基于非结构化网格的中心回线瞬变电磁法2.5维有限元正演
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摘要
瞬变电磁法(简称TEM)属于时间域电磁法,是近年来迅速发展的地球物理勘探方法之一。目前,瞬变电磁法资料解释水平较低,基本上停留在一维阶段,二维和三维反演解释技术离真正实用阶段仍有相当大的距离。在地球物理学中,正演是资料处理和数据反演的基础,因此我们有必要首先研究正演计算。2.5维瞬变电磁法数值模拟问题尚未妥善解决,但其具有很大的实用价值,因此很有必要进一步研究。
本文从麦克斯韦方程组出发,详细推导了瞬变电磁法2.5维问题中异常场偏微分定解问题、边界条件、变分问题等；着重分析了对程序实现有重要影响的几个关键问题：拉普拉斯逆变换、傅里叶逆变换以及非走向分量的计算。利用matlab语言编写了2.5维有限元程序；并通过对水平层状模型的数值模拟验证了算法的正确性。除此之外,本文还计算了矩形回线在水平层状地电模型表面激励的瞬变电磁响应,分析比较了几种层状结构介质的瞬变电磁异常场和总场响应特征。
针对前人在瞬变电磁2.5维正演中采用结构化网格剖分所存在的不足,本文采取非结构化策略来实现网格剖分。通过非结构化中常用的Delaunay三角剖分方法,实现了对复杂地质模型的剖分,使现有瞬变电磁2.5维正演算法应用范围得到了扩展。与传统的结构化网格剖分方式相比,本文所采用的非结构化网格剖分方式在取得相同计算精度的情况下其网格节点数和单元数得到了大幅的降低,可以减少了不必要的节点计算量。
Transient Electromagnetic Method (referred to as TEM) belong to the time domain electromagnetic method,it's a new geophysical exploration method developed in recent years. Currently, TEM is low levels of data interpretation, basically stuck in one-dimensional stage, two-dimensional and three-dimensional inversion interpretation techniques for the real practical use is still a considerable distance. In geophysics, forward modeling is the basis of data processing and data inversion, we need to first study the forward problem.2.5-dimensional numerical simulation of transient electromagnetic method that is one of difficult problems in geophysical calculation and not yet properly solved, but is valuable in practical.
This article from the Maxwell equations and deduced transient electromagnetic anomaly field in the 2.5-dimensional problem set solutions of partial differential of the problem, boundary conditions, functional extrema, etc.; and focus on implementation of several key Question that's have a major impact on the program:Laplace inverse transform, inverse Fourier transform and the calculation of non-direction component. Language using program matlab accomplish 2.5 dimensional finite element program, and examined the algorithm through horizontal layered models' numerical simulation, the paper calculated the rectangular back to the line in the horizontal surface layer geoelectric model of the transient electromagnetic response of incentives, analysis and comparison of the layered structure of several anomaly field of media and the total transient electromagnetic field response characteristics.
For the previous use structured mesh's shortcomings in the transient electromagnetic 2.5-D problem forward, this strategy adopted unstructured mesh to achieve the meshing. Unstructured mesh generation by using the commonly used method of Delaunay triangulation method, and realized the subdivision of complex geological model, the range of applications of existing 2.5-D transient electromagnetic forward algorithm has been expanded. With traditional structured mesh generation as compared to the unstructured grid used in this paper partition means to achieve the same accuracy in the case of the grid, the number of nodes and cells were significantly reduced, to reduce the unnecessary computation nodes.
本文从麦克斯韦方程组出发,详细推导了瞬变电磁法2.5维问题中异常场偏微分定解问题、边界条件、变分问题等；着重分析了对程序实现有重要影响的几个关键问题：拉普拉斯逆变换、傅里叶逆变换以及非走向分量的计算。利用matlab语言编写了2.5维有限元程序；并通过对水平层状模型的数值模拟验证了算法的正确性。除此之外,本文还计算了矩形回线在水平层状地电模型表面激励的瞬变电磁响应,分析比较了几种层状结构介质的瞬变电磁异常场和总场响应特征。
针对前人在瞬变电磁2.5维正演中采用结构化网格剖分所存在的不足,本文采取非结构化策略来实现网格剖分。通过非结构化中常用的Delaunay三角剖分方法,实现了对复杂地质模型的剖分,使现有瞬变电磁2.5维正演算法应用范围得到了扩展。与传统的结构化网格剖分方式相比,本文所采用的非结构化网格剖分方式在取得相同计算精度的情况下其网格节点数和单元数得到了大幅的降低,可以减少了不必要的节点计算量。
Transient Electromagnetic Method (referred to as TEM) belong to the time domain electromagnetic method,it's a new geophysical exploration method developed in recent years. Currently, TEM is low levels of data interpretation, basically stuck in one-dimensional stage, two-dimensional and three-dimensional inversion interpretation techniques for the real practical use is still a considerable distance. In geophysics, forward modeling is the basis of data processing and data inversion, we need to first study the forward problem.2.5-dimensional numerical simulation of transient electromagnetic method that is one of difficult problems in geophysical calculation and not yet properly solved, but is valuable in practical.
This article from the Maxwell equations and deduced transient electromagnetic anomaly field in the 2.5-dimensional problem set solutions of partial differential of the problem, boundary conditions, functional extrema, etc.; and focus on implementation of several key Question that's have a major impact on the program:Laplace inverse transform, inverse Fourier transform and the calculation of non-direction component. Language using program matlab accomplish 2.5 dimensional finite element program, and examined the algorithm through horizontal layered models' numerical simulation, the paper calculated the rectangular back to the line in the horizontal surface layer geoelectric model of the transient electromagnetic response of incentives, analysis and comparison of the layered structure of several anomaly field of media and the total transient electromagnetic field response characteristics.
For the previous use structured mesh's shortcomings in the transient electromagnetic 2.5-D problem forward, this strategy adopted unstructured mesh to achieve the meshing. Unstructured mesh generation by using the commonly used method of Delaunay triangulation method, and realized the subdivision of complex geological model, the range of applications of existing 2.5-D transient electromagnetic forward algorithm has been expanded. With traditional structured mesh generation as compared to the unstructured grid used in this paper partition means to achieve the same accuracy in the case of the grid, the number of nodes and cells were significantly reduced, to reduce the unnecessary computation nodes.
引文
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[3]刘国兴,王喜臣,张小路,等.大功率激电和瞬变电磁法在青海锡铁山深部找矿的应用[J].吉林大学学报(地球科学版),2003,33(4)：551-554
[4]刘树才,刘志新,姜志海.瞬变电磁法在煤矿采区水文勘探中的应用[J].中国矿业大学学报,2005,34(7)：414-417
[5]于景邮,刘志新,汤金云,等.用瞬变电磁法探查综放工作面顶板水体的研究[J].中国矿业大学学报,2007,36(4)：542-546
[6]张保祥,刘春华.瞬变电磁法在地下水勘查中的应用综述[J].地球物理学进展,2004,19(3)：537～542
[7]薛国强,宋建平,马宇,等.用瞬变电磁法探测灰岩溶洞[J].长安大学学报(地球科学版),2003,25(6)：50-53
[8]薛国强,李貅.瞬变电磁隧道超前预报成像技术[J].地球物理学报,2008,51(3)：894～900.
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[40]Swidinsky A, Edwards R. N. The transient electromagnetic response of a resistive sheet:straightforward but not trivial [J]. Geophysics journal international,2009,179:1488～1498
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[6]张保祥,刘春华.瞬变电磁法在地下水勘查中的应用综述[J].地球物理学进展,2004,19(3)：537～542
[7]薛国强,宋建平,马宇,等.用瞬变电磁法探测灰岩溶洞[J].长安大学学报(地球科学版),2003,25(6)：50-53
[8]薛国强,李貅.瞬变电磁隧道超前预报成像技术[J].地球物理学报,2008,51(3)：894～900.
[9]吕国印.瞬变电磁法的现状与发展趋势[J].物探化探计算技术,2007,29(增刊)：11]～115
[10]薛国强,李貅等.瞬变电磁法正反演问题研究进展[J].地球物理学进展,2008,23(4)：1165～1172
[11]闫述,陈明生,傅君眉.瞬变电磁场的直接时域数值分析[J].地球物理学报,2002,45(2)：275～284
[12]罗延钟,张胜业,王卫平.时间域航空电磁法一维正演研究[J].地球物理学报,2003,46(5)：719～724
[13]Coggon J.H. Electromagnetic and electrical modeling by the finite-element method.Geophysics,1971,36(1):132～155
[14]Kuo J. T, Cho D. H. Transient time-domain electromagnetics[J]. Geophysics,1980,45(2):271～291
[15]Goldman M. M, Stoyer C. H.Finitte-difference calculations of the transient field of an axially symmetric earth for vertical magnetic diple excitation[J]. Geophysics,1983,48(7):953～963
[16]M.E.Everett and R. N. Edwards.Transient marine electromagnetics:the 2.5-D forward problem[J]. Geophys,1992,113:545～561
[17]Yu L,1994. Computation of the electrical responses of mid-ocean ridgee structures,Ph.D thesis, University of Toronto
[18]Meng Y. L, Li W. D, Zhdanov M. S, et al.2.5-D electromagnetic forward modeling in the time and frequency domains using the finite element method[J].69th annual SEG meeting extended abstracts, Salt lake city, USA,1999:42～45
[19]王华军.中心回线瞬变电磁法2.5维正反演方法研究[D].武汉：中国地质大学,2001
[20]王华军,罗延钟.中心回线瞬变电磁法2.5维有限单元算法[J].地球物理学报,2003,46(6)：855～862
[21]熊彬.大回线瞬变电磁2.5维正演算法及其资料解释方法中若干关键技术研究[D].武汉：中国地质大学,2004
[22]熊彬,罗延钟.电导率分块均匀的瞬变电磁2.5维有限元数值模拟[J].地球物理学报,2006,49(2)：590-597
[23]熊彬.关于瞬变电磁法2.5维正演中的几个问题[J].物探化探计算技术,2005,28(2)：124～129
[24]Xiong B. A new formula based on the independent electric and magnetic fields for 2.5-D forward of TEM [Z]. The 19th international workshop on electromagnetic induction in the earth,2008,536-539
[25]Borner R. U, Ernst 0. G, Spitzer K. Fast 3-D simulation of transient electromagnetic fields by model reduction in the frequency domain using Krylov subspace projection[J]. Geophysics journal international,2008,173:766～780
[26]Um E. S, Harris J. M, Alumbaugh D. L. A finite element algorithm for 3-D transient electromagnetic modeling[C].79th annual SEG meeting extended abstracts, Houston, USA,2009:659～663
[27]Snyder D D A method for modeling the resistivity and induced polarization response of two dimensional bodies 1976(5)
[28]Stoyer C H Numerical solution of the response of a 2-D earth to an oscillating magnetic dipole source with application to a ground water study. Ph. D. thesis 1975
[29]Goldman M. M, Stoyer C. H. Finite-difference calculations of the transient field of an axially symmetric earth for vertical magnetic dipole excitation[J]. Geophysics,1983,48(7):953～963
[30]Oristaglio M. L, Hohmann G. W. Diffusion of electromagnetic fields into a two-dimensional earth:A finite- difference approach [J]. Geophysics,1984,49(7):870～894
[31]Adhidjaja J.T, Hohmann G. W, Oristaglio M. L. Two-dimensional transient electromagnetic responses[J]. Geophysics,1985,50(12): 2849～2861
[32]Leppin M. Electromagnetic modeling of 3-D sources over 2-D inhomgeneities in the time domain [J]. Geophysics,1992,57(8):994～ 1003
[33]Wang T, Hohmann G. W. A finite-difference, time-domain solution for three-dimensional electromagnetic modeling[J]. Geophysics,1993, 58(6):797～809
[34]Wang T, Tripp A. C, Hohmann G. W. Studying the TEM response of a 3-D conductor at a geological contact using the FDTD method[J]. Geophysics,1995,60(4):1265～1269
[35]Commer M, Newman G. A parallel finite-difference approach for 3D transient electromagnetic modeling with galvanic sources[J]. Geophysics,2004,69(5):1192～1202
[36]Sanfilipo W. A, Hohmann G. W. Integral equation solution for the transient electromagnetic response of a three-dimensional body in a conductive half-space [J]. Geophysics,1985,50(5):798～809
[37]Sanfilipo W. A, Eaton P. A, Hohmann G. W. The effect of a conductive half-space on the transient electromagnetic response of a three-dimensional body[J]. Geophysics,1985,50(7):1144～1162
[38]Newman G. A, Hohmann, G. W, Anderson W. L. Transient electromagnetic response of a three-dimensional body in a layered earth[J]. Geophysics,1986,51(8):1608～1627
[39]Newman G. A, Hohmann, G. W. Transient electromagnetic response of high-contrast prisms in a layered earth[J]. Geophysics,1988,53(5): 691～706
[40]Swidinsky A, Edwards R. N. The transient electromagnetic response of a resistive sheet:straightforward but not trivial [J]. Geophysics journal international,2009,179:1488～1498
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