Modelagem 2,5D por elementos finitos dos efeitos da topografia do terreno sobre dados obtidos com o método eletromagnético a multifrequência

Abstract

This dissertation shows the numerical modeling results of the effect of the terrain topography on the multi-frequency electromagnetic method (EMMF). In this method the source is a very large square current loop, with a side of a few hundreds meters. The used numerical method is the Finite Element (FE) method in a 2,5D formulation. The geo-electrical models are composed of two-dimensional structures inside layered one-dimensional media. The formulation uses the separation of the EM field in two parts called the primary field (the field of the same source in the layered medium only) and the secondary field (the difference between the complete field in the 2D model and the primary field), to avoid the difficulty of representing the singular source in the discrete representation of the media in the form of the FE mesh. The discretized domain is build with a non-structured triangular mesh. In order to calculate the field components that are derived from those given by the FE solution in a given node, it is necessary to calculate numerical derivatives on the discrete solutions. Here we have used the average value of the derivatives of the basis functions around the node, which is a simple and effective way of estimating the derivative. The resulting modeling code allow us to quantitatively analyse the influence of topographic gradients on the measured electromagnetic fields from this method.