复杂介质频率域地面可控源电磁法2.5维快速成像
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摘要
基于微分方程法的复杂介质地面可控源电磁数据的正反演算法研究比较成熟,但其涉及复杂计算过程及昂贵的计算代价。采用体积分方程法,结合Anderson解析算法、稳定型双共轭梯度-快速傅里叶变换算法降低计算量及存储量要求;采用对比源反演算法,利用伴随算子及快速傅里叶变换算法提高多频率数据的反演迭代效率,开展复杂介质可控源电磁频率域数据的2. 5维快速正反演算法研究。3个不同复杂度模型算例表明,积分方程法2. 5维算法在复杂地形及大尺度地下目标体的模拟中具有独特优势;对比源反演过程避免了病态雅可比矩阵及其逆矩阵计算,无需正演算子,反演迭代稳定收敛。
Geophysical exploration for complex objects in deep depth is very important as the exploration of resource in shallow depth or known regions is well done in current years. With the traditional methods,such as differential equation modeling,the forward and inversion solvers have found a wide application for complex objects detection with ground controlled source electromagnetic( CSEM) method. However,the solvers based on differential equations have to deal with the huge computation. Thus,a fast imaging solver in 2. 5 dimensional( 2. 5D) is proposed for complex objects detection with frequency domain CSEM in this paper. In forward process,Anderson analytic calculation and BCGS-FFT are used to accelerate the computation of integral equation( IE). Inner solver and FFT are also applied in contrast source inversion( CSI) to fast imaging. Three complex case studies demonstrate the effectiveness of 2. 5D IE modeling and CSI to geophysical exploration with ground CSEM in frequency.
Geophysical exploration for complex objects in deep depth is very important as the exploration of resource in shallow depth or known regions is well done in current years. With the traditional methods,such as differential equation modeling,the forward and inversion solvers have found a wide application for complex objects detection with ground controlled source electromagnetic( CSEM) method. However,the solvers based on differential equations have to deal with the huge computation. Thus,a fast imaging solver in 2. 5 dimensional( 2. 5D) is proposed for complex objects detection with frequency domain CSEM in this paper. In forward process,Anderson analytic calculation and BCGS-FFT are used to accelerate the computation of integral equation( IE). Inner solver and FFT are also applied in contrast source inversion( CSI) to fast imaging. Three complex case studies demonstrate the effectiveness of 2. 5D IE modeling and CSI to geophysical exploration with ground CSEM in frequency.
引文
[1]沈金松,詹林森,王鹏飞,等.可控源海洋电磁勘探中空气波影响的理论分析和数值模拟[J].地球物理学报,2012,55(7):2473-2488.
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[3]张斌,谭捍东.带地形的可控源音频大地电磁法二维正演[J].物探与化探,2014,38(1):151-156.
[4]戴世坤,王顺国,张钱江,等.频率域可控源电磁法2.5 D正反演[J].中国有色金属学报,2013,23(9):2513-2523.
[5]滕吉文.强化第二深度空间金属矿产资源探查,加速发展地球物理勘探新技术与仪器设备的研制及产业化[J].地球物理学进展,2010,25(3):729-748.
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[8]胡英才,李桐林,范翠松,等.基于矢量有限元法的三维张量CSAMT正演模拟[J].应用地球物理,2015,12(1):35-46.
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[11]熊彬,蔡红柱,罗天涯,等.基于非结构化网格的人工源频率域三维电磁场数值模拟[J].桂林理工大学学报,2015,35(3):423-430.
[12]Bakr S A,Pardo D,Mannseth T.Domain decomposition Fourier finite element method for the simulation of 3D marine CSEM measurements[J].Journal of Computational Physics,2013,255:456-470.
[13]Oh S,Noh K,Seol S J,et al.3D CSEM frequency-domain modeling and inversion algorithms including topography[C]//SEG Technical Program Expanded Abstracts 2015,2015:828-832.
[14]Yoon D,Zhdanov M S,Cai H Z,et al.A hybrid finite difference and integral equation method for modeling and inversion of marine CSEM data[C]//SEG Technical Program Expanded Abstracts 2015,2015:823-827.
[15]杨大方.结合实际数据的三维可控源电磁法正反演研究[D].长春:吉林大学,2015.
[16]杨波,徐义贤,何展翔,等.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[J].地球物理学报,2012,55(4):1390-1399.
[17]韩波,胡祥云,Schultz A,等.复杂场源形态的海洋可控源电磁三维正演[J].地球物理学报,2015,58(3):1059-1071.
[18]Key K,Ovall J.A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modelling[J].Geophysical Journal International,2011,186(1):137-154.
[19]柳建新,汤文武,童孝忠.基于双二次插值的2.5维FC-SEM有限元正演模拟[J].中南大学学报(自然科学版),2014,45(2):474-482.
[20]白洪涛,范翠松,李昂,等.基于OpenMP+MPI的2.5维电磁场正演并行化方法[J].石油地球物理勘探,2015,50(1):170-176.
[21]殷长春,张博,刘云鹤,等.2.5维起伏地表条件下时间域航空电磁正演模拟[J].地球物理学报,2015,58(4):1411-1424.
[22]Key K.Marine electromagnetic studies of seafloor resources and tectonics[J].Surveys in geophysics,2012,33(1):135-167.
[23]刘云,王绪本.大地电磁二维自适应地形有限元正演模拟[J].地震地质,2010,32(3):382-391.
[24]柳建新,孙丽影,童孝忠,等.基于自适应有限元的起伏地形MT二维正演模拟[J].地球物理学进展,2012,27(5):2016-2023.
[25]董浩,魏文博,叶高峰,等.基于有限差分正演的带地形三维大地电磁反演方法[J].地球物理学报,2014,57(3):939-952.
[26]刘云.起伏地形大地电磁,时间域瞬变电磁二维数值模拟及直接反演法[D].成都:成都理工大学,2012.
[27]张继锋,智庆全,李貅,等.起伏地形电偶源2.5维有限元数值模拟[J].中国有色金属学报,2013,23(9):2540-2550.
[28]陈桂波,汪宏年,姚敬金,等.用积分方程法模拟各向异性地层中三维电性异常体的电磁响应[J].地球物理学报,2009,52(8):2174-2181.
[29]李静和,何展翔.地井垂直电磁Walkaway剖面法油藏开发三维模型电场响应特征[J].石油地球物理勘探,2012,47(4):653-664.
[30]李静和,何展翔.三维井间电磁最小二乘法反演[J].石油地球物理勘探,2014,49(3):586-595.
[31]Jia Y,Liu Q H,He Z X.Fast Three-dimensional electromagnetic nonlinear inversion method for imaging in a layered medium with application in geophysical exploration using BCGS-FFT[C]//SEG Technical Program Expanded Abstracts2014,2014:654-657.
[32]陈清.2.5维可控源电磁测深数据反演方法研究[D].北京:中国地质大学(北京),2011.
[33]龙剑波.2.5维航空瞬变电磁数据的非线性共轭梯度反演[D].长沙:中南大学,2014.
[34]杨悦.可控源电场数据三维反演及应用[D].长春:吉林大学,2015.
[35]Song L P,Liu Q H,Li F,et al.Reconstruction of three-dimensional objects in layered media:numerical experiments[J].IEEE Transactions on Antennas and Propagation,2005,53(4):1556-1561.
[36]Anderson W L.Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering[J].Geophysics,1979,44(7):1287-1305.
[2]向葵,胡文宝,严良俊,等.川黔地区页岩复电阻率的频散特性[J].石油地球物理勘探,2014,49(5):1013-1019.
[3]张斌,谭捍东.带地形的可控源音频大地电磁法二维正演[J].物探与化探,2014,38(1):151-156.
[4]戴世坤,王顺国,张钱江,等.频率域可控源电磁法2.5 D正反演[J].中国有色金属学报,2013,23(9):2513-2523.
[5]滕吉文.强化第二深度空间金属矿产资源探查,加速发展地球物理勘探新技术与仪器设备的研制及产业化[J].地球物理学进展,2010,25(3):729-748.
[6]Zaslavsky M,Druskin V,Davydycheva S,et al.Hybrid finitedifference integral equation solver for 3D frequency domain anisotropic electromagnetic problems[J].Geophysics,2011,76(2):F123-F137.
[7]Kamm J,Pedersen L B.Inversion of airborne tensor VLF data using integral equations[J].Geophysical Journal International,2014,198(2):775-794.
[8]胡英才,李桐林,范翠松,等.基于矢量有限元法的三维张量CSAMT正演模拟[J].应用地球物理,2015,12(1):35-46.
[9]Schwarzbach C,B9rner R U,Spitzer K.Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics-a marine CSEM example[J].Geophysical Journal International,2011,187(1):63-74.
[10]王若,王妙月,底青云,等.CSAMT三维单分量有限元正演[J].地球物理学进展,2014,29(2):839-845.
[11]熊彬,蔡红柱,罗天涯,等.基于非结构化网格的人工源频率域三维电磁场数值模拟[J].桂林理工大学学报,2015,35(3):423-430.
[12]Bakr S A,Pardo D,Mannseth T.Domain decomposition Fourier finite element method for the simulation of 3D marine CSEM measurements[J].Journal of Computational Physics,2013,255:456-470.
[13]Oh S,Noh K,Seol S J,et al.3D CSEM frequency-domain modeling and inversion algorithms including topography[C]//SEG Technical Program Expanded Abstracts 2015,2015:828-832.
[14]Yoon D,Zhdanov M S,Cai H Z,et al.A hybrid finite difference and integral equation method for modeling and inversion of marine CSEM data[C]//SEG Technical Program Expanded Abstracts 2015,2015:823-827.
[15]杨大方.结合实际数据的三维可控源电磁法正反演研究[D].长春:吉林大学,2015.
[16]杨波,徐义贤,何展翔,等.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[J].地球物理学报,2012,55(4):1390-1399.
[17]韩波,胡祥云,Schultz A,等.复杂场源形态的海洋可控源电磁三维正演[J].地球物理学报,2015,58(3):1059-1071.
[18]Key K,Ovall J.A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modelling[J].Geophysical Journal International,2011,186(1):137-154.
[19]柳建新,汤文武,童孝忠.基于双二次插值的2.5维FC-SEM有限元正演模拟[J].中南大学学报(自然科学版),2014,45(2):474-482.
[20]白洪涛,范翠松,李昂,等.基于OpenMP+MPI的2.5维电磁场正演并行化方法[J].石油地球物理勘探,2015,50(1):170-176.
[21]殷长春,张博,刘云鹤,等.2.5维起伏地表条件下时间域航空电磁正演模拟[J].地球物理学报,2015,58(4):1411-1424.
[22]Key K.Marine electromagnetic studies of seafloor resources and tectonics[J].Surveys in geophysics,2012,33(1):135-167.
[23]刘云,王绪本.大地电磁二维自适应地形有限元正演模拟[J].地震地质,2010,32(3):382-391.
[24]柳建新,孙丽影,童孝忠,等.基于自适应有限元的起伏地形MT二维正演模拟[J].地球物理学进展,2012,27(5):2016-2023.
[25]董浩,魏文博,叶高峰,等.基于有限差分正演的带地形三维大地电磁反演方法[J].地球物理学报,2014,57(3):939-952.
[26]刘云.起伏地形大地电磁,时间域瞬变电磁二维数值模拟及直接反演法[D].成都:成都理工大学,2012.
[27]张继锋,智庆全,李貅,等.起伏地形电偶源2.5维有限元数值模拟[J].中国有色金属学报,2013,23(9):2540-2550.
[28]陈桂波,汪宏年,姚敬金,等.用积分方程法模拟各向异性地层中三维电性异常体的电磁响应[J].地球物理学报,2009,52(8):2174-2181.
[29]李静和,何展翔.地井垂直电磁Walkaway剖面法油藏开发三维模型电场响应特征[J].石油地球物理勘探,2012,47(4):653-664.
[30]李静和,何展翔.三维井间电磁最小二乘法反演[J].石油地球物理勘探,2014,49(3):586-595.
[31]Jia Y,Liu Q H,He Z X.Fast Three-dimensional electromagnetic nonlinear inversion method for imaging in a layered medium with application in geophysical exploration using BCGS-FFT[C]//SEG Technical Program Expanded Abstracts2014,2014:654-657.
[32]陈清.2.5维可控源电磁测深数据反演方法研究[D].北京:中国地质大学(北京),2011.
[33]龙剑波.2.5维航空瞬变电磁数据的非线性共轭梯度反演[D].长沙:中南大学,2014.
[34]杨悦.可控源电场数据三维反演及应用[D].长春:吉林大学,2015.
[35]Song L P,Liu Q H,Li F,et al.Reconstruction of three-dimensional objects in layered media:numerical experiments[J].IEEE Transactions on Antennas and Propagation,2005,53(4):1556-1561.
[36]Anderson W L.Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering[J].Geophysics,1979,44(7):1287-1305.