Modelling the electromagnetic response in complex geological structures using the 3D finite-element method based on the hexahedral and the tetrahedral edge-element technique

Abstract

The demand for an accurate and efficient general electromagnetic (EM) program to model the EM field in complex geological structures led us to the development of the three-dimensional edge finite-element program. It has the capability to model the frequency- and time-domain electromagnetic (EM) fields in the inhomogeneous complex structures at any resistivities contrasts and at any survey types. The use of the edge finite-element method instead of the conventional nodal finite-element method is necessary to satisfy the inherent continuity constraint across the interface of the adjacent finite-element cells. The program is developed based on the edge hexahedral element with the linear basis function. Rather than solving for the electric field we reformulated the program to solve for the Schelkunoff?s potentials resulting in the improvement of its performance significantly. On the desktop computer the program required less than 2 minutes computation time per frequency per station to compute the response of a complex large model in the domain of 2 km x 2 km x1 km. The run time is adequate for some application, but it is still considered significant for the time-domain EM field computation and for modelling the airborne survey. Subsequently we increase the number of the unknowns in each element by subdividing the hexahedral element into 5 tetrahedral elements to enable the program to use bigger cells and reducing its cell number requirement. The modelling of the EM response of 2 interacting targets and complex geological structures example are demonstrated to show the ability of the program in solving complex problems.