A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

摘要

The application of unstructured grids can improve the solution of total field electromagnetic problems as these grids allow the efficient local refinement of the mesh at the locations of high gradient of the fields. This study investigates the generalization of the standard Yee's staggered scheme to unstructured tetrahedral-Vorono? grids. We discretize the Helmholtz equation for the electric field using a finite volume approach and then solve the problem to find the projection of the total electric field along the edges of the tetrahedral elements. To compute the electric and magnetic fields at the observation points an interpolation technique is employed which uses the edge vector basis functions of the tetrahedral elements. Two examples from the preliminary results are included which show the computation of the total and secondary fields due to electric and magnetic sources in halfspaces that contain anomalous bodies. The results show good agreement with those from the literature and analytical solutions.