基于GEMTIP模型的CR三维有限元数值模拟

3D Finite Element Numerical Simulation of CR Method Based on GEMTIP Model

本文提出了基于广义等效介质激电(GEMTIP)模型的复电阻率三维有限元数值模拟方法,首先介绍了GEMTIP模型及在不同参数影响下的复电阻率变化特征,而后给出双点电源的复电阻率法三维正演所满足的变分问题,采用六面体单元对研究区域进行网格剖分,在单元内对复电位、复电导率均进行线性插值,将变分方程转为线性方程组;采用不完全LU分解的稳定双共轭梯度算法(BICGSTAB算法)求解线性方程组,得到异常复电位值.设计一个两层极化大地模型,将数值解与解析解进行对比,验证了文中算法的正确性.设计两个典型地电模型的数值模拟结果表明,采用GEMTIP模型研究宏观尺度下的激电效应是有效的,可为进一步研究复电阻率异常响应特征提供一种新的途径.

A 3D finite element method for complex resistivity simulation based on generalized equivalent medium induced polarization( GEMTIP) model was introduced. First,the GEMTIP model and the complex resistivity variation characteristics of GEMTIP model under the influence of different parameters was introduced,Then,the variation equations were established for two – point sources of 3D modeling of complex resistivity method. The computing area was divided into hexahedral elements. The complex potential and the complex conductivity of rocks within each triangular lattice were described by a linear interpolation to create a linear equations system from the variation equation. The BICGSTAB( Bi-conjugate gradient stabilized method) algorithm with incomplete LU decomposition for preconditioning was used to solve the system linear equation to calculate the anomalous complex potential of all nodes and the apparent complex resistivity on the surface. Finally,this approach was verified through the calculations of a two layered model. Two typical geoelectric models were designed to test the correctness and efficiency of the algorithm. The results show that it provide new way to further study the induced polarization effect of rock and ore on the acroscopic scale.