The generalized effective-medium theory of the induced polarization model (GEMTIP) is a mathematical-physical model derived from the Maxwell equations based on the effective-medium approach. Compared to the Cole-Cole model, the GEMTIP parameters are better related to the structural parameters of reservoir rocks, such as rock composition, mineral particle size, porosity, and specific surface; therefore, it can better describe the induced polarization (IP) characteristics of tight oil and gas reservoirs. However, GEMTIP is not suitable for high-resistivity perturbed media, and it does not account for interfacial polarization, which occurs between two media that share the same resistivity. Starting from the theoretical assumptions of the GEMTIP model, we derived an extended GEMTIP model (MGEMTIP) by adding an equivalent surface current term into the Maxwell equations for a heterogeneous medium. The complex resistivity parameters predicted by two models are compared through numerical simulation, and the results demonstrate that MGEMTIP can more accurately predict the DC resistivity and the chargeability of heterogeneous media. MGEMTIP is suitable for characterizing the polarization phenomena of rock with high salinity, low porosity, low hydraulic permeability, and a disseminated perturbed medium. Furthermore, the testing of rock samples for the inversion of IP parameters with MGEMTIP revealed that the predicted chargeability is higher than the inverted chargeability from the experimental data. This difference is strongly correlated with rock hydraulic permeability. MGEMTIP provides a petrophysical basis for the forward modeling and inversion of IP parameters of compacted rocks. The quantitative relationships between model IP parameters and reservoir parameters also provide a theoretical foundation for predicting reservoir permeability using electromagnetic methods.

中文翻译：

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修改压实岩石中诱导极化模型的广义有效介质理论

感应极化模型（GEMTIP）的广义有效介质理论是基于有效介质方法从麦克斯韦方程组推导的数学物理模型。与Cole-Cole模型相比，GEMTIP参数与储层岩石的结构参数更好地相关，例如岩石成分，矿物粒度，孔隙度和比表面。因此，它可以更好地描述致密油气藏的感应极化（IP）特性。但是，GEMTIP不适合高电阻率扰动的介质，并且不能解释界面极化，该极化发生在共享相同电阻率的两种介质之间。从GEMTIP模型的理论假设开始，我们通过将等效表面电流项添加到非均质介质的Maxwell方程中，得出了扩展的GEMTIP模型（MGEMTIP）。通过数值模拟比较了两个模型预测的复电阻率参数，结果表明MGEMTIP可以更准确地预测异质介质的直流电阻率和带电性。MGEMTIP适用于表征高盐度，低孔隙度，低水力渗透率和分散的扰动介质的岩石的极化现象。此外，用MGEMTIP对岩石样品进行IP参数反演的测试表明，从实验数据来看，预测的荷电率高于反向荷电率。这种差异与岩石的水力渗透率密切相关。MGEMTIP为压实岩石IP参数的正演建模和反演提供了岩石物理基础。模型IP参数和储层参数之间的定量关系也为使用电磁方法预测储层渗透率提供了理论基础。