Finite-Volume Modelling of Geophysical Electromagnetic Data on Unstructured Grids Using Potentials

jahandari, h. ; farquharson, c.g.;

The solution of the geophysical electromagnetic (EM) modelling problem on unstructured tetrahedral-Vorono¨ı grids using EM potentials is investigated. Unstructured grids enable accurate representation of geological structures and interfaces and allow local refinements that
can be beneficial in the mesh, for example, at the observation points and at the source. The time-harmonic Helmholtz equation in terms of EM potentials together with the equation of conservation of charge are discretized on staggered tetrahedral-Voronoı grids using a finite volume method and solved in a total-field approach. The solutions are the total-field quantities of vector and scalar potentials along the edges and at the nodes of the tetrahedral elements, respectively. Two benchmark models with electric and magnetic sources are employed for
verification. Also, to illustrate the versatility of the scheme, data for a model of the Ovoid ore body at Voisey’s Bay, Labrador, Canada, are synthesized and compared with real helicopterborne data. The finite-volume results show good agreement with those from the literature and
with the real data. The Coulomb gauge is used for ensuring the uniqueness of the potentials in order to study the galvanic and inductive components of the solutions. The results indicate an agreement between the relative importance of these two components and the anticipated coupling of the source with the conductivity model. The solution of the gauged and ungauged schemes using iterative and direct solvers is studied and compared with the solution of a direct EM-field scheme. The results demonstrate that the potential-based schemes can be solved by iterative solvers unlike the corresponding EM-field scheme. An accuracy study is also conducted
which showed the higher accuracy of the solutions from the potential method compared to those from the direct EM-field method.