电流线追踪电位电阻率层析成像方法初探
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摘要
电阻率层析成像技术尽管已有了一些比较好的结果，但从国内外发表的文章可以看出，基本上采用的都是有限元方法而电阻率层折成像的核心问题也就是雅可比矩阵（即电位对电阻率等的偏导数系数矩阵）的求取问题．有限元方法能够很好地实现该问题的求解，但需要的计算机内存及计算时间相当的大，为此我们类比地震学中走时射线追踪技术，开展了电流线追踪电位电阻率层析成像方法研究．文中首先简明地论述了电流线追踪的原理，给出了程序框图，在实现追踪手段上又作了改进，对方程求解实行降维处理，使得该方法能适合复杂大模型的计算．经和有限元方法比较，我们发现电流线追踪利用计算机内存仅为有限元方法的1／20计算时间仅用1／100．这就充分显示了电流线追踪技术的优越性，为该方法的推广应用提供了扎实的基础．
The resistivity tomography had obtained some good results, but according to the published papers, most or the authors did the work using the finite elemcnt method. The key problem of the resistivity tomography is to solve the Jacobin matrix(that is thecooefficiency matrix derivated potental by eletric resistance). The Fmite e1ement method can solve the problem, but it need more the computer memory and coputing time. Wedevelope the method of the resistivity tomography by tracing the electric ray borrowing from the method of tracing the seismic ray. In the paper, we discuss the principle or tracing eIectric ray, and give the programme frame. After improving the tracing method and solving the equhons by using the reduced dimension, this method can compute the more complex models. Comparing this method with the finite element method, we find that the computer memory used by tracing electric current ray is only 1 /10 that used by the FEM, the computer time can save ten times. It shows that the method of tracing electric current ray has great advantage, and makes the fundation to be widely used.
The resistivity tomography had obtained some good results, but according to the published papers, most or the authors did the work using the finite elemcnt method. The key problem of the resistivity tomography is to solve the Jacobin matrix(that is thecooefficiency matrix derivated potental by eletric resistance). The Fmite e1ement method can solve the problem, but it need more the computer memory and coputing time. Wedevelope the method of the resistivity tomography by tracing the electric ray borrowing from the method of tracing the seismic ray. In the paper, we discuss the principle or tracing eIectric ray, and give the programme frame. After improving the tracing method and solving the equhons by using the reduced dimension, this method can compute the more complex models. Comparing this method with the finite element method, we find that the computer memory used by tracing electric current ray is only 1 /10 that used by the FEM, the computer time can save ten times. It shows that the method of tracing electric current ray has great advantage, and makes the fundation to be widely used.
引文
[1]冯锐等,层析技术在工程中的应用研究,论文集,国家地震局地球物理研究所,1993年
[2] T.J.Yorkey et al. Companng Reconstruction Algorithms for Electncal Impedance Tomogrophy,IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, Vol, Bem-34, No.11, 1987,p843-852.
[3] Yulasa Sasaki, Resolution of Resistivlty Tomography Inferred From Numerical simulation;Geophysical Prospecting, Vol.40, 1992, p453—464,
[4] Muyal, T. and Kagawa, Y, Electrlcal Impedance Com puted Tomography Based on a Finite Element Model, IEEE TRANS,bIOME.ENG, BME、32, 1985, p177- 184.
[5] Robertv.kohn and Michael Vogelius, Relaxation of a Variational Method for Impedance ComputedTomography, Communications on pure and Applied Mattiematics, Vol.XL, p745—777, 1987.
[6] Tytaka sadaki, Three-Dimensionaal Inversion in Resistivity and lp Methods,物理探查第45卷第1号,P3～9.
[7]黄联捷等,用于图像重建的波前法射线追踪,地球物理学报,3 5,223—233,1992.
[8] Qin, F., etc, Solution of the eckonal equation by a tmite-dlrrerence methed, SEG 60th Ann. International Metting, 1004- 1007, 1990.
[9]黄鑫,王妙月,地震层析成像技术在测井和地面反射波资料集中的应用研究,地球物理学报,32,319—328,1989
[10] R.T.Culter, etc,, A tomographic solution to the travel-time problem in general inverseseismology, Advance in Geophysical Data Proassing, Vol.2, 1985.
[2] T.J.Yorkey et al. Companng Reconstruction Algorithms for Electncal Impedance Tomogrophy,IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, Vol, Bem-34, No.11, 1987,p843-852.
[3] Yulasa Sasaki, Resolution of Resistivlty Tomography Inferred From Numerical simulation;Geophysical Prospecting, Vol.40, 1992, p453—464,
[4] Muyal, T. and Kagawa, Y, Electrlcal Impedance Com puted Tomography Based on a Finite Element Model, IEEE TRANS,bIOME.ENG, BME、32, 1985, p177- 184.
[5] Robertv.kohn and Michael Vogelius, Relaxation of a Variational Method for Impedance ComputedTomography, Communications on pure and Applied Mattiematics, Vol.XL, p745—777, 1987.
[6] Tytaka sadaki, Three-Dimensionaal Inversion in Resistivity and lp Methods,物理探查第45卷第1号,P3～9.
[7]黄联捷等,用于图像重建的波前法射线追踪,地球物理学报,3 5,223—233,1992.
[8] Qin, F., etc, Solution of the eckonal equation by a tmite-dlrrerence methed, SEG 60th Ann. International Metting, 1004- 1007, 1990.
[9]黄鑫,王妙月,地震层析成像技术在测井和地面反射波资料集中的应用研究,地球物理学报,32,319—328,1989
[10] R.T.Culter, etc,, A tomographic solution to the travel-time problem in general inverseseismology, Advance in Geophysical Data Proassing, Vol.2, 1985.
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