Modelagem eletromagnética 2.5-D de dados geofísicos através do método de diferenças finitas com malhas não-estruturadas

Abstract

We present a 2.5D electromagnetic formulation for modelling of the marine controlledsource electromagnetic (mCSEM) using a Finite Diference frequency domain (FDFD) method. The formulation is in terms of secondary fields thus removing the source point singularities. The components of the electromagnetic field are derived from the solution of the magnetic vector potential and electric scalar potential, evaluated in the entire problem domain that must be completely discretized for the use of the FDFD. Finite difference methods result in large sparse matrix equations that are efficiently solved by sparse matrix algebra preconditioned iterative methods. To overcome limitations imposed by structured grids in the traditional FDFD method, the new method is based upon unstructured grids allowing a better delineation of the geometries. These meshes are completely adaptable to the models we work with, promoting a smooth design of their structures, and may only be refined locally in regions of interest. We also present the development of RBF-DQ method, (radial basis function differential quadrature) which makes use of the technique of functions approximation by linear combinations of radial basis functions (RBF) and the technique of differential quadrature (DQ) for approximation of the derivatives. Our results show that the FDFD method with unstructured grids when applied to geophysical modeling problems, yield improved quality of modeled data in comparison with the results obtained by traditional techniques of FDFD method.