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| Fractal model-based 2.5 D finite element modeling of complex resistivity method |
Long Xiu-Jie1( ), Chen Han-Bo2(), Mo Ya-Jun1, Ou Xiao-Yi1, Lu Sheng-Hui1 |
1. Guangxi Geophysical Investigation Institute,Liuzhou 545005,China
2. College of Earth Sciences, Guilin University of Technology,Guilin 541006,China |
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Abstract This study proposed the variational problem of 2.5D finite element forward modeling of the complex resistivity method and detailed the process of solving stiff matrix of finite equations. The Fractal model was introduced as a research model for studying the equivalent induced polarization anomalies of spectra. Furthermore, the complex conductivity and complex potential of a grid unit were linearly interpolated. Then, to obtain anomalous complex potential, finite element linear equations were solved using the biconjugate gradient stabilized method with incomplete LU decomposition. The results of three typical geoelectric models validated the correctness and accuracy of the algorithm proposed in this study. Furthermore, this study analyzed the abnormal response characteristics of 2.5D complex resistivity under different frequencies.
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Received: 09 July 2021
Published: 17 August 2022
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Corresponding Authors:
Chen Han-Bo
E-mail: 496178747@qq.com;chenhanbo@glut.edu.cn
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The amplitude (a) and phase (b) of complex resistivity for different frequency exponent
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Sketch of finite element mesh
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Parent element (a) and sub-element(b) of linear interpolation
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| n | h/m | ρ0/(Ω·m) | m | δr | τ/μs | τf/ms | η | τ0/ps | 1
2 | 5
∞ | 100
10 | 0.906
0.885 | 4.959
4.877 | 23.43
18.72 | 10
100 | 0.20
0.44 | 1.0
1.0 |
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parameters of the first model
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Comparison of 2.5D FEM result with numerical filter wave numerical solution
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Cross section of second model
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| Kind | ρ0/(Ω·m) | m | δr | τ/μs | τf/ms | η | τ0/ps | 半空间
异常体 | 5200
1470 | 0.906
0.885 | 4.959
4.877 | 23.43
18.72 | 10
100 | 0.20
0.44 | 1.0
1.0 |
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Fractal parameters of the second model
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The pseudo section of amplitude and phase of apparent complex resistivity in dipole-dipole array for giving the frequencies
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The pseudo section of real and imaginary component of apparent complex resistivity in four-pole array for giving the frequencies
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Cross section of second model
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| Kind | ρ0/
(Ω·m) | m | δr | τ/μs | τf/ms | η | τ0/ps | | 半空间 | 1000 | 0.906 | 4.959 | 23.43 | 10 | 0.20 | 1.0 | 异常体
(左) | 100 | 0.885 | 4.877 | 18.72 | 100 | 0.44 | 1.0 | 异常体
(右) | 100 | 0.885 | 4.877 | 18.72 | 100 | 0.44 | 1.0 |
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Fractal parameters of the second model
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The pseudo section of real and imaginary component of apparent complex resistivity in four-pole array for giving the frequencies
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The pseudo section of real and imaginary component of apparent complex resistivity in dipole-dipole array for giving the frequencies
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The pseudo section of real and imaginary component of apparent complex resistivity in pole-dipole array for giving the frequencies
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The pseudo section of real and imaginary component of apparent complex resistivity in pole-pole array for giving the frequencies
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