基于Debye模型的时间域航空电磁激电效应正演模拟

Forward Modeling of Airborne Electromagnetic Induced Polarization Effect in Time-Domain Based on Debye Model

时间域航空电磁法是一种高效的地球物理勘查方法。由于激电效应的存在,晚期道电磁数据经常会出现符号反转现象。此时,传统的不考虑激电效应的成像和反演方法无法恢复地下真实电性结构,因此需要开发含激电效应的电磁正反演模拟技术。本文提出了一种基于非结构有限元的时间域航空电磁激电效应三维正演算法。为描述介质的激电效应,引入Debye模型,利用频时转换将其变成时间域导数形式,进而采用无条件稳定的二阶后推欧拉方法进行时间离散。之后,采用基于非结构四面体网格的矢量有限元法,对麦克斯韦方程进行空间离散,实现含激电效应的时间域航空电磁正演问题求解。通过与均匀半空间模型的一维半解析解进行对比,验证了该算法的准确性。最后,计算了半空间和三维地质体具有不同极化条件时的电磁响应,发现可以根据航空电磁响应曲线的衰减特征,有效识别围岩及异常体的极化特征。此外,激电参数对时间域航空电磁系统的影响特征研究表明,地质体电阻率越高或者充电率越强,极化效应影响越严重。

The time-domain airborne electromagnetic(AEM)method is an efficient geophysical exploration technique.Yet,due to the presence of the induced polarization(IP)effect,electromagnetic(EM)data from late-time channels often exhibit a phenomenon known as sign reversal.The traditional imaging and inversion methods without considering the IP effect cannot recover the real electrical structure of the underground,so it is necessary to develop the EM forward and reverse modeling technology with IP effect.This study introduces a three-dimensional(3D)forward algorithm for AEM with IP effect in the time-domain built upon the unstructured finite-element method.To capture the IP effect within the medium,we use the Debye model,transforming it into a derivative form in the time-domain through frequency-time conversion.For temporal discretization,an unconditionally stable second-order backward Euler's scheme is applied.Maxwell's equations are discretized in space using a vector finite element method based on an unstructured tetrahedral mesh.The algorithm's accuracy is verified through a comparison with the 1D semi-analytical solution of the uniform half-space model.We compute EM responses for both a half-space and 3D geological formations under various polarization conditions.We observe that the polarization characteristics of surrounding rocks and anomalous bodies can be effectively identified according to the attenuation characteristics of the AEM response curves.In addition,by studying the characteristics of the influence of IP parameters on the time-domain AEM system,we show that the larger the resistivity of the geological body or the larger the chargeability,the stronger the IP effect.