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Proportional views

Export File

Citation

Format

Content