五极纵轴激电测深三维有限元正演模拟

本文研究了五极纵轴激电测深三维有限元正演模拟方法。首先，从三个点电流源总电位的边值问题出发，导出了异常电位的边值问题，证明了与异常电位的边值问题对应的变分问题。然后，基于三维连续电性介质模型，推导了有限元法求解变分问题的计算过程，编制了五极纵轴激电测深的三维模拟程序。最后，通过模拟水平层状介质模型的五极纵轴激电测深曲线，发现最大相对误差小于0.25%，耗费时间为18 s；从精度和效率的角度验证了算法和程序是正确的，为后续模拟复杂地电模型五极纵轴激电测深曲线、分析曲线异常特征规律以及开展反演工作奠定了基础。

3D Finite Element Forward Modeling of Five-Pole Longitude Induced Polarization Sounding

The authors develop a three-dimensional(3D) finite element forward modeling method for five-pole longitude induced polarization (IP) soundingin this paper. Boundary value problems of the secondary potential field are derived from that of the primary potential field with the three-point current sources, it also proves the corresponding variation equation saccording to the boundary value problem of the secondary potential field. Then we solved the variation equations of the secondary potential field using a finite element method (FEM) based on a 3D continuous model of the electrical conductivity, specifically for five-pole longitude array. Finally, we calculate the induced polarization sounding curve with the five-pole longitude array based on the horizontal layered medium, the results show that the maximum relative error is less than 0.25% and the total computational time is about 18 seconds. Three examples indicate the accuracy and efficiency of the proposed algorithm, which will facilitate the application of the five-pole longitude IP sounding for complex geoelectrical structure, understanding of the IP sounding curve anomaly, and further carrying out the inversion.