基于二次插值的线源可控源有限元数值模拟  

Finite Element Numerical Simulation on Line Controlled Source Based on Quadratic Interpolation

作　　者：张继锋[1,2] 汤井田[2] 喻言[3] 刘长生[2,4] 

机构地区：[1]长安大学地质工程与测绘学院,西安710054 [2]中南大学信息物理工程学院,长沙410083 [3]武汉理工大学土木工程与建筑学院,武汉430070 [4]长沙航空职业技术学院,长沙410014

出　　处：《吉林大学学报（地球科学版）》2009年第5期929-935,共7页Journal of Jilin University：Earth Science Edition

基　　金：国家'863'计划项目(2007AA060601);国家自然科学基金项目(40874072);湖南省科技计划项目(2008FJ4181)

摘　　要：在准静态近似条件下,采用矩形网格单元和双二次函数插值就频率域二维线源边值问题进行了有限元数值模拟。在二维地电条件下,给出了边值问题和变分问题,并通过有限单元法对模型进行单元剖分、插值、积分和整体合成,最后通过求解复系数方程组得到了地表视电阻率响应。引入伪delta函数模拟线源,消弱了源带来的奇异性。通过与均匀大地以及层状介质模型的解析解对比,平均相对误差分别为0.71%和1.12%。建立了两个异常体模型,数值模拟表明异常响应比较明显,为进一步实现三维可控源电磁法有限元数值模拟提供了基础。Under the quasi-static conditions, finite element numerical simulation of 2D line source boundary value problem was performed using rectangular grid unit and dual quadratic function interpolation on the frequency-domain. Under 2D geoelectric conditions, the boundary value problem and variational problems were given, and the finite element method was used for element subdivision, interpolation, integration and general synthesis. By solving the complex equations, the surface apparent resistivity response was obtained. Pseudo-delta function was introduced to simulate line source, weakening singularity of the source. Through comparison with the analytic solution for the earth with uniform and layered media models, the average relative error amount to 0.71% and 1.12% respectively. And the establishment of two abnormal body models was created and numerical simulation shows that the abnormal response is more obvious, and it provided the foundation for three-dimensional controlled-source electromagnetic method of finite element numerical simulation.

关 键 词：二次插值 有限元 数值模拟 可控源电磁法 

分 类 号：P631.3[天文地球—地质矿产勘探]