基于时域有限差分法的电性源感应-极化效应三维数值模拟

Three-Dimensional Numerical Simulation of Induction-Polarization Effect of Electrical Sources Based on Finite-Difference Time-Domain Method

时域电性源电磁探测法是一种可以有效快速探测矿产资源的方法。极化效应会导致电性源电磁响应快速衰减,发生符号反转现象。本文采用Cole-Cole模型描述极化效应,利用整数阶有理逼近算法实现任意分数阶Cole-Cole模型有理化;采用Yee氏网格对仿真区域进行剖分,基于时域有限差分(finite-difference time-domain, FDTD)法实现电性源感应-极化效应三维数值模拟。本文对三种典型模型(均匀半空间模型、极化半空间模型和三维极化体模型)的电磁响应进行数值模拟,结果表明:均匀半空间模型的电磁响应与解析解基本吻合,并且相对误差小于10%,证明了三维数值模拟方法的正确性;极化半空间模型与三维极化体模型的电磁响应均在晚期出现了负响应,与极化理论结果相符合。

The time-domain electrical source electromagnetic detection method is an effective and fast method for detecting mineral resources.The polarization effect can lead to rapid attenuation of the electromagnetic response and even a symbol reversal phenomenon.In this paper,the Cole-Cole model is used to describe the polarization effect,and arbitrary fractional Cole-Cole models are rationalized by using the integer order rational approximation algorithm.Yee’s grid is used to divide the simulation area,and the three-dimensional numerical simulation of induction-polarization effect of electrical sources is realized based on the finite difference time domain(FDTD)method.The electromagnetic responses of three typical models,namely uniform half-space model,polarized half-space model and three-dimensional polarized body model,are numerically simulated.The results show that the electromagnetic response of uniform half-space model is basically consistent with the analytical solution,and the relative error is less than 10%,which proves the feasibility of the three-dimensional numerical simulation method.The electromagnetic responses of polarized half-space model and three-dimensional polarized body model both have negative responses in the late stage,which is consistent with the polarization theoretical results.