激电介质的人工源频率域电场模拟及其响应特征分析

doi:10.11720/wtyht.2024.1045

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摘要

激电介质可通过随频率变化的复电阻率参数来表征其电阻和电容特性。为能够准确、高效地模拟人工源激发下激电介质的电磁响应特征,本文通过频率域Maxwell方程建立复电阻率法三维正演控制方程,并以交错网格有限差分法进行差分离散,利用复全局拟最小残差法(QMR)求解离散复线性方程组,并在正演中考虑了电磁效应的作用。首先通过简单层状模型的半解析解对计算精度进行检验,并分别建立较大规模和埋深的金属矿藏模型与较小规模和埋深的有机质渗漏模型,依次计算了两种不同激电模型在低频(1 Hz)、中频(10 Hz)、高频(100 Hz)的电场响应。各模型不同频率的计算结果均表明,残差范数均能随迭代次数较快收敛,验证了该算法的适用性和有效性。最后依据计算结果分析了激电介质电容特性对电场幅值和相位的影响,认为激电介质中电容特性对电场幅值的影响非常小,但对相位的影响非常明显,且激电效应越强,对相位的影响越显著。

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	万伟
	孙启隆
	鲁瑶

关键词 ：激电效应, 复电阻率, 三维正演, 电场响应

Abstract：

The resistive and capacitive properties of induced polarization(IP) medium can be characterized by complex resistivity parameters that vary with frequency. To accurately and efficiently simulate the electromagnetic responses of IP media when excited by artificial sources, this study establishes a three-dimensional forward modeling framework for complex resistivity method based on the frequency-domain Maxwell's equations. The equation takes into account the impact of electromagnetic effects and is discretized using the staggered grid finite difference method. The complex globally convergent quasi-minimum residual (QMR) method is employed to solve the discretized complex linear equation system. Initially, the accuracy of the calculations is verified through a semi-analytical solution of a simple layered model. Then, Models of large-scale and deep-seated metal ore deposits and smaller-scale and shallow-buried organic matter leakage are then established, and the electric field responses of the two induced polarization models are computed at low frequency (1 Hz), medium frequency (10 Hz), and high frequency (100 Hz). The results at different frequencies for both models indicate rapid convergence of the residual norms with iteration numbers, validating the applicability and effectiveness of the algorithm. Finally, based on the computational results, the influence of capacitive characteristics of the induced polarization medium on the electric field amplitude and phase is analyzed. It is concluded that capacitive characteristics have a minimal impact on the electric field amplitude but a significant effect on the phase, and the stronger the induced polarization effect, the more pronounced the impact on the phase.

Key words： induce polarization effects complex resistivity 3D forward electric field

收稿日期: 2024-02-05 修回日期: 2024-07-30 出版日期: 2025-06-20

ZTFLH:

P631

基金资助:自然资源部地球物理电磁法探测技术重点实验室开放课题(KLGEPT202301)

作者简介: 万伟(1989-),男,2019年博士毕业于北京大学,主要从事地球物理电磁法正反演及应用研究工作。Email:wanwei@ecut.edu.cn

引用本文:

万伟, 孙启隆, 鲁瑶. 激电介质的人工源频率域电场模拟及其响应特征分析[J]. 物探与化探, 2025, 49(3): 670-678.
Wan Wei, Sun Qi-Long, Lu Yao. Simulation and analysis of frequency domain electric field response for induced polarization media. Geophysical and Geochemical Exploration, 2025, 49(3): 670-678.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2024.1045 或 https://www.wutanyuhuatan.com/CN/Y2025/V49/I3/670

Fig.1 层状模型一维半解析解与三维数值解对比

Fig.2 矿体三维模型及人工源电磁法观测系统

Fig.3 图2中矿体模型不同频率计算的残差范数随迭代次数变化曲线

Fig.4 含激电矿体模型的不同频率电场幅值 $E x I P$ 及相对不含激电矿体模型电场幅值 $E x N o I P$ 的变化量ΔE_x

Fig.5 含激电矿体模型的不同频率电场相位φ^IP及相对不含激电矿体模型电场相位φ^NoIP的变化量Δφ

Fig.6 地表污染渗漏三维模型及人工源电磁观测系统

Fig.7 图6模型不同频率计算的残差范数随迭代次数变化曲线

Fig.8 含激电渗漏模型的不同频率电场幅值 $E x I P$ 及相对不含激电矿体模型电场幅值 $E x N o I P$ 的变化量ΔE_x

Fig.9 含激电渗漏模型的不同频率电场相位φ^IP及相对不含激电矿体模型电场相位φ^NoIP的变化量Δφ

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