Finite element numerical simulation on line controlled source based on quadratic interpolation

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.