2.5D IP finite element numerical simulation in the time domain based on quadratic interpolation
Zhang Zhiyong1,2, Zhou Feng2, Li Zelin2,3
1. School of Geosciences and Info-Physics, Central South University, Changsha, Hunan 410083, China;
2. School of Nuclear Engineering and Geophysics, East China Institute of Technology, Nanchang, Jiangxi 330013, China;
3. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, Hubei 430074, China
Abstract：This paper presents an induced polarization numerical simulation in the time domain. We adopt the 2.5D finite element method based on the triangular element discrete and quadratic interpolated function. A cole-cole model is adopted to descript the complex resistivity of the discrete element. Then a boundary value problem of 2.5D complex resistivity is deduced. At last, a filtering algorithm based on Guptasarma is used to transform IP from the frequency-domain to the time domain. We design a fast algorithm suitable for 2.5D IP forward modeling in the time domain and a direct method for linear equations on symbolic analysis is used in this algorithm. The algorithm firstly processes approximately the boundary condition. So the obtained stiffness matrixes have only some relation with frequency and wave number, not with source point positions. Which the workload of matrix decomposition is reduced in the linear equations solution. Secondly, this algorithm achieves fast matrix LDLT decomposition with matrix rearrangement and element fill-in based on graph theory. The calculation scheme is optimized according to stiffness matrix and LDLT characteristics, so only one symbolic analysis is needed for the same domain discrete and only one LDLT decomposition is needed for all source points with the same frequency and wave number. Finally apparent resistivity, apparent polarization, and apparent dispersion rate of the synthetic model are analyzed.
张志勇, 周峰, 李泽林. 二次插值的时间域激电2.5维有限元数值模拟[J]. 石油地球物理勘探, 2015, 50(5): 999-1006.
Zhang Zhiyong, Zhou Feng, Li Zelin. 2.5D IP finite element numerical simulation in the time domain based on quadratic interpolation. OGP, 2015, 50(5): 999-1006.
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