Fractal model-based 2.5 D finite element modeling of complex resistivity method
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摘要: 复电阻率法在油气资源、矿产勘查中发挥了重要的作用,为了深刻认识复电阻率法异常特征变化规律,本文对复电阻率2.5D正演问题展开研究。首先直接给出复电阻率法2.5D有限元正演所满足的变分问题,并详细地推导相应的刚度矩阵的计算过程。引入Fractal模型作为等效模型研究频谱激电异常特征。对单元内的复电导率及复电位均进行线性插值,而后,采用不完全LU分解的稳定双共轭梯度算法求解有限元线性方程组,获得异常复电位值。设计3个典型的地电模型验证了本文算法的正确性及精确性,并分析了不同装置下,不同频率的2.5D复电阻率异常响应特征。数值模拟结果表明,采用Fractal模型研究激发极化异常特征是可行、有效的;不同装置、不同频率下的复电阻率法异常特征有着显著的差异。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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Key words:
- finite element method /
- complex resistivity /
- Fractal model /
- anomalous complex potential
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