起伏海底地形时间域海洋电磁三维自适应正演模拟
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摘要
本文基于自适应非结构有限元算法实现海洋电磁起伏海底地形三维正演模拟.通过采用隐式后推欧拉时间离散技术,保证在较大的时间步长条件下获得正确结果.为获得多时间道海洋电磁正演模拟的有效网格,我们采用基于法向电流连续的后验误差估计的自适应方法和网格融合技术;同时为了控制网格数量和保证正演模拟稳定性,我们还在网格融合过程中应用了随机网格挑选技术.对于方程组求解我们使用MUMPUS直接求解器.当时间步长不变时,只需对系数矩阵进行一次分解,大大提高计算速度.将本文计算结果与半空间模型解析解进行对比,验证了本文算法精度.针对海洋电磁半拖曳式和双船拖曳式工作方式,我们通过典型模型的模拟计算,研究海底地形影响及海底高阻层识别特征.
We realize 3D modeling for time-domain marine controlled-source electromagnetic(CSEM)method using adaptive unstructured finite-element method.For the time discretization,we use the implicit backward Euler technique to ensure a stable and accurate modeling even for large time intervals.To obtain an effective mesh for accurate multichannel MCSEM modeling,we use adaptive method based on the continuity of normal current for the posterior errors estimation and mesh integration technique.To control the number of grids while maintaining stability for the forward modeling,we run a random choice in the process of mesh integration.We use MUMPUS to solve the system of linear equations that needs only to decompose the matrix once and thus enhances the modeling speed.Checking against the semi-analytical solution for a halfspace under the ocean verify the accuracy of our algorithm.Via numerical experiments for both semi-towed and dual-ship towed MCSEM systems,we can easily investigate the EM characteristic of topographic ocean floor and the resistive target underneath.
We realize 3D modeling for time-domain marine controlled-source electromagnetic(CSEM)method using adaptive unstructured finite-element method.For the time discretization,we use the implicit backward Euler technique to ensure a stable and accurate modeling even for large time intervals.To obtain an effective mesh for accurate multichannel MCSEM modeling,we use adaptive method based on the continuity of normal current for the posterior errors estimation and mesh integration technique.To control the number of grids while maintaining stability for the forward modeling,we run a random choice in the process of mesh integration.We use MUMPUS to solve the system of linear equations that needs only to decompose the matrix once and thus enhances the modeling speed.Checking against the semi-analytical solution for a halfspace under the ocean verify the accuracy of our algorithm.Via numerical experiments for both semi-towed and dual-ship towed MCSEM systems,we can easily investigate the EM characteristic of topographic ocean floor and the resistive target underneath.
引文
Avdeeva A,Commer M,Newman G A.2007.Hydrocarbon reservoir detectability study for marine CSEM methods:time-domain versus frequency-domain.∥2007SEG Annual Meeting.San Antonio:SEG.
Chave A D,Cox C S.1982.Controlled electromagnetic Sources for measuring electrical conductivity beneath the oceans:1.Forward problem and model study.Journal of Geophysical Research:Solid Earth,87(B7):5327-5338,doi:10.1029/JB087iB07p05327.
Cheesman S J,Edwards R N,Chave A D.1987.On the theory of sea-floor conductivity mapping using transient electromagnetic systems.Geophysics,52(2):204-217,doi:10.1190/1.1442296.
Commer M,Newman G A.2004.A parallel finite-difference approach for 3Dtransient electromagnetic modeling with galvanic sources.Geophysics,69(5):1192-1202,doi:10.1190/1.1801936.
Edwards R N,Chave A D.1986.A transient electric dipole-dipole method for mapping the conductivity of the sea floor.Geophysics,51(4):984-987,doi:10.1190/1.1442156.
Everett M E,Edwards R N.1992.Transient marine electromagnetics:the 2.5-D forward problem.Geophysical Journal International,113(3):545-561,doi:10.1111/j.1365-246X.1993.tb04651.x.
Jin J M.1998.Electromagnetic Finite-Element Method(in Chinese).Wang J G,trans.Xi′an:Xidian University Press.
Newman G A,Alumbaugh D L.1995.Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences.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.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013.A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling.Geophysical Journal International,194(2):700-718,doi:10.1093/gji/ggt154.
Ren Z Y,Tang J T.2010.3Ddirect current resistivity modeling with unstructured mesh by adaptive finite-element method.Geophysics,75(1),H7-H17,doi:10.1190/1.3298690.
Schwarzbach C,B9rner R,Spitzer K.2011.Three-dimensional adaptive higher order finite element simulation for geo-electromagnetic-a marine CSEM example.Geophysical Journal International,187(1):63-74,doi:10.1111/j.1365-246X.2011.05127.x.
Swidinsky A,Edwards R N.2010.The transient electromagnetic response of a resistive sheet:an extension to three dimensions.Geophysical Journal International,182(2):663-674,doi:10.1111/j.1365-246X.2010.04649.x.
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.
Um E S.2011.Three-dimensional finite-element time-domain modeling of the marine controlled-source electromagnetic method[Ph.D.thesis].San Francisco:Stanford University.
Um E S,Alumbaugh D L,Harris J M,et al.2012.Numerical modeling analysis of short-offset electric-field measurements with a vertical electric dipole source in complex offshore environments.Geophysics,77(5):E329-E341,doi:10.1190/GEO2011-0442.1.
Yin C C,Zhang B,Liu Y H,et al.2016.A goal-oriented adaptive finite-element method for 3Dscattered airborne electromagnetic method modeling.Geophysics,81(5):E337-E346,doi:10.1190/GEO2015-0580.1.
Zhang B,Yin C C,Ren X Y,et al.2018.Adaptive finite element for 3Dtime-domain airborne electromagnetic modeling based on hybrid posterior error estimation.Geophysics,83(2):WB71-WB79.
Zhdanov M S,Lee S K,Yoshioka Ken.2006.Integral equation method for 3D modeling of electromagnetic fields in complex structures with inhomogeneous background conductivity.Geophysics,71(6):G333-G345,doi:10.1190/1.2358403.
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.
Chave A D,Cox C S.1982.Controlled electromagnetic Sources for measuring electrical conductivity beneath the oceans:1.Forward problem and model study.Journal of Geophysical Research:Solid Earth,87(B7):5327-5338,doi:10.1029/JB087iB07p05327.
Cheesman S J,Edwards R N,Chave A D.1987.On the theory of sea-floor conductivity mapping using transient electromagnetic systems.Geophysics,52(2):204-217,doi:10.1190/1.1442296.
Commer M,Newman G A.2004.A parallel finite-difference approach for 3Dtransient electromagnetic modeling with galvanic sources.Geophysics,69(5):1192-1202,doi:10.1190/1.1801936.
Edwards R N,Chave A D.1986.A transient electric dipole-dipole method for mapping the conductivity of the sea floor.Geophysics,51(4):984-987,doi:10.1190/1.1442156.
Everett M E,Edwards R N.1992.Transient marine electromagnetics:the 2.5-D forward problem.Geophysical Journal International,113(3):545-561,doi:10.1111/j.1365-246X.1993.tb04651.x.
Jin J M.1998.Electromagnetic Finite-Element Method(in Chinese).Wang J G,trans.Xi′an:Xidian University Press.
Newman G A,Alumbaugh D L.1995.Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences.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.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013.A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling.Geophysical Journal International,194(2):700-718,doi:10.1093/gji/ggt154.
Ren Z Y,Tang J T.2010.3Ddirect current resistivity modeling with unstructured mesh by adaptive finite-element method.Geophysics,75(1),H7-H17,doi:10.1190/1.3298690.
Schwarzbach C,B9rner R,Spitzer K.2011.Three-dimensional adaptive higher order finite element simulation for geo-electromagnetic-a marine CSEM example.Geophysical Journal International,187(1):63-74,doi:10.1111/j.1365-246X.2011.05127.x.
Swidinsky A,Edwards R N.2010.The transient electromagnetic response of a resistive sheet:an extension to three dimensions.Geophysical Journal International,182(2):663-674,doi:10.1111/j.1365-246X.2010.04649.x.
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.
Um E S.2011.Three-dimensional finite-element time-domain modeling of the marine controlled-source electromagnetic method[Ph.D.thesis].San Francisco:Stanford University.
Um E S,Alumbaugh D L,Harris J M,et al.2012.Numerical modeling analysis of short-offset electric-field measurements with a vertical electric dipole source in complex offshore environments.Geophysics,77(5):E329-E341,doi:10.1190/GEO2011-0442.1.
Yin C C,Zhang B,Liu Y H,et al.2016.A goal-oriented adaptive finite-element method for 3Dscattered airborne electromagnetic method modeling.Geophysics,81(5):E337-E346,doi:10.1190/GEO2015-0580.1.
Zhang B,Yin C C,Ren X Y,et al.2018.Adaptive finite element for 3Dtime-domain airborne electromagnetic modeling based on hybrid posterior error estimation.Geophysics,83(2):WB71-WB79.
Zhdanov M S,Lee S K,Yoshioka Ken.2006.Integral equation method for 3D modeling of electromagnetic fields in complex structures with inhomogeneous background conductivity.Geophysics,71(6):G333-G345,doi:10.1190/1.2358403.
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.