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

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.