虚拟波动域三维海洋可控源电磁场正演模拟
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摘要
本文基于对应原理将似稳态条件下频率域电磁场扩散方程转换成虚拟波动域电磁场波动方程,采用高阶时域有限差分进行求解,引入复频移完全匹配层吸收边界条件,降低了内存需求,提高了计算效率,并在虚拟波动域用伪δ函数离散电偶极源,实现了虚拟波动域任意取向电偶极源三维海洋可控源电磁场高阶时域有限差分正演算法.通过与拟解析解和频率域三维可控源电磁场数值模拟结果的对比,验证了本文算法的正确性和高效性,且探讨了网格参数和边界条件对不同频率电磁场模拟结果的影响.
In this paper,we transform quasi-state frequency domain diffusion equations to wave equations in the fictitious wave domain.A complex frequency shifted perfectly matched layer(CFS-PML)boundary condition is adopted to the high-order finite difference time domain(FDTD)algorithm for reducing storage requirements and improving computational efficiency.We divide the dipole source by the pseudo-delta function for simulating electromagnetic response of arbitrary orientation electric dipole.By comparing the numerical solution with 1 Danalytical solution and3Dfrequency controlled source electromagnetic(CSEM)results,we verify the validity,the accuracy and the efficiency of the algorithm,and then investigate and analyze the influence of different grid parameters and boundary conditions on numerical result at different frequency.
In this paper,we transform quasi-state frequency domain diffusion equations to wave equations in the fictitious wave domain.A complex frequency shifted perfectly matched layer(CFS-PML)boundary condition is adopted to the high-order finite difference time domain(FDTD)algorithm for reducing storage requirements and improving computational efficiency.We divide the dipole source by the pseudo-delta function for simulating electromagnetic response of arbitrary orientation electric dipole.By comparing the numerical solution with 1 Danalytical solution and3Dfrequency controlled source electromagnetic(CSEM)results,we verify the validity,the accuracy and the efficiency of the algorithm,and then investigate and analyze the influence of different grid parameters and boundary conditions on numerical result at different frequency.
引文
Avdeeva A,Commer M,Newman G A.2007.Hydrocarbon reservoir detectability study for marine CSEM methods:timedomain versus frequency-domain.∥77th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Berenger J P.1994.A perfectly matched layer for the absorption of electromagnetic waves.Journal of Computational Physics,114(2):185-200,doi:10.1006/jcph.1994.1159.
Chen Y H,Chew W C,Oristaglio M L.1997.Application of perfectly matched layers to the transient modeling of subsurface EM problems.Geophysics,62(6):1730-1736,doi:10.1190/1.1444273.
Christ M L.2000.High-order finite difference methods for wave equations[Ph.D.thesis].Colorado:University of Colorado.
Commer M,Newman G.2004.A parallel finite-difference approach for 3Dtransient electromagnetic modeling with galvanic sources.Geophysics,69(5):1192-1202,doi:10.1190/1.1801936.
Constable S,Srnka L J.2007.An introduction to marine controlledsource electromagnetic methods for hydrocarbon exploration.Geophysics,72(2):WA3-WA12,doi:10.1190/1.2432483.
Constable S.2010.Ten years of marine CSEM for hydrocarbon exploration.Geophysics,75(5):75A67-75A81,doi:10.1190/1.3483451.
de Hoop A T.1996.A general correspondence principle for timedomain electromagnetic wave and diffusion fields.Geophysical Journal International,127(3):757-761.
Druskin V,Knizhnerman L.1994.Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains.Radio Science,29(4):937-953,doi:10.1029/94rs00747.
Ge D B,Yan Y B.2011.Finite-Difference Time-Domain Method for Electromagnetic Waves(in Chinese).3rd ed.Xi'an:Xidian University Press.
Han B,Hu X Y,Huang Y F,et al.2015a.3-D frequency-domain CSEM modeling using aparallel direct solver.Chinese Journal of Geophysics(in Chinese),58(8):2812-2826,doi:10.6038/cjg20150816.
Han B,Hu X Y,Schultz A,et al.2015b.Three-dimensional forward modeling of the marine controlled-source electromagnetic field with complex source geometries.Chinese Journal of Geophysics(in Chinese),58(3):1059-1071,doi:10.6038/cjg20150330.
Han B,Li Y G,Li G.2018.3Dforward modeling of magnetotelluric fields in general anisotropic media and its numerical implementation in Julia.Geophysics,83(4):F29-F40.
Hu Y P,Egbert G,Ji Y J,et al.2017.A novel CFS-PMLboundary condition for transient electromagnetic simulation using a fictitious wave domain method.Radio Science,52(1):118-131,doi:10.1002/2016rs006160.
Kane Y.1966.Numerical solution of initial boundary value problems involving maxwell′s equations in isotropic media.IEEETransactions on Antennas and Propagation,14(3):302-307,doi:10.1109/tap.1966.1138693.
Kong F M,Li K,Liu X.2006.Accurate analysis of planar optical waveguide devices using higher-order FDTD scheme.Optics Express,14(24):11796-11803,doi:10.1364/oe.14.011796.
Lee K H,Liu G,Morrison H F.1989.A new approach to modeling the electromagnetic response of conductive media.Geophysics,54(9):1180-1192,doi:10.1190/1.1442753.
Li G,Li Y G,Han B,et al.2018.Application of the perfectly matched layer in 3-D marine controlled-source electromagnetic modelling.Geophysical Journal International,212(1):333-344,doi:10.1093/gji/ggx382.
Li Y G,Constable S.2010.Transient electromagnetic in shallow water:insights from 1Dmodeling.Chinese Journal of Geophysics(in Chinese),53(3):737-742,doi:10.3969/j.issn.0001-5733.2010.03.029.
Li Y G,Duan S M.2014.Data preprocessing of marine controlledsource electromagnetic data.Periodical of Ocean University of China,44(10):106-112,doi:10.16441/j.cnki.hdxb.2014.10.015
Li Y G,Li G.2016.Electromagnetic field expressions in the wavenumber domain from both the horizontal and vertical electric dipoles.Journal of Geophysics and Engineering,13(4):505-515,doi:10.1088/1742-2132/13/4/505.
Liu Y,Li Y G,Han B.2017.Adaptive edge finite element modeling of the 3DCSEM field on unstructured grids.Chinese Journal of Geophysics(in Chinese),60(12):4874-4886,doi:10.6038/cjg20171227.
MaaF A.2007.Fast finite-difference time-domain modeling for marine-subsurface electromagnetic problems.Geophysics,72(2):A19-A23,doi:10.1190/1.2434781.
Mitsuhata Y.2000.2-D electromagnetic modeling by finite-element method with a dipole source and topography.Geophysics,65(2):465-475,doi:10.1190/1.1444740.
Mittet R.2010.High-order finite-difference simulations of marine CSEM surveys using a correspondence principle for wave and diffusion fields.Geophysics,75(1):F33-F50,doi:10.1190/1.3278525.
Mittet R.2015.Seismic wave propagation concepts applied to the interpretation of marine controlled-source electromagnetics.Geophysics,80(2):E63-E81,doi:10.1190/Geo2014-0215.1.
Oristaglio M L,Hohmann G W.1984.Diffusion of electromagnetic fields into a two-dimensional earth:a finite-difference approach.Geophysics,49(7):870-894,doi:10.1190/1.1441733.
Puzyrev V,Koldan J,de la Puente J,et al.2013.A parallel finiteelement method for three-dimensional controlled-source electromagnetic forward modelling.Geophysical Journal International,193(2):678-693,doi:10.1093/gji/ggt027.
Sasaki Y,Meju M A.2009.Useful characteristics of shallow and deep marine CSEM responses inferred from 3Dfinite-difference modeling.Geophysics,74(5):F67-F76,doi:10.1190/1.3168616.
Streich R.2009.3Dfinite-difference frequency-domain modeling of controlled-source electromagnetic data:direct solution and optimization for high accuracy.Geophysics,74(5):F95-F105,doi:10.1190/1.3196241.
Um E S,Harris J M,Alumbaugh D L.2010.3Dtime-domain simulation of electromagnetic diffusion phenomena:A finiteelement electric-field approach.Geophysics,75(4):F115-F126,doi:10.1190/1.3473694.
Wang T,Hohmann G W.1991.A finite-difference time-stepping solution for three-dimensional electromagnetic modeling.∥61th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,432-435,doi:10.1190/1.1889155.
Weiss C J,Constable S.2006.Mapping thin resistors and hydrocarbons with marine EM methods,part II-modeling and analysis in 3D.Geophysics,71(6):G321-G332,doi:10.1190/1.2356908.
Yang B,Xu Y X,He Z X,et al.2012.3Dfrequency-domain modeling of marine controlled source electromagnetic responses with topography using finite volume method.Chinese Journal of Geophysics(in Chinese),55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04.035.
Young P D,Cox C S.1981.Electromagnetic active source sounding near the East Pacific Rise.Geophysical Research Letters,8(10):1043-1046,doi:10.1029/GL008i010p01043.
葛德彪,闫玉波.2011.电磁波时域有限差分方法.3版.西安:西安电子科技大学出版社.
韩波,胡祥云,黄一凡等.2015a.基于并行化直接解法的频率域可控源电磁三维正演.地球物理学报,58(8):2812-2826,doi:10.6038/cjg20150816.
韩波,胡祥云,Schultz A等.2015b.复杂场源形态的海洋可控源电磁三维正演.地球物理学报,58(3):1059-1071,doi:10.6038/cjg20150330
李予国,Constable S.2010.浅水区的瞬变电磁法:一维数值模拟结果分析.地球物理学报,53(3):737-742,doi:10.3969/j.issn.0001-5733.2010.03.029.
李予国,段双敏.2014.海洋可控源电磁数据预处理方法研究.中国海洋大学学报,44(10):106~112,doi:10.16441/j.cnki.hdxb.2014.10.015
刘颖,李予国,韩波.2017.可控源电磁场三维自适应矢量有限元正演模拟.地球物理学报,60(12):4874-4886,doi:10.6038/cjg20171227.
杨波,徐义贤,何展翔等.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模拟.地球物理学报,55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04.035.
Berenger J P.1994.A perfectly matched layer for the absorption of electromagnetic waves.Journal of Computational Physics,114(2):185-200,doi:10.1006/jcph.1994.1159.
Chen Y H,Chew W C,Oristaglio M L.1997.Application of perfectly matched layers to the transient modeling of subsurface EM problems.Geophysics,62(6):1730-1736,doi:10.1190/1.1444273.
Christ M L.2000.High-order finite difference methods for wave equations[Ph.D.thesis].Colorado:University of Colorado.
Commer M,Newman G.2004.A parallel finite-difference approach for 3Dtransient electromagnetic modeling with galvanic sources.Geophysics,69(5):1192-1202,doi:10.1190/1.1801936.
Constable S,Srnka L J.2007.An introduction to marine controlledsource electromagnetic methods for hydrocarbon exploration.Geophysics,72(2):WA3-WA12,doi:10.1190/1.2432483.
Constable S.2010.Ten years of marine CSEM for hydrocarbon exploration.Geophysics,75(5):75A67-75A81,doi:10.1190/1.3483451.
de Hoop A T.1996.A general correspondence principle for timedomain electromagnetic wave and diffusion fields.Geophysical Journal International,127(3):757-761.
Druskin V,Knizhnerman L.1994.Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains.Radio Science,29(4):937-953,doi:10.1029/94rs00747.
Ge D B,Yan Y B.2011.Finite-Difference Time-Domain Method for Electromagnetic Waves(in Chinese).3rd ed.Xi'an:Xidian University Press.
Han B,Hu X Y,Huang Y F,et al.2015a.3-D frequency-domain CSEM modeling using aparallel direct solver.Chinese Journal of Geophysics(in Chinese),58(8):2812-2826,doi:10.6038/cjg20150816.
Han B,Hu X Y,Schultz A,et al.2015b.Three-dimensional forward modeling of the marine controlled-source electromagnetic field with complex source geometries.Chinese Journal of Geophysics(in Chinese),58(3):1059-1071,doi:10.6038/cjg20150330.
Han B,Li Y G,Li G.2018.3Dforward modeling of magnetotelluric fields in general anisotropic media and its numerical implementation in Julia.Geophysics,83(4):F29-F40.
Hu Y P,Egbert G,Ji Y J,et al.2017.A novel CFS-PMLboundary condition for transient electromagnetic simulation using a fictitious wave domain method.Radio Science,52(1):118-131,doi:10.1002/2016rs006160.
Kane Y.1966.Numerical solution of initial boundary value problems involving maxwell′s equations in isotropic media.IEEETransactions on Antennas and Propagation,14(3):302-307,doi:10.1109/tap.1966.1138693.
Kong F M,Li K,Liu X.2006.Accurate analysis of planar optical waveguide devices using higher-order FDTD scheme.Optics Express,14(24):11796-11803,doi:10.1364/oe.14.011796.
Lee K H,Liu G,Morrison H F.1989.A new approach to modeling the electromagnetic response of conductive media.Geophysics,54(9):1180-1192,doi:10.1190/1.1442753.
Li G,Li Y G,Han B,et al.2018.Application of the perfectly matched layer in 3-D marine controlled-source electromagnetic modelling.Geophysical Journal International,212(1):333-344,doi:10.1093/gji/ggx382.
Li Y G,Constable S.2010.Transient electromagnetic in shallow water:insights from 1Dmodeling.Chinese Journal of Geophysics(in Chinese),53(3):737-742,doi:10.3969/j.issn.0001-5733.2010.03.029.
Li Y G,Duan S M.2014.Data preprocessing of marine controlledsource electromagnetic data.Periodical of Ocean University of China,44(10):106-112,doi:10.16441/j.cnki.hdxb.2014.10.015
Li Y G,Li G.2016.Electromagnetic field expressions in the wavenumber domain from both the horizontal and vertical electric dipoles.Journal of Geophysics and Engineering,13(4):505-515,doi:10.1088/1742-2132/13/4/505.
Liu Y,Li Y G,Han B.2017.Adaptive edge finite element modeling of the 3DCSEM field on unstructured grids.Chinese Journal of Geophysics(in Chinese),60(12):4874-4886,doi:10.6038/cjg20171227.
MaaF A.2007.Fast finite-difference time-domain modeling for marine-subsurface electromagnetic problems.Geophysics,72(2):A19-A23,doi:10.1190/1.2434781.
Mitsuhata Y.2000.2-D electromagnetic modeling by finite-element method with a dipole source and topography.Geophysics,65(2):465-475,doi:10.1190/1.1444740.
Mittet R.2010.High-order finite-difference simulations of marine CSEM surveys using a correspondence principle for wave and diffusion fields.Geophysics,75(1):F33-F50,doi:10.1190/1.3278525.
Mittet R.2015.Seismic wave propagation concepts applied to the interpretation of marine controlled-source electromagnetics.Geophysics,80(2):E63-E81,doi:10.1190/Geo2014-0215.1.
Oristaglio M L,Hohmann G W.1984.Diffusion of electromagnetic fields into a two-dimensional earth:a finite-difference approach.Geophysics,49(7):870-894,doi:10.1190/1.1441733.
Puzyrev V,Koldan J,de la Puente J,et al.2013.A parallel finiteelement method for three-dimensional controlled-source electromagnetic forward modelling.Geophysical Journal International,193(2):678-693,doi:10.1093/gji/ggt027.
Sasaki Y,Meju M A.2009.Useful characteristics of shallow and deep marine CSEM responses inferred from 3Dfinite-difference modeling.Geophysics,74(5):F67-F76,doi:10.1190/1.3168616.
Streich R.2009.3Dfinite-difference frequency-domain modeling of controlled-source electromagnetic data:direct solution and optimization for high accuracy.Geophysics,74(5):F95-F105,doi:10.1190/1.3196241.
Um E S,Harris J M,Alumbaugh D L.2010.3Dtime-domain simulation of electromagnetic diffusion phenomena:A finiteelement electric-field approach.Geophysics,75(4):F115-F126,doi:10.1190/1.3473694.
Wang T,Hohmann G W.1991.A finite-difference time-stepping solution for three-dimensional electromagnetic modeling.∥61th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,432-435,doi:10.1190/1.1889155.
Weiss C J,Constable S.2006.Mapping thin resistors and hydrocarbons with marine EM methods,part II-modeling and analysis in 3D.Geophysics,71(6):G321-G332,doi:10.1190/1.2356908.
Yang B,Xu Y X,He Z X,et al.2012.3Dfrequency-domain modeling of marine controlled source electromagnetic responses with topography using finite volume method.Chinese Journal of Geophysics(in Chinese),55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04.035.
Young P D,Cox C S.1981.Electromagnetic active source sounding near the East Pacific Rise.Geophysical Research Letters,8(10):1043-1046,doi:10.1029/GL008i010p01043.
葛德彪,闫玉波.2011.电磁波时域有限差分方法.3版.西安:西安电子科技大学出版社.
韩波,胡祥云,黄一凡等.2015a.基于并行化直接解法的频率域可控源电磁三维正演.地球物理学报,58(8):2812-2826,doi:10.6038/cjg20150816.
韩波,胡祥云,Schultz A等.2015b.复杂场源形态的海洋可控源电磁三维正演.地球物理学报,58(3):1059-1071,doi:10.6038/cjg20150330
李予国,Constable S.2010.浅水区的瞬变电磁法:一维数值模拟结果分析.地球物理学报,53(3):737-742,doi:10.3969/j.issn.0001-5733.2010.03.029.
李予国,段双敏.2014.海洋可控源电磁数据预处理方法研究.中国海洋大学学报,44(10):106~112,doi:10.16441/j.cnki.hdxb.2014.10.015
刘颖,李予国,韩波.2017.可控源电磁场三维自适应矢量有限元正演模拟.地球物理学报,60(12):4874-4886,doi:10.6038/cjg20171227.
杨波,徐义贤,何展翔等.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模拟.地球物理学报,55(4):1390-1399,doi:10.6038/j.issn.0001-5733.2012.04.035.